This paper summarizes important points from Why Don’t ...
A summary of
Why Don’t Students
Like
School?
A Cognitive Scientist Answers Questions About How The Mind Works And What It Means For The Classroom
By Daniel Willingham
Summarized by Bud Nye, R.N., M.S.
Contents
1. Why do we find it difficult to make school enjoyable for students? 3
2. How useful or useless should we consider fact learning? 7
3. What makes something stick in memory and what will likely slip away? 12
4. Why do we find abstract ideas so difficult to understand, and so difficult to apply when expressed in new ways? 19
5. Does the cognitive benefit of drill make it worth the potential cost to motivation? 23
6. What can we do to get students to think like scientists, historians and mathematicians? 27
7. How should a teacher adjust their teaching to different types of learners? 31
8. How can we optimize school for students who don’t have the raw intelligence that other students have? 34
9. What about the teacher’s thinking? 39
10. Summary table 43
My comments in brackets [ ].
This paper summarizes important points from Why Don’t Students Like School? A cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom, by Daniel Willingham, 2009, John Wiley & Sons, Inc. It reduces a 180 page book to 43 pages so, obviously, it leaves out many examples and much detail. You will find a summary table on page 43.
[I think that it would make good sense to share information in at least chapters 1, 2, 5 and 8 with students. They really need to know these things to help with motivational issues. Research shows that students having this kind of knowledge perform significantly better than those without it. Use PowerPoint? Conceptual Change Model inquiries? Some combination of these? A student suggests that students read it, write a response, and then discuss it in class. (Perhaps one section at a time?) Repeat/review during the year.]
Question 1: Why do we find it difficult to make school enjoyable for students?
Answer: Contrary to popular belief, human brains do not naturally and easily think. On the contrary, because the brain does not think very well, it works hard to save us from having to think.
Critical principle 1: People exhibit naturally curious behavior but do not naturally think well. We usually avoid thinking unless the right cognitive conditions exist.
For this reason, in order to maximize the likelihood that they will get the pleasurable rush that comes from successful thought, teachers need to carefully consider how they encourage their students to think. (Thinking here refers to solving problems, reasoning, reading complex material, or doing any mental work that requires some effort.) Henry Ford described the situation well with his cynical observation, “Thinking is the hardest work there is, which is the probable reason why so few people engage in it.” Humans don’t think very often because nature created our brains not for thought, but for avoiding thought. Thinking occurs not only with great effort, but also slowly and unreliably.
The mind’s poor design for thinking
If we all do so badly with thinking, how does anyone get through the day? How do we find our way to work or spot a bargain at the grocery store? The answer? When we can get away with it, we don’t think. Instead, we rely on memory. Most of the problems we face, we have solved before, so we just do what we have done in the past. You may think that you have a terrible memory, and it proves true that your memory system does not work as reliably as your visual or movement system—sometimes you forget, sometimes you think you remember when you don’t—but your memory system works much more reliably than your thinking system, and it provides answers quickly and with little effort.
We usually think of memory as storing personal events (memories of my wedding) and facts (George Washington was the first president of the United States), but memory also store strategies and procedures to guide what we should do, such as where to turn when driving home, how to handle a conflict at work, what to do when the pot on the stove starts to boil over, how to divide a number by 10, and so on. So we don’t have to think through these things each time we encounter them. “Most of the time what we do is what we do most of the time.” Using memory doesn’t take much of our attention so we have the freedom to daydream even as we stop for red lights, pass cars, watch for pedestrians, and so on. A task that initially takes a great deal of thought, with practice becomes a task that requires little or no thought.
What implications does this have for education? If people think badly and try to avoid it, what does this say about student’s attitudes toward school? Fortunately, the story doesn’t end with people stubbornly refusing to think. Despite the fact that we don’t think well, we actually like to think. We naturally feel curious, and we look for opportunities to engage in certain types of thought. But because we find thinking so hard, we have to have the right conditions for this curiosity to thrive or we easily quit thinking.
Though naturally curious, our curiosity remains fragile
Solving problems brings pleasure. When we say “problem solving” here, we mean any cognitive work that succeeds. This might involve understanding a difficult passage of prose, planning a garden, learning to play a riff on the guitar, passing a football, or sizing up an investment opportunity. We get a sense of satisfaction, of fulfillment, in successful thinking. When you solve a problem, your brain may reward itself with a small dose of dopamine, a naturally occurring chemical important to the brain’s pleasure system. Even though we don’t completely understand it yet, it seems undeniable that people take pleasure in solving problems.
Notably, we get the pleasure in solving the problem. We do not find it pleasurable to work on a problem with no sense that we make progress on it. Then too, we don’t get great pleasure in simply knowing the answer. Even if someone doesn’t tell you the answer to a problem, once you have received too many hints you lose the sense that you have solved it yourself. This works much like a joke, funnier if you get it than if someone has to explain it to you. Mental work appeals to us because it offers the opportunity for that pleasant feeling when it succeeds.
The content of a problem—whether about sex or human motivation—may prove sufficient to prompt your interest, but it won’t maintain it. If content does not keep our attention, when does curiosity have staying power? The answer probably lies in the difficulty of the problem. We get little or no pleasure if we find the problem too easy or too difficult. We like to think—or more properly, we like to think if we judge that the mental work will pay off with the pleasurable feeling we get when we solve a problem. So no inconsistency exists in claiming that people avoid thought and in claiming that people have natural curiosity. Curiosity prompts us to explore new ideas and problems. But when we do this exploration, we quickly evaluate how much mental work it will take to solve the problem. If it’s too much or too little work, we stop working on the problem if we can.
This analysis of the kinds of mental work that people seek out or avoid provides one answer to why more students don’t like school. Students find it rewarding to work on problems at the right level of difficulty, but they find it unpleasant to work on problems either too easy or too difficult. Students can’t opt out of these problems the way adults often can. If the student routinely gets work a little too difficult or too easy, little wonder exists for why they don’t like school. Few people would care to work on the Sunday New York Times crossword puzzle for several hours each day.
How thinking works
Understanding a bit about how thinking happens will help you understand what makes thinking hard. That will in turn help you understand how to make thinking easier for your students, and therefore help them enjoy school more.
[pic]
The diagram above shows a very simple model of the mind. On the left you see the environment, full of things to see and hear, problems to solve, and so on. It holds the stuff you interact with and think about. The arrow from the environment to working memory shows that working memory works as the part of your brain where you experience awareness of the things happening around you: the sight of a shaft of light falling onto a dusty table, the sound of a dog barking in the distance, and so forth. You can consider working memory synonymous with consciousness. Of course, you can also experience awareness of things not currently in the environment; for example, you can recall the sound of your mother’s voice, even if not present (or indeed no longer living). Long-term memory exists as the vast storehouse in which you maintain your factual knowledge of the world: that lady bugs have spots, that you find chocolate your favorite flavor of ice cream, that your three-year-old surprised you yesterday by mentioning kumquats, and so on. Factual knowledge can occur abstractly, for example, it would include the idea that triangles form closed figures with three sides, and your knowledge of what a dog generally looks like. It lies quietly until needed, at which time it enters working memory and so becomes conscious. For example, if someone asked you, “What color is a polar bear” you would say, “white” almost immediately. You had that information stored in long-term memory thirty seconds ago, but did not experience awareness of it until someone posed the question that made it relevant to ongoing conscious thought, at which time it entered working memory.
Thinking occurs when you combine information (from the environment and long-term memory) in new ways. That combining happens in working memory. Think about some problem that you don’t immediately know the answer to, perhaps how to multiply 18 by 7. Notice what it feels like to have working memory absorbed by the problem. Also notice that your having knowing how to combine and rearrange ideas in working memory proves essential to successful thinking. If you have had experience with this particular type of problem, then you likely have information in long-term memory about how to solve it, even if you don’t have the information in a foolproof way.
So, our long-term memory contains not only factual information, such as the color of polar bears and the value of 8 x 7, but it also contains what we may call procedural knowledge, you knowledge of your knowledge of the mental procedures necessary to execute tasks. If thinking something involves combining information in working memory, then procedural knowledge provides a list of what to combine and when—it works like a recipe to accomplish a particular kind of thought “cake”. You may have stored procedures for the steps needed to calculate the area of a triangle, or to duplicate a computer file using Windows, or to drive from your home to our office.
It seems pretty obvious that having the appropriate procedure stored in long-term memory helps a great deal when we think. This accounts for why we may find it easy to solve one math problem but not another. But how about factual knowledge? Does that help you think as well? It does in several different ways discussed soon. For now, note that solving the 18 x 7 math problem required retrieving factual information, such as the fact that 8 x 7 = 56. Thinking entails combining information in working memory. Often the information provided in the environment does not prove sufficient to solve a problem, and you need to supplement it with information from long-term memory.
We have a final necessity for thinking: the information we work with cannot take up too much space. Working memory has limited space, so thinking becomes increasingly difficult as working memory gets crowded.
Summary. Successful thinking relies on four factors: information from the environment, facts in long-term memory, procedures in long-term memory, and the amount of space in working memory. If one of these factors occurs inadequately, thinking will likely fail. We do not find people’s minds especially well-suited to thinking; thinking occurs slowly, it requires significant effort, and it happens unreliably. For these reasons, deliberate thinking does not guide people’s thinking in most situations. Rather, we rely on our memories, following courses of action that we have taken before. Nevertheless, we find successful thinking pleasurable. We like solving problems, understanding new ideas, and so forth. Thus we will seek out opportunities to think, but we use selectivity when doing so; we choose problems that pose some challenge but that seem likely we will have the ability to solve, because these problems lead to feelings of pleasure and satisfaction. To solve problems, the thinker needs adequate information from the environment, room in working memory, and the required facts and procedures in long-term memory.
Classroom implications
From a cognitive perspective, an important factor involves whether or not a student consistently experiences the pleasurable rush of solving a problem. What can teachers do to help ensure that each student gets that pleasure?
• Make sure that students have problems to solve. By “problems”, we mean cognitive work that poses moderate challenge, including activities such as understanding a poem or thinking of novel uses for recyclable materials. Avoid long strings of teacher explanations with little opportunity for students to solve problems! With your lessons, keep an eye on the cognitive work the students will actually do. How often does this work occur in the lesson? Does it get intermixed with cognitive breaks at least every 15 to 20 minutes? Might negative outcomes occur such as failing to understand what you want them to do, not having the ability to do it, or just guessing? [From The Physics Teacher, Oct., 2009, in cognitive science we define problem solving as a process that minimizes the difference between the current state and a desired goal; ability to apply prior knowledge in new, somewhat unfamiliar situations. We contrast this with exercises, which give practice with a skill in familiar situations.]
• Respect students’ cognitive limits. Do they have the necessary background knowledge in memory to consider this question or problem? If students lack the appropriate background knowledge, they will quickly consider the question you pose “boring”. If they lack the background knowledge to engage with a problem, save it for another time when they have that knowledge. [I did with osmosis when I turned from that to the small particle model after realizing that they had no knowledge of it.] Remember working memory limits! People can keep only so much information in mind at once. Multistep instructions, lists of unconnected facts, chains of logic more than two or three steps long, and applying a just-learned concept to new material (unless quite simple) overloads working memory. [Remember that many of your students have trouble reading, writing, and performing the simplest math operations. This, alone, can easily overload working memory!] What serves as the solution to working memory overload problem? Slow the pace and use memory aids such as writing on the board, thus saving the student from keeping too much information in working memory. [But this may frustrate the students who do have the knowledge to boredom, so differentiate instruction to the greatest extent possible.]
• Clarify problems to solve. How can you make the problem interesting? A common strategy involves trying to make the material “relevant”—but this will only rarely help. Remember: our curiosity gets provoked when we perceive a problem that we believe we can solve. Ask yourself: What question will engage students and help them want to know the answer?
Sometimes we feel so anxious for our students to know the answers that we do not devote sufficient time to developing the questions. But the questions pique people’s interest. Someone’s telling you an answer doesn’t do anything for you. When you plan a lesson, start with the information you want students to know at its end, then consider what might work best as the key questions that will have the right level of difficulty to engage your students while you respect their cognitive limits.
• Think about when to puzzle students. The goal of puzzling students involves making them curious. But consider whether you might use these strategies not only at the beginning of a lesson, but also after they have learned the basic concepts. If students don’t know the basic principles behind a demonstration it seems like a magic trick. [This magic makes it a “discrepant event”, clashing with their existing conceptions of how the world presumably works.] They get a momentary thrill, but their curiosity to learn may not last very long. Another strategy might involve doing the demonstration after students know the principle involved. Every fact or demonstration that would puzzle students before they have the relevant background knowledge has the potential to become an experience that will puzzle students momentarily later, and then lead to the pleasure of problem solving.
• Accept and act on variation in student preparation. You do not need to accept that “some students just are not very bright” and so we ought to track them into less demanding classes. Neither do you need naively to pretend that all students come to your class equally prepared to excel. Students have different preparations, as well as different levels of support at home and different biological strengths and weaknesses. They therefore differ in their abilities. With these and related truths, you will find it self-defeating to give all of your students the same work. The less capable students will find it too difficult and will struggle against their brain’s bias to mentally walk away from schoolwork. Meanwhile, the more capable students will not find it sufficiently challenging to maintain their interest [differentiate instruction]. To the extent that you can, you will benefit your students and yourself to assign work to individuals or groups of students appropriate to their current level of competence. Naturally, you need to do this in a sensitive way, minimizing the extent to which some students will judge themselves as behind others and create helpless beliefs by attributing this to permanent, unchangeable personal characteristics. [See Learned Helplessness and Power Therapy. Create CCM inquiries related to such thinking and start early with some of these?] But the fact remains that some are behind others, and giving them work beyond them will probably not help them catch up; doing this will more likely make them fall still further behind. [So, how can you practically do the needed individualization? You need different levels of labs, worksheets and tests. [Remember Singapore Math in Alaska. Dr. Schenck suggests knowledge- or skill-matched groups—but you would need to do this in a sensitive way that does not produce “dumb” and “smart” groups! Using language that emphasizes student’s having background knowledge and skills should help with this.]
• Change the pace. We all lose the attention of our students, at times, and this happens more often when they feel confused. They mentally check out. Happily, we can fairly easily get them back. How? Change grabs attention. When you change topics, start a new activity, or in some other way show that you have shifted gears, virtually every student’s attention will come back to you and you will have a new chance to engage them. So plan shifts and monitor your class’s attention to see if you need to change things more often or less frequently [in general, every 15 to 20 minutes].
• Keep a diary or lesson notes. The core idea in this chapter involves the fact that solving a problem gives people pleasure—but—the individual has to consider the problem easy enough to solve yet difficult enough to take some mental effort. [This holds true for teachers and their teaching as well as for students.] A teacher does not easily find this sweet spot of difficulty. Your experience in the classroom serves as your best guide: whatever works, do again; whatever doesn’t, discard. But don’t expect that you will really remember how well a lesson plan worked a year later. Whether a lesson goes brilliantly well or down in flames, we tend to think at the time that we will never forget what happened; but the ravages of memory can surprise us, so write it down. Even if just a quick scratch on a sticky note, make a habit of recording your success in gauging the level of difficulty in the problem you pose for your students. [Add a “Reflections” section to all labs/inquiries that you do, and then do that reflection immediately afterward.]
Question 2: How useful or useless should we consider fact learning?
Answer: For sure, having students memorize lists of dry facts will not help. But it also proves true, and many people appreciate it much less, that one cannot possibly teach students skills such as analysis or synthesis in the absence of factual knowledge. The kinds of skills that we want our students to develop require extensive factual knowledge.
Critical principle 2: Factual knowledge must precede skill.
Here, we define thinking as combining information in new ways. The information can come from long-term memory—facts you have memorized—or from the environment [Note this regarding inquiry learning and the Cognitive Change Model. These methods strongly encourage students directly to use the environment for information.]. In today’s world, do we have a reason to memorize anything? We can find any factual information we might need in seconds via the Internet; we can calculate using a calculator. Then too, things change so quickly that half of the information you commit to memory will go out of date within five years—or so the arguments go. Perhaps instead of learning facts, it works better to practice critical thinking, to have students work at evaluating all the information available on the Internet rather than trying to commit some small part of it to memory.
In this chapter, we find this argument false. Data from the last thirty years lead to a conclusion not scientifically challengeable: thinking well requires knowing facts, and that holds true not simply because you need something to think about. We find the very processes teachers care about most—critical thinking processes such as problem solving—intertwined intimately with factual knowledge stored in long-term memory, not just that found in the environment.
Many people find it hard to conceive of thinking processes as intertwined with knowledge. Most people believe that thinking processes work like the functions of a calculator. A calculator has available a set of procedures (addition, multiplication, and so on) that can manipulate numbers, and one can apply these procedures to any set of numbers. With this calculator model, the data (the numbers) and the operations that manipulate the data exist separately. Thus, if you learn a new thinking operation (for example, how to critically analyze historical documents), you can apply that operation to all historical documents, just as a fancier calculator that computes sines can do so for all angles.
But the human brain does not work that way. When we learn to think critically about, say, the start of the Second World War, it does not mean that we can also think critically about a chess game or about the current situation in the Middle East or even about the start of the American Revolutionary War. On the contrary, we find that critical thinking processes depend strongly on background knowledge (although this happens much less so when we have accumulated quite a bit of experience, as described in Chapter Six). So, we have a straightforward conclusion from cognitive science: we must ensure that students acquire background knowledge in parallel with practicing critical thinking skills. In this chapter, you learn how cognitive scientists know that thinking skills and knowledge bind together.
Knowledge proves essential to reading comprehension
We need background knowledge to help us understand what someone says or writes. If you have a vocabulary word or a concept missing from your long-term memory, you will likely feel confused. But the need for background knowledge goes much deeper than just the need for definitions.
Suppose a sentence contains two ideas—call them A and B. Even if you know the vocabulary and you understand A and B, you still might need background knowledge to understand the sentence. For example, suppose you read the following sentence in a novel:
“I’m not trying my new barbecue when the boss comes to dinner!” Mark yelled.
We can say that idea A involves Mark trying out his new barbecue, and idea B that he won’t do it when his boss comes to dinner. But to understand the sentence, you need to understand the relationship between A and B. But at this point you have two pieces of information missing that would help you bridge A and B: that people often make mistakes the first time they try a new appliance and that Mark would like to impress his boss in a positive way. Putting those facts together would help you understand that Mark feels afraid he’ll ruin the food the first time he uses his new barbecue, and he doesn’t want that to happen to the meal he serves to his boss.
Reading comprehension (and listening) depend on combining the ideas in a passage, not just comprehending each idea on its own. And all writing contains gaps—lots of gaps—where the writer omits information necessary to understand the logical flow of ideas. Writers (and speakers) assume that the reader has the knowledge to fill the gaps. In the example just given, the writer assumed that the reader would know the relevant fact about new appliances and about bosses.
Why do writers leave gaps? Don’t they run the risk that the reader won’t have the right background knowledge, and so will feel confused? Yes, that exists as a risk, but writers simply can’t include all the factual details. If they did, prose would become impossibly long and tedious.
How do writers (and speakers) decide what to omit? It depends on whom they write for (or speak to). They write or speak to a selected audience that they assume has the needed background knowledge. Similarly, when asked a question we calibrate our answers, providing more or less (or different) information depending on our judgment of what the other person knows, thereby deciding what we can safely leave out and what we need to explain.
What happens when the reader or listener does not have the needed missing information? They misunderstand or feel confused. So background knowledge in the form of vocabulary and concepts proves necessary not only in order to understand a single idea (call it A), but also in order to understand the connection between two ideas (A and B). In still other situations writers and speakers present multiple ideas at the same time—A, B, C, D, E, and F—expecting that the reader or listener will knit them together into a coherent whole. These tasks occur in our limited working memory—the part of your brain in which you combine and manipulate information, pretty much synonymous with consciousness.
We call the phenomenon of tying together separate pieces of information from the environment chunking. This has the obvious advantage that you can keep more stuff in working memory if you can chunk it. However, chunking works only when you have the needed factual knowledge in long-term memory. You will see CNN as meaningful only if you already know what CNN refers to. [Mike Byster’s Brainetics largely teaches people how to chunk more effectively, as well as practicing extended attention focusing.]
So, factual knowledge in long-term memory allows chunking, and chunking increases space in working memory. What does the ability to chunk have to do with reading comprehension? If you read ideas A, B, C, D, E, and F, you would need to relate them to one another in order to comprehend their meaning. That adds up to a lot of stuff to keep in working memory. But suppose you could chunk A through E into a single idea? Then you would find comprehension much easier.
A number of studies have shown that people understand what they read much better if they already have some background knowledge about the subject. Part of the reason involves chunking. A clever study on this point occurred with junior high school students. Standard reading tests classified half of them as good readers and half as poor readers. The researchers asked the students to read a story that described half an inning of a baseball game. As they read, the researchers periodically stopped the students and asked them to show that they understood the story by using a model of a baseball field and players. Some of the students knew a lot about baseball and some knew just a little. (The researchers made sure that everyone could comprehend individual actions, for example, what happened when a player got a double.) Dramatically, the students’ knowledge of baseball determined how much they understood of the story. Whether classified as “good readers” or “bad readers” didn’t matter nearly as much as what they knew.
Thus, background knowledge allows chunking, which makes more room in working memory, which makes it easier to relate ideas, and therefore to comprehend. Background knowledge also clarifies details that would otherwise remain ambiguous and confusing.
We’ve listed four ways that background knowledge has importance in reading comprehension: (1) it provides vocabulary; (2) it allows you to bridge logical gaps that writers leave; (3) it allows chunking, which increases room in working memory and thereby makes it easier to tie ideas together; and (4) it guides the interpretation of ambiguous sentences. Background knowledge helps reading in other ways as well, but these cover the high points.
Some observers believe that this phenomenon—that knowledge makes one a good reader—works as a factor in fourth-grade slump, which refers to students from underprivileged homes often reading at grade level through the third grade, but then suddenly in the forth grade they fall behind, and with each succeeding year they fall even farther behind. The interpretation involves the idea that reading instruction through third grade focuses mostly on decoding—figuring out how to sound out words using the printed symbols—so reading tests emphasize this. By the time the fourth grade rolls around, most students have become good decoders, so reading tests start to emphasize comprehension. As described here, comprehension depends on background knowledge, and kids from privileged homes have an edge here. They come to school with a bigger vocabulary and more knowledge about the world than underprivileged kids. And because knowing things makes it easier to learn new things (as described in the next section), the gap between privileged and underprivileged kids widens.
One needs background knowledge for cognitive skills
Not only does factual knowledge make you a better reader, but we also need it to become a good thinker. The process we most hope to engender in our students—thinking critically and logically—cannot happen without background knowledge.
You need to know that much of the time when we see someone apparently engaged in logical thinking, they actually do memory retrieval. Memory serves as the cognitive process of first resort. When faced with a problem, you will first search for a solution in memory, and if you find one, you will very likely use it. Doing so works quickly and easily, and will fairly likely work effectively. To appreciate this effect, try working a problem for which you don’t have relevant background knowledge.
In fact, people draw on memory to solve problems more often that you might expect. For example, it appears that much of the difference among the world’s best chess players lies not in their ability to reason about the game or to plan the best move; rather it lies in their memory for game positions. Psychologists estimate the top class chess players may have fifty thousand board positions in long-term memory. Thus background knowledge proves decisive even in chess, which we might think serves as the prototypical game of reasoning. This does not mean to suggest that we solve all problems by comparing them to cases we have seen in the past. We do, of course, sometimes reason, and even when we do, background knowledge can help.
We need to make a final point about knowledge and thinking skills. Much of what experts tell us they do in the course of thinking about their field requires background knowledge, even if they don’t describe it that way. Consider a science example. We could tell students a lot about how scientists think, and they could memorize those bits of advice. For example, we could tell students that when interpreting the results of an experiment, scientists feel especially interested in unexpected (anomalous) outcomes. Unexpected outcomes indicate incomplete knowledge. But to have unexpected outcomes, you have to have an expectation! Meanwhile, one has an expectation about an outcome based on their knowledge of the field. Thus students will find it impossible to use most or all of what we tell them about scientific thinking strategies without appropriate background knowledge.
The same holds true for history, language arts, music, and so on. Generalizations that we can offer students about how to think and reason successfully in the field may look like they don’t require background knowledge, but when you consider how to apply them, they actually do.
Factual knowledge improves memory
When it comes to knowledge, those who know more gain more. Many experiments have confirmed the benefit of background knowledge to memory using the same basic method. The researchers bring into the laboratory some people who have some expertise in a field (for example, football or dance or electronic circuitry) and some who do not. Everyone reads a story or a brief article—material simple enough that the people without expertise have no difficulty understanding it; they can tell you what each sentence means. But the next day the people with background knowledge remember substantially more of the material than the people who do not have the background knowledge.
One might think that this effect really occurs due to attention. From this view, if I enjoy basketball, I will enjoy reading about basketball and will pay close attention, whereas if I don’t enjoy basketball, reading about it will bore me. But other studies have actually created experts out of novices. These researchers had people learn either a lot or just a little about subjects new to them (for example, Broadway musicals). Then they had them read other, new facts about the subject, and they found that the “experts” (those who had earlier learned a lot of facts about the subject) learned new facts more quickly and easily than the “novices” (who had earlier learned just a few facts about the subject).”
Why do we find it easier to remember material if we already know something about the topic? If you know more, you can better understand new information, and better understanding means better memory. For example, people who know about baseball understand baseball story better than people who don’t. We remember much better if something has meaning. Note that these effects don’t come from comprehension: you can comprehend something despite a lack of background knowledge. But mere comprehension lacks richness and depth, because if you have background knowledge, your mind can connect the material you read with what you already know about the topic, even if you have no awareness of this process happening. Those connections help you remember later. Remember: remembering things involves cues to memory. We dredge up memories when we think of things related to what we wish to remember.
The final effect of background knowledge involves the fact that having factual knowledge in long-term memory makes it easier to acquire still more factual knowledge. This means that the amount of information you retain depends largely on what you already have. So, if you have more than I do, you retain more than I do, which means you gain more than me. The rich get richer. We also know where the riches lie. If you want exposure to new vocabulary and new ideas, go to books, magazines, and newspapers. Unfortunately, the sorts of content that students tend to lean toward, such as television, video games, social networking Internet sites, music sites and the like, for the most part prove unhelpful. Researchers have painstakingly analyzed the contents of many ways that students can spend their leisure time. Books, newspapers, and magazines singularly help in introducing new ideas and new vocabulary to students.
We began this chapter with a quote from Einstein: “Imagination is more important than knowledge.” I hope that you now feel persuaded that Einstein had this wrong. Knowledge proves more important, because it exists as a prerequisite for imagination, or at least for the sort of imagination that leads to problem solving, decision making, and creativity.
Classroom implications
The fact that factual knowledge makes cognitive processes work better obviously implies that we must help students learn background knowledge. How can we ensure that that happens?
• Evaluate which knowledge to encourage construction of. Which knowledge should we teach students? This question often quickly opens politically charged debates, but a cognitive scientist sees the issues differently. The question moves from What knowledge should we consider important? to What knowledge yields the greatest cognitive benefit? This question has two answers and the first answer relates to reading. The students must know whatever information the writer has assumed that they know and has thus left out. This knowledge will vary depending on what the student reads. The second answer relates to core subjects such as science, history and math. What should students know of science, history and math? This question differs from the first in that these subject areas use knowledge differently that general reading does. General reading requires relatively shallow knowledge to understand the word meanings while science and math require knowing much more.
Students can’t learn everything, so what should they know? Cognitive science leads to the rather obvious conclusion that students must learn the concepts that come up again and again—the unifying ideas of each discipline. Some educational thinkers have suggested that we should teach a limited number of unifying ideas in great depth, beginning in the early grades and carrying through the curriculum for years as students take up different topics and view the topics through the lens of one or more of the unifying ideas. From a cognitive perspective, that makes good sense.
• When you require critical thinking, assure that the students have most of the needed knowledge base in place. Our goal does not involve just having students know a lot of stuff—we want them to know stuff in service of thinking effectively, and thinking effectively requires background knowledge. Critical thinking does not amount to a set of procedures that students can practice and perfect while divorced from background knowledge. Thus it makes sense to consider whether students have the necessary background knowledge to carry out a critical thinking task you might assign.
• Consider shallow knowledge better than no knowledge. Some of the benefits of factual knowledge require fairly deep knowledge. For example, to chunk, we need detailed knowledge. But other benefits accrue from shallow knowledge. For example, we usually do not need to have detailed knowledge of a concept to understand its meaning in context when reading. Of course having deep knowledge works better than shallow knowledge, but we can’t have deep knowledge of everything, and shallow knowledge certainly helps much more than no knowledge.
• Do whatever you can to get kids to read. Books expose children to more facts and to a broader vocabulary than virtually any other activity, and persuasive data indicate that people who read for pleasure enjoy cognitive benefits throughout their lifetime. Nudge students toward books at the appropriate reading level. A student doesn’t gain much from reading books several grades below their reading level. Just as obviously, a too difficult book probably won’t work very well either. The student won’t understand it and will probably just end up frustrated.
• Knowledge acquisition can occur incidentally. Learning factual knowledge can happen simply by exposure rather than only by concentrated study or memorization. Think about all you have learned by reading books and magazines for pleasure, or by watching documentaries and the news on television, or through conversation with friends. School offers many of the same opportunities.
• Start early. A child who starts behind in knowledge will fall even farther behind unless some intervention occurs. There seems little doubt that this factor plays an important role in why some children fare poorly in school. Home environments vary a great deal. What sort of vocabulary do parents use? Do they take their child to the museum or aquarium? Do they make books available? Do they read to their children? Do the children observe their parents reading? All of these factors and many others play a role in what children know on their first day of school. Before a child meets her first teacher, she may be quite far behind the child sitting next to her in terms of how easy she will find learning. The teacher’s greatest challenge involves trying to level the playing field. Neither any shortcuts nor alternatives exist to trying to increase the factual knowledge that the child has not picked up at home.
• Knowledge must have meaning. Teachers should not take the importance of knowledge to mean that they should create lists of facts for students to learn —whether shallow or detailed. Sure, some benefits might accrue, but only small ones. Knowledge pays off when it occurs conceptually and when the facts relate to one another. That does not happen with list learning. Also, such drilling would do far more harm by making students miserable and by encouraging the belief that school exists as a place of boredom and drudgery, not excitement and discovery.
Question 3: What makes something stick in memory and what will likely slip away?
Answer: We can’t store everything we experience in memory because too much happens. So what should the memory system tuck away? What about things that happen again and again? What about things that cause emotion? Our non-conscious thinking and memory system lay their bets this way: if you think about something carefully, you will probably have to think about it again, so store it.
Critical principle 3: Memory occurs as the residue of thought.
People remember whatever they think about; the more the thinking, the better and longer the memory. So, to teach well we need to pay careful attention to what an assignment will actually get students to think about—not what we hope they will think about—because they will remember that.
The importance of memory
Every teacher has had this experience: you teach what you consider a terrific lesson, full of lively examples, deep content, engaging problems to solve, and a clear message, but the next day students remember nothing of it except a joke you told and an off-the-subject aside about your family. Or worse, when you say, while struggling to keep your voice calm, “The point of yesterday’s lesson was that one plus one equals two”, they look at you incredulously and say, “One plus one equals two?” If the message of Chapter Two involved the idea that “background knowledge matters”, then we must closely consider the question How we can help assure that students acquire this background knowledge? So why do students remember some things and forget other things? One or more of four things may happen.
First, they may not have paid attention to it. If you don’t pay attention to something, you can’t learn it! Second, the process by which we draw things from long-term memory may fail. (We discuss this in Chapter Four.) Third, the information may no longer reside in long-term memory; we may have forgotten it. Regarding this, a common myth has it that the mind records in exquisite detail everything that happens to you, like a video camera, but you just can’t get at most of it—memory failures always occur as problems of access. If given the right cue, the hypothesis holds, you could recover anything that ever happened to you. Although this idea has appeal, it does not reflect the truth. Hypnosis, for example, does not aid memory. Researchers have tested this many times, and hypnosis doesn’t help. Memory researchers see no reason to believe that all memories get recorded forever. Fourth, sometimes you do pay attention, so the material rattles around in working memory for a while, but it never makes it to long-term memory. Then, what else needs to happen besides attention for storage in long-term memory to occur?
One reasonable guess involves the idea that we remember things that have some emotional reaction attached to them. Don’t you likely remember especially happy or sad moments? Naturally we pay more attention to emotional events, and we probably talk about them later, so scientists had to conduct very careful studies to show that the emotion, and not the repeated thought about these events, provides the boost to memory. Emotion does indeed have a real effect on memory, and researchers have actually worked out some of the biochemistry behind it, but emotion has to have reasonable strength to have much impact on memory. If memory depended on emotion, we would remember little of what we encounter in school. So the answer that Things go into long-term memory if they create an emotional reaction does not quite fit. We will remember things that create an emotional reaction better, but we do not require emotion for learning.
Repetition serves as another obvious candidate for what makes learning work. Repetition proves very important, and we discuss it in Chapter Five, but it turns out that just any repetition will not do. In fact, you may repeat material almost indefinitely and still it may not stick in your memory. For example, given a selection of many variations in the appearance of a penny, something you have seen and handled hundreds of times, you probably won’t recognize the correct one. So repetition alone won’t do it.
Equally clear, wanting to remember something does not serve as the magic ingredient. Experiments have shown that even telling subjects that they will receive pay for each remembered word doesn’t help much. So wanting to remember has little or no effect. Interestingly, memory gets a big boost if subjects think about whether they consider a word pleasant or unpleasant. Judging pleasantness causes you to think about what the word means and about other words related to that meaning. Thus, if you saw the word oven, you might think about cakes and roasts and about your kitchen oven, which stopped working so well, and so on. But if you judged whether oven contained an A or Q, you wouldn’t have to think about the meaning at all.
So it seems that we can say that thinking about meaning has a positive effect on memory. We have gotten close, but still not quite right. The penny example doesn’t fit that generalization. In fact, the penny example shows just the opposite. You have handled pennies thousands of times, and most of that time you thought about the meaning of the penny—it’s function, its monetary value. But having thought about the meaning of a penny doesn’t help when you try to remember what the penny looks like.
Think about it like this. Suppose you see someone muttering something. You can’t hear what they say, but you can tell by their tone that they feel angry. You could focus on several different things. You could think about the sound of the voice, how they look, or about the meaning of the incident. Each of these thoughts will lead to different memories of the event the next day. If you thought only about the sound of the voice, you won’t remember the appearance. If you focused on the visual details, you won’t remember the voice, and so on. In the same way, even though you have handled many pennies, you probably have not focused your attention on and thought much about their visual details.
Whatever you think about (focus your attention on), you remember. Memory works as the residue of thought. Once stated, the conclusion seems impossibly obvious. Given that you can’t store everything, how should you pick what to store and what to drop? Your brain lays its bets this way: If you don’t think about something very much, then you probably won’t want to think about it again, so your brain need not store it. On the other hand, if you do think about something, then you will likely want to think about it in the same specific way in the future. If I think about the mutter’s appearance, I’ll probably want to know about that when I think about that person later.
We need to draw out a couple of subtleties from this obvious conclusion. First, when we talk about school, we usually want students to remember what things mean. Sometimes we may consider what things look like important—for example the beautiful façade of the Parthenon, or the shape of Benin—but much more often we want students to think about meaning. Probably 95% of what students learn in school concerns meaning, not what things look or sound like. Therefore the teacher’s goal should always involve getting their students to think about some particular meaning.
The second subtlety relates to the idea that the same material can have different meaning. For example, the word piano has lots of meaning-based characteristics. One might think about its making music, its fine quality wood, its great expense, or the difficulty in moving it because of its size and weight. We cannot just focus on meaning, we have to have our students think about the particular aspect of meaning that we which them to remember.
Summary: To learn material—for it to end up in long-term memory—it must reside for some period in working memory. This means that a student must pay attention to it. Furthermore, how the student thinks of the experience completely determines what will end up in long-term memory. Obviously, then, teachers must design lessons that will ensure that students think about the particular important meaning of the material (and not something else). Similarly, a self-motivated student must focus on the particular important meanings that they wish to remember. But how do we make sure that students think about the particular important meaning?
What good teachers have in common
If you read Chapter One, you might guess that a common technique not recommended for getting students to think about meaning involves trying to make the subject matter relevant to the student’s interests. This sounds odd in that it contradicts some common folk wisdom concerning teaching, so let’s elaborate.
Trying to make the material relevant to student’s interests doesn’t work. As noted in Chapter One, content seldom works as the decisive factor in whether one maintains their interest. For example, you may love teaching, but this does not mean that you will not sometimes get bored at professional workshops or conferences. Another problem with trying to use content to engage interest relates to the fact that this often proves very difficult to do, and the whole enterprise usually comes off as artificial. How would a math instructor make algebra relevant to a sixteen-year-old? With a “real-world” example using cell phone minutes? Any material has different aspects of meaning. If the instructor used a math problem with cell phone minutes, might not the student think about cell phone minutes rather than about the problem? And might thoughts about cell phones lead to thoughts about the text message they received earlier, which would remind them about changing their picture on their Facebook profile, which would lead them to think about the zit they have on their nose?
So, if content won’t do it, how about the teaching style? Students often refer to good teachers as those who “make the stuff interesting”. The teacher doesn’t relate the material to the students’ interests—rather, the teacher has a way of interacting with students that they find engaging. One teacher may effectively act as a comedian, another as a den mother, another as a storyteller, and another as a showman. Students refer to each of these as teachers who make boring material interesting, and each can get students to think about meaning. Each style works well for the person using it, although obviously not everyone would feel comfortable taking on some of these styles. It works as a matter of personality.
Students do notice style, but that serves as only part of what makes these teachers effective. Analysis of student surveys of different teachers boils down to just two questions. Does the teacher seem like a nice person, and do they have a well organized class? The emotional bond between students and teacher—for better or worse—accounts for whether students learn. The brilliantly well-organized teacher whom students see as mean will not have much effectiveness. But the funny teacher, or the gentle storytelling teacher with poorly organized lessons won’t do much good either. Effective teachers have both qualities. They can connect personally with students, and they organize the material in a way that makes it interesting and easy to understand.
When we think of a good teacher, we tend to focus on personality and on the way the teacher presents. But that accounts for only half of good teaching. The jokes, the stories, and the warm manner all generate goodwill and help students to pay attention. But then how do we make sure they think about meaning? There, the second property of good teaching comes in—organizing the ideas in a lesson plan in a coherent way so that students will understand and remember. A set of principles that cognitive psychologists know about concerning how to help students think about the meaning of a lesson follows.
The power of stories
The human mind seems exquisitely tuned to understand and remember stories—so much so that psychologists sometimes refer to stories as “psychologically privileged,” meaning that memory treats them differently than other types of material. Organizing a lesson plan like a story works as an effective way to help students comprehend and remember.
Most sources point to the following four principles for creating a story, often summarized as the four Cs:
Character—A good story builds around strong, interesting characters, and action serves as the key to developing them.
Conflict—A story has a main character pursuing a goal, but they cannot reach that goal due to some obstacle.
Complications—Complications involve sub-problems that arise from the main goal.
Causality—Events have causal relations to one another. For example, in a story one would not say “I saw Jane; I left the house” because that just chronologically lists events. On the other hand saying, “I saw Jane, my hopeless old love; I left the house.” establishes a causal relation between seeing Jane and leaving the house.
Using a story structure brings several advantages in communicating with others. First, people find them easy to understand because the audience knows the structure, which helps to interpret the action. For example, the audience knows that events don’t happen randomly in a story, so if they cannot immediately see cause they will think carefully about previous action to try to connect to present events.
Second, people find stories interesting. Readers consistently rate stories more interesting than other formats such as expository prose, even if each presents the same information. Recall that problems have interest if neither too easy nor too difficult. Stories demand these medium-difficulty inferences. (People rate stories as less interesting if they include too much information, thus leaving no inferences for the listener to make. You can kill a story with too much information.)
Third, we easily remember stories for at least two reasons. (1) Because comprehending stories requires lots of medium-difficulty inferences, you must think about the story’s meaning throughout, and thinking about meaning facilitates memory. (2) The causal structure also aids memory. If you remember one part of the plot, a good probability exists that this caused the next thing that happened.
Putting story structure to work
But what does this have to do with the classroom? Simply telling stories will often work well, but consider this possibility: you can use a story structure to organize the material that you encourage your students to think about. Structure your lessons using the four Cs: character, conflict, complications and causality. This doesn’t mean that you must do most of the talking. You can use small group work, projects, or any other method.
In some cases, the way to structure a lesson plan as a story will seem rather obvious. For example, we can view history as a series of stories. Events cause other events, often with conflict involved, and so on.
Using a story structure to teach history seems easy, but can you really use it in a math class? Certainly. Suppose that in an introductory statistics class you want to introduce the concept of a Z-score—a common way to transform data. Begin with the simplest and most familiar example of probability—the coin flip. The conflict for this lesson will involve raising questions about how we (the characters) can determine the probability of an event occurring by chance. Here, we do not have Darth Vader as our adversary in pursuit of this goal, but the fact that most events we care about do not work like coin flips—they don’t have a limited number of outcomes (heads or tails) for which we know the probability (50 percent). So, here we have a complication, which we address with a particular type of graph called a histogram; but implementing this approach leads to a further complication: we need to calculate the area under the curve of the histogram, a complex computation. We solve this problem by the Z-score, the point of the lesson.
In doing this, we might spend a good bit of time—often ten or fifteen minutes of a 75-minute class—setting up the goal, persuading students of the importance of knowing the probability of a chance event. The material covered during this setup only partially relates to the lesson. Talking about coin flips and advertising campaigns doesn’t have much to do with Z-scores, but this elucidates the central conflict of the story. Spending a lot of time clarifying the conflict follows a formula from Hollywood. The central conflict in a Hollywood film starts about twenty minutes into the standard 100-minute movie. The screenwriter uses that 20 minutes to acquaint you with the characters and their situation so that when the main conflict arises, you already have involvement and you care about what happens to the characters. A film may start with an action sequence, but that sequence seldom relates to what will become the main story line of the movie.
When it comes to teaching, you might think of it this way: The material you want students to learn actually answers questions. On its own, the answer almost never has much interest. But if you know the question, then the answer may seem quite interesting. For this reason, making the question clear has great importance. But sometimes as teachers we get so focused on getting to the answer that we spend insufficient time making sure that students understand the question and appreciate its significance.
But what if it has no meaning?
This chapter started by posing the question, How can we get students to remember something? From cognitive science, we have a straightforward answer: get them to think about what it means. Using story structure serves as one method for getting students to think about meaning. But we sometimes have material close to meaningless that students must learn. For example, how can you emphasize meaning when helping students to learn the odd spelling of Wednesday, or that enfranchise means to give voting rights, or that travailler refers to the French verb for work? Sometimes, some material just doesn’t have much meaning. Such material seems especially prevalent when one enters a new field or domain of knowledge. A chemistry teacher might want students to learn in order the symbols for a few elements of the periodic table—but how can students think of the symbols H, He, Li, Be, B, C, N, O, and F in a deep, meaningful way when they don’t know any chemistry?
We commonly call memorizing meaningless material rote memorization. Times occur when a teacher may consider it important for a student to have such knowledge ready in long-term memory as a stepping-stone to understanding something deeper. (For example, multiplication and addition facts, foreign language or scientific vocabulary, or physics and chemistry equations.) How can a teacher help the student get that material into long-term memory?
A group of memory tricks called mnemonics, help people memorize meaningless material:
|Mnemonic |How It Works |Example |
|Peg word |Memorize a series of peg words by using a rhyme—for |To learn the list radio, shell, nurse you might imagine a |
| |example, one = bud, two = shoe, three = tree, and so on. |radio sandwiched in a bun, a shoe on a beach with a conch in |
| |Then memorize new material by associating it via visual |it, and a tree growing nurses’ hats like fruit. |
| |imagery with the pegs. | |
|Method of loci |Memorize a series of locations on a familiar walk—for |To learn the list radio, shell, nurse you might visualize a |
| |example, the back porch of your house, a dying pear tree, |radio hanging by your back porch, someone grinding shells to |
| |your gravel driveway, and so on. Then visualize new |use as fertilizer to revitalize the dying tree, and a nurse |
| |material at each “station” of the walk. |shoveling fresh gravel into your driveway. |
|Link method |Visualize each of the items connected to one another in |To learn the list radio, shell, nurse you might imagine a |
| |some way. |nurse listening intently to a radio while wearing large conch|
| | |shells on her feet instead of shoes. |
|Acronym |Create an acronym for the to-remember words, then remember |To learn the list radio, shell, nurse you might memorize the |
| |the acronym. |word RAISIN using the capitalized letters as cues for the |
| | |first letter of each word. |
|First letter of word |Similar to the acronym method, this method has you think of|To learn the list radio, shell, nurse you could memorize the |
| |a phrase, the first letter of which corresponds to the |phrase “Roses smell nasty”, then use the first letter of each|
| |first letter of the to-remember material. |word as a cue for the words on the list. |
|Songs |Think of a familiar tune to which you can sing the words. |To learn the list radio, shell, nurse you might sing the |
| | |words to “Happy Birthday to You”. |
|Short story method |Create a short story that relates the items or words. |To learn the list radio, shell, nurse you might think of how |
| | |you were at the beach listening to the radio, cut your foot |
| | |on a shell, then called a nurse. |
People can find the peg word and method of loci methods hard to use for different sets of material because confusion can occur. For example, if you use your mental walk to learn some elements, can you use the same walk to learn the conjugations for some French verbs? The two lists might interfere in some places. One can partly work around this by visually walking in different familiar places for different topics, but it remains a problem.
The other methods have more flexibility because students can create a unique mnemonic for each thing they learn, but they do need some familiarity with the material. Setting information to learn to music, chanting it to a rhythm, creating a poem, or creating a rap, also work quite well. For example, most of us learned the letters of the alphabet by singing the ABC song, and the “Battle Hymn of the Republic” presents state capitals. (Internet searches will produce songs for many lists.) Music and rhythm can make words remarkably memorable, and the song doesn’t have to have especially good melody.
Why do mnemonics work? Primarily by giving you cues. The acronym ROY G. BIV gives you the first letter of each color in the spectrum of visible light. The first letter of a word serves as quite a good cue to memory. As we will discuss in the next chapter, memory works on the basis of cues. If you don’t know anything about a topic, or if you need to remember something arbitrary, mnemonics help by imposing some order on the material.
To summarize, if we agree on the importance of background knowledge, then we must think carefully about how students acquire that background knowledge—how learning works. Many factors influence learning, but one factor trumps the others: students remember what they think about. That principle highlights the importance of getting students to think about the right thing at the right time. We usually want students to understand what things mean, and that sets the agenda for a lesson plan. How can we ensure that students think about meaning? One suggestion involves using the structure of a story because people easily comprehend and remember stories, and find them interesting. But one can’t get students to think about meaning if the material has no meaning. In those cases one may appropriately use mnemonic devices.
Classroom implications
Thinking about meaning helps memory. How can teachers ensure that students think about the desirable meaning in the classroom? Here you have some practical suggestions.
• *Review each lesson plan regarding what the student will likely think about. This sentence my serve as the most general and useful idea that cognitive psychology can offer teachers. The most important thing about schooling involves what students will remember after the school day has ended, and a direct relationship exists between what they think during the day and their later memory. So it proves useful to double-check every lesson plan to anticipate what the lesson will actually encourage students to think about rather than what you hope it will encourage them to think about. If you do this, it may often become clear that students will not very likely get what you intended out of the lesson, and then you will need to make some changes.
For example, doing a project that involves computers may get students thinking much more about how to use the computer and software than on what you intended with the project. You may get a lot of enthusiasm, but not about what you intended with the lesson. Think carefully about how your students will react to an assignment, and what it will actually prompt them to think about.
• Think carefully about attention grabbers. Teachers often like to start class with an attention grabber. They reason that if you hook students early in the lesson, they should feel curious to know the principles behind whatever surprised or awed them. But attention grabbers may not always work. After piquing the class’s interest and following with an age-appropriate explanation, the students may not retain that information. They may continue thinking about various aspects of the cool demonstration, and people remember what they think about. [This describes the traditional “tell ‘em and test ‘em” approach, not inquiry methods that do not give answers to questions, but instead lead students to answer the questions themselves over time. Indeed, the inquiry methods probably work much better than traditional largely because students remain curious and keep thinking about the questions and how best to answer them.]
Certainly, it makes sense to use the beginning of class to build student interest in the material, or to develop the conflict in a story. You might consider, however, whether the students need an attention grabber at the beginning of class. The transition from one subject to another (or for older students from one classroom and teacher to another) works well enough to buy at least a few minutes of attention from students. Usually, the middle of the lesson needs a little drama or physical activity to draw the students back from whatever reverie they may have fallen into. [See Schenck.] But regardless of when you use it, think hard about how you will draw a connection between the attention grabber and the point you really wish it to make. Will your students understand the connection, and will they set aside the excitement of the attention grabber and move on? If not, can you change the attention grabber to help students make that transition? Perhaps for a Roman lesson you could wear a toga over your street clothes and remove it after the first few minutes of class. Perhaps some demonstrations would work better done after the students have learned the basic principles and they have predicted what might happen based on their newly constructed knowledge, thus not relying on their prior beliefs—or just guessing. [Perhaps better yet, use the Conceptual Change Model.]
• Use inquiry learning with care. In inquiry learning students learn by exploring objects, discussing problems with classmates, designing experiments, or any of a number of other techniques that use student inquiry rather than the teacher telling students things. Indeed, the teacher ideally serves more as a resource than as a class director. Inquiry learning has much to recommend it, especially when it comes to the level of student engagement. An important risk, however, involves the lower predictability about what students will think about. If you leave students to explore ideas on their own—one of the options for managing inquiry learning—they may well explore unprofitable mental paths. [This depends on the kind of inquiry methods used! Inquiry covers a wide range of student freedom, and Willingham does not seem to understand that here, referring only to one extreme of the continuum.] If memory serves as the residue of thought, then students may remember their alternative conceptions as well as the scientifically accepted ones.
• Design assignments so that students will unavoidably think about meaning. If you have as the goal of a lesson plan to get students to think about the meaning of some material, then clearly the best approach will involve making their thinking about that meaning unavoidable. For example, telling people that you will test their memory of a list of words later won’t work very well because people don’t know how to make the words memorable. But if you give a simple task in which they must think about the word meanings—for example, by rating how much they like each word—then they will remember the words quite well.
For example, asking fourth graders to bake biscuits probably will not work very well as a way to get them to appreciate the life on the Underground Railroad because they will spend too much time thinking about measuring flour and milk. The goal involves getting them to think about the experience of runaway slaves. So a more effective lesson would involve leading the students to consider the experience by, for example, asking them where they supposed runaway slaves got food, how they could prepare it, how they could pay for it, and so forth.
• Use mnemonics. As bad as a classroom would seem if a teacher used only mnemonics, they do have their time and place and teachers should not have this instructional technique taken away from them. When does a teacher appropriately ask students to memorize something before it has much meaning? Not very often, but times occur when a teacher makes the judgment that students must learn material now in order to move further ahead in the long term, even though it seems meaningless to them now. Typical examples might include learning letter-sound associations prior to reading, learning vocabulary in both their native language and foreign languages, learning number facts in arithmetic, and important equations in physics. One might also appropriately use mnemonics to memorize some material in parallel with other work that emphasizes meaning. You should have your students do this kind of learning in small amounts over a long period of time (weeks and months). This helps reduce boredom and gives the benefits of frequent, active recall and repetition—practice.
• Organize a lesson plan, and sequence of them, around the story-related conflict(s). If you look for it, you can find a story-related conflict in almost any lesson plan. In other words, the material we want students to know answers a question or solves a problem; the question or problem serves as the conflict. Having great clarity about the conflict(s) yields a natural progression for topics. In a movie, play, or novel, characters trying to resolve a conflict often leads to new complications. That frequently holds true for school material too. Use these conflicts to build and maintain curiosity, engagement, and motivation.
Question 4: Why do we find abstract ideas so difficult to understand, and so difficult to apply when expressed in new ways?
Answer: Schooling has the important goal of abstraction. The teacher wants students to have the ability to apply classroom learning in new contexts, including those outside of school. But this involves the challenge that the mind does not like abstractions. Our minds prefer the concrete. For this reason, when we encounter an abstract principle—for example a law in physics such as net force = mass x acceleration—we ask for a concrete example to help us understand.
Critical principle 4: We understand new things in the context of things that we already know, and most of what we know, we know concretely.
For this reason, we find it difficult to comprehend abstract ideas, and difficult to apply them in new situations. The surest way to help students understand an abstraction involves exposing them to many different versions of the abstraction—for example, to have them solve area calculation problems about tabletops, soccer fields, envelopes, doors, and so on. Some promising new techniques may speed up this process. [Or in physics, chemistry, math or biology, use multiple representations: pictures and diagrams and students writing and speaking to describe the situation in their own words, and then using technical words and graphs and (finally) symbols and equations. (Note this progression.)]
Understanding: remembering in disguise
Factual knowledge has great importance in schooling, and we have discussed how to make sure that students acquire those facts and how things get into memory. But we must not assume that from accomplishing these things students understand what we wish to teach them. Students often find it difficult to understand new ideas, especially ideas really novel to them—meaning the new ideas don’t relate to other things they have already learned. What do cognitive scientists know about how students understand things? The answer: People understand new ideas (things they don’t know) by relating them to old ideas (things they do know). This helps us understand some familiar principles.
1) The usefulness of analogies. Analogies help us understand something new by relating it to something we already know about. For example, we commonly and usefully use water as an analogy for Ohm’s law in electricity.
2) Our need for familiar, concrete examples. Students find it hard to understand abstractions like “net force equal mass times acceleration”, even after defining all of the terms. They need concrete examples to illustrate what the abstractions mean. For example, before they can feel confident that they understand iambic pentameter, they need to hear:
Is this the face that launched a thousand ships?
And burnt the topless towers of Illium?
and
Rough winds do shake the darling buds of May
And summer’s lease hath all too short a date.
and other examples.
Examples require something more than just making abstractions concrete. For an example to help, the student must have familiarity with it. A concrete example will not help much if the student does not have familiarity with it. Suppose we had the following conversation:
Me: Different scales of measurement provide different kinds of information. Ordinal scales provide ranks, whereas on an interval scale the differences between measurement points have meaning.
You: That sounded like utter gobbledygook to me.
Me: OK, I will give you some concrete examples. The Mohs scale of mineral hardness works as an ordinal scale, whereas the Rasch model provides an interval measurement. See?
You: I think I’ll go get a coffee now.
So just giving concrete examples will not necessarily help. They must also have familiarity to the person and most people have no familiarity with the Mohs scale and Rasch model. Importantly, the familiarity helps, not the concreteness. But most of what students have familiarity with also falls into the concrete category because we have concrete experiences in our day-to-day lives and people find it hard to understand abstractions.
So, understanding new ideas mostly involves getting the right old, familiar ideas into working memory and then rearranging them—making comparisons we had not made before, or thinking about a feature we had previously ignored. Consider the acceleration outcomes that occur when using a bat to strike the windshield of a car compared with striking a ball. [Show photos here.] Each illustrates Fnet = ma. You know what happens when you hit a ball with a bat, and when you hit a windshield with a bat. But have you ever before held those two ideas in mind at the same time and considered how the different outcomes relate to the difference in mass? Have you ever rearranged the equation with these images in mind to see how [pic]? Have you ever considered what happens to “a” as “m” gets larger or smaller for a given net force?
Now perhaps you can better see why we claim that understanding largely equals remembering in disguise. As much as we may wish it, and as much as traditional education methods may try, no one can pour new ideas into a student’s head directly. The student must build every new idea on ideas that they already know. To get a student to understand, a teacher (or parent or book or television program) must ensure that the student pulls the right familiar ideas from their long-term memory and put them into working memory. In addition, they must attend to the right features of these memories and then compare, combine, or manipulate them appropriately. Thus, for me to help you understand the difference between ordinal and interval measurement, I cannot just say, “Think of a thermometer and think of a horse race.” Doing so may get those concepts into working memory, but I also have to make sure that you combine them in the right way.
All teachers know, however, that it does not really work this simply. When we give students one explanation and one set of examples, do they understand? Usually not. Suppose that I tell you the following:
We have four, and only four, ways that units on a scale relate to one another. On a nominal scale, each number refers to one thing but the numbers occur arbitrarily—for example, the number on a football player’s jersey tells you nothing about the quality of the player. It only names the player. On an ordinal scale, the numbers have meaning, but they tell you nothing about the distance between them. In a horse race, for example, you know that the first place horse ended ahead of the second place finisher, but you don’t know by how much. On an interval scale, not only do the numbers occur in an ordered way, but also the intervals have meaning—for example, the interval between 80 and 90 degrees on a thermometer. Even so, the inventor set the “zero” on an interval scale arbitrarily. For example, zero degrees Celsius does not mean no temperature. A ratio scale, on the other hand, such as age or the Kelvin temperature scale, has a true zero point. Zero years means the absence of any years; zero Kelvins means the absence of any temperature.
Having read this, would you say that you “understand” measurement scales? You probably know more than you did before, but your knowledge probably does not feel very deep and you may not feel confident that you could identify the scale measurement for a new example, say, centimeters on a ruler.
To dig deeper into what helps students understand, we need to address these two issues. First, even when students “understand”, degrees of comprehension occur. Understanding does not occur in an all-or-none way. One student may have a shallow understanding while another’s understanding has much more depth. Second, even if students understand in the classroom, this knowledge may not transfer well to the world outside the classroom. When students see a new version of what lies at the heart of an old problem, they may feel stumped, even though they recently solved the same problem. They may not know that they actually know the answer! The next two sections elaborate on these two issues.
Why do students have shallow knowledge?
You ask a student a question in class and they respond using the exact words you used when you explained the idea, or with the exact words from the textbook. Although they have certainly given a correct answer, you can’t help but wonder whether the student has simply memorized the definition by rote and really does not understand much of what they have said. Rote knowledge might lead to giving some right response, but it does not mean that the student understands or can think using that knowledge.
Actually, rote knowledge probably occurs only rarely. As used here, rote knowledge means you have no understanding of the material. You have just memorized words. On the other hand, shallow knowledge occurs much more commonly than rote knowledge. This means that students have some understanding of the material but it remains limited. People come to understand new ideas by relating them to old ideas. If they have shallow knowledge, the process stops there. Their knowledge remains tied to the analogy or explanation provided, and they can understand it only within that narrow context.
On the other hand, a person with deep knowledge knows much more about the subject, and the pieces of knowledge more richly interconnect. The student understands not just the parts, but also the whole. This understanding allows the student to apply the knowledge in many different contexts, to talk about it in different ways, to imagine how the system as a whole would change if one part of it changed, and so forth. The aspects of knowledge interrelate like the parts of a machine, and what-if questions suggest the replacement of one part with another. Students with deep knowledge can predict how the machine would work after changing a part.
Obviously, teachers want their students to have deep knowledge, and most teachers try to instill it. Why then would students end up with shallow knowledge? One obvious reason might involve the student not paying attention to the lesson. A poem’s mention of “rosebuds” might lead a student to think about the time they fell off their Razor scooter into the neighbor’s rose bush, and the rest of the poem becomes lost to them.
Other less obvious reasons exist for why students might end of with shallow knowledge. Deep knowledge means understanding essentially everything—both the abstraction and the examples, and how they fit together. So, we can easily understand why most students have shallow knowledge, at least when they begin to study a new topic: People find it harder to construct deep knowledge than shallow; it takes more work and more time.
Why doesn’t knowledge transfer?
If someone understands an abstract principle, we expect it will show transfer. When knowledge transfers, that means the person can successfully apply old knowledge to a new problem. In a sense, one might argue that every actual “problem” occurs as a new one. [This does not hold true for an exercise, which refers to practicing something already known.] Even if we see the same problem twice, we might see it in a different setting, and because some time has passed, we could say we have changed, even if only a little bit. Most often when psychologists talk about transfer they mean the new problem looks different from the old one, but we do have the knowledge needed to solve it. A problem looking different means that it has the same deep structure—because it requires the same steps for solving—but it has a different surface structure.
The surface structure of a problem remains unimportant to its solution, and we expect that a student who can solve the first problem to have the ability to solve the second, because the deep structure matters, not the surface structure. Nevertheless, people seem much more influenced by surface structure than we might think. Typically, only about 30 percent of people can solve a second problem, even though they had just heard the conceptually identical problem and its solution.
Why does transfer occur so poorly? The answer goes back to how we understand things. Our minds assume that new things we read (or hear) will relate to what we’ve just read (or heard). In general, this makes understanding faster and smoother. Unfortunately, it also makes it harder to see the deep structure of problems. This happens because our cognitive processing always struggles to make sense of what we read or hear, to find relevant background knowledge that will help us interpret words, phrases, and sentences. But the background knowledge that seems to apply almost always concerns the surface structure. We take the first problem as about one thing, and the second problem seems to involve something else.
The solution to this problem seems self-evident: Just tell people to think about the deep structure as they read or listen. But the deep structure of a problem does not appear obvious. Even worse, an almost limitless number of deep structures might apply. As you read about a particular problem, you find it hard to think about possible deep structures. To see the deep structure, you must understand how all parts of the problem relate to one another, and you must know which parts have importance and which do not. The surface structure, on the other hand, remains perfectly obvious.
When given a hint about deep structure in common with an earlier problem, almost everyone can solve the problem. The analogy becomes easy to see. So the transfer problem may involve a person simply not realizing the analogous nature of the problems.
At other times, we may get poor transfer even when students know that a new problem shares deep structure with another problem they have solved. When a problem has lots of components and lots of steps in its solution, transfer will less likely occur due to mapping difficulty from a solved problem to the new one.
This discussion makes it sound like knowledge cannot possibly transfer, but obviously that does not accurately describe the situation. Some people do think of using the problem they used before to solve a new one, although only a surprisingly small percentage. In addition, when faced with a novel situation an adult will usually approach it in a more fruitful way than a child will. Somehow, the adult makes use of their experience so that knowledge transfers. So, we should not think that our old knowledge transfers to a new problem only when the source of that background knowledge appears obvious to us. We have strategies for coming up with solutions, even though they may often not work. Those strategies grow out of our experience—based on other problems we’ve solved, things we know, and so on. In that sense, we always transfer knowledge of facts and of problem solutions, even when we think we’ve never seen this sort of problem before. However, we don’t know very much about this type of transfer precisely because of the difficulty determining where it comes from.
Classroom implications
The message of this chapter seems depressing: we find it hard to understand stuff, and when at last we do it won’t transfer to new situations very well. Though not quite that grim, one should not underestimate the difficulty of deep understanding. If understanding came easily, we would find teaching easy. Some ideas on how to meet this challenge in the classroom follow.
• To help student comprehension, provide examples and ask students to compare them. Experience helps students to see deep structure, so provide that experience via lots of examples. Another strategy that might help (although not extensively tested) involves asking students to compare different examples. The students (possibly with some prompting) might come to see what each example has in common with the others.
• Make deep knowledge the spoken and unspoken emphasis. You will likely let your students know that you expect them to learn what things mean—the deep structure. You should also ask yourself whether you send unspoken messages that match that emphasis. What kind of questions do you pose in class? Some teachers pose mostly factual questions in a rapid-fire manner: “What does b stand for in the formula?” or “What happens when Huck and Jim get back on the raft?” The low-level facts do have great importance, but if you ask only those questions, it sends a message to students that only those really matter.
Assignments and assessments also serve as sources of implicit messages about importance. When you assign a project, does it demand deep understanding or can one complete it with just the surface knowledge of the material? If you have students old enough to take quizzes and tests, make sure that these test deep knowledge. Students draw a strong implicit message from the content of tests. They conclude: “If it’s on the test, it’s important.”
• Make your expectations for deep knowledge realistic. Although you have deep knowledge as your goal, you should remain clear-eyed about how quickly students can achieve it. Deep knowledge comes only with long, hard work, the product of much focused practice. Don’t despair if your students don’t yet have a deep understanding of a complex topic. Shallow knowledge proves much better than no knowledge at all, and shallow knowledge serves as a natural step on the way to deeper knowledge. It may take years for your students to develop a truly deep understanding, and the best that any teacher can do involves starting them down that road or continuing their progress at a good pace. [With this idea, you may feel a little better about not getting 100% of a class up to the level of understanding that you hope to achieve.]
Question 5: Does the cognitive benefit of drill make it worth the potential cost to motivation?
Answer: The bottleneck in our cognitive system involves the extent to which we can juggle several ideas in our thinking simultaneously. Our brains have a few tricks for working around this problem, one of the most effective related to practice. Why does this work? Because it reduces the amount of “room” that mental work requires.
Critical principle 5: It proves virtually impossible to become proficient at a mental task without extended practice.
You cannot become a good soccer player if as you dribble you still focus on how hard to hit the ball, which surface of your foot to use, and so on. Low-level processes like this must become automatic, leaving room for higher-level concerns such as game strategy. [Mike Byster’s Brainetics “Breakthrough Math and Memory System” probably works by doing this: giving people sufficient practice with low-level processes that these processes become automatic, thus freeing working memory for other tasks.] Similarly, you cannot get good at algebra without knowing many math facts and procedures fluently by memory. Students must practice some things. But they don’t need to practice all material. In this chapter, you learn why practice has such importance, which material to consider important enough to merit practice, and how to implement practice in a way that students find maximally useful and interesting.
Why practice? One reason involves gaining a minimum level of competence. For example, a child practices tying their shoelaces with a parent or teacher’s help until they can reliably tie the laces without supervision. We also practice tasks that we can perform but that we would like to improve. A professional tennis player can hit a serve into their opponent’s court every time, but they nevertheless practice serving in an effort to improve speed and placement of the ball. In an educational setting, both reasons—mastery and skill development—seem sensible. Students might practice long division until they master that process, until they can reliably work long-division problems. They might perform other skills adequately, such as writing a persuasive essay, but even after students have the rudiments down, they should continue to practice the skill in an effort to refine and improve their abilities.
The two reasons to practice—to gain competence and to improve—seem self-evident and probably not very controversial. On the other hand, the reasons to practice skills when it appears you have mastered something and it does not obviously make you better seems less obvious. Odd as it may seem, that sort of practice proves essential to schooling. Why? Because it yields three important benefits: it reinforces the basic skills required for learning more advanced skills, it protects against forgetting, and it improves transfer.
Practice enables further learning
Practice has so much importance for students’ learning for two reasons: (1) working memory serves as the site of thinking and thinking occurs when we combine information in new ways (refer to the diagram above), but (2) it has limited space. If you try to juggle too many facts, or to compare them in too many ways, you lose track of what you do. This lack of space in working memory forms a fundamental bottleneck for human cognition. Unfortunately, no way exists to increase a person’s working memory capacity; each of us has a more or less fixed size of it. You get what you get and practice does not change it.
However, ways exist to cheat this limitation. One way to keep more information in working memory involves compressing it using a process called chunking (described in chapter two), where you keep several things as a single unit. For example, instead of maintaining the letters c, o, g, n, i, t, i, o, and n separately in working memory, you chunk them into the single word cognition. A whole word takes up about the same amount of room in working memory as a single letter does. But chunking letters into a word requires that you know the word. If you don’t have the word in long-term memory, you can’t chunk the letters. [This surely holds true for concepts as well. And this points to the importance of vocabulary, which students most effectively gain through general reading.] Thus we see the importance of factual knowledge; it allows efficient chunking. [Again, Mike Byster’s Brainetics “Breakthrough Math and Memory System” probably works by doing this: giving people sufficient practice with low-level processes that they begin chunking more efficiently.]
So the first way to cheat the limited size of your working memory works through factual knowledge. A second way exists to make the processes that manipulate information in working memory more efficient. In fact, you can make them so efficient that they have virtually no cost. [Byster’s Brainetics again!] Think about learning to tie your shoes. Initially, it requires your full attention and thus absorbs all of working memory, but with practice you can tie your shoes automatically. What used to take all of working memory now takes almost no room. As an adult, you can tie your shoes while holding a conversation or even while working math problems in your head. Driving a car, riding a bicycle and walking serve as other everyday examples. When you first learn these, they take up all of your working-memory capacity.
So mental processes can become automatized, and automatic processes require little or no working memory capacity. They also tend to occur quite rapidly in that you seem to know just what to do without even making a conscious decision to do it. [Byster’s Brainetics, and others…. People need enough practice with important fundamentals that they become automatic. Byster and others do this by creating fun games that give the needed practice.]
These same principles play out in mathematics. When students first learn arithmetic, they often solve problems by using counting strategies. For example, they solve 5 + 4 by beginning with 5 and counting up four more numbers [things or dots] to yield the answer 9 [or 9 dots]. This strategy suffices to solve simple problems, but you can see what happens as problems become more complex. For example, in a multi-digit problem like 97 + 89, a counting strategy becomes much less effective. This more complex problem demands that one carry out more processes in working memory. The student might add 7 and 9 by counting and get 16 as the result. Now the student must remember to write down the 6, then solve 9 + 8 by counting, while remembering to add the carried 1 to the result.
Notice how much simpler this problem becomes if the student has memorized the fact that 7 + 9 = 16. Knowing this, they arrive at the correct answer for that subcomponent of the problem at a much lower cost to working memory. Finding a fact in long-term memory and putting it into working memory places almost no demands on working memory. So it comes as no wonder that students who have memorized math facts and procedures do better in all sorts of math tasks than students who do not have that knowledge, or only spotty or uncertain knowledge, of math facts and procedures. Research has shown that practicing math facts helps low-achieving students do better on more advanced mathematics. [Byster…. And math serves as the best predictor of success in college (FICSS).]
Besides sounds going with letters and math facts, other sorts of automatization entail other processes. Notable examples include handwriting and keyboarding. Initially, forming or keyboarding letters proves laborious and consumes all of working memory. One finds it hard to think of the content of what one writes because you have to focus on getting the letters right; but with practice you can focus on content.
To review, although we can’t make our working memory larger, we can make the contents of working memory smaller in two ways: (1) by making facts take up less room through chunking, which requires knowledge in long-term memory (and discussed in Chapter Two); and (2) by shrinking the processes we use to bring information into working memory or to manipulate it once it has gotten there.
So now we get to the payoff: What must happen to make these processes shrink, to get them to become automatized? You know the answer: practice. If any workaround or cheat exists whereby you can reap the benefits of automaticity without paying the price of practicing, neither science nor the collected wisdom of the world’s cultures has revealed it. As far as anyone knows, the only way to develop mental facility involves repeating the target process again and again and again.
Now you can see why practice (and over-practicing) enables further learning. You may have “mastered” reading in the sense that you know which sounds go with which letters, and you can reliably string together sounds into words. So, why keep practicing if you know the letters? You do not practice only to get faster. It proves important to get so good at recognizing letters that retrieving the sound becomes automatic. If it happens automatically, you have freed working memory space that you used to devote to retrieving the sounds from long-term memory—space that you can now devote to thinking about meaning.
What holds true of reading holds true of most or all school subjects, and of the skills we want out students to have. They work hierarchically. Several basic processes (like retrieving math facts or using deductive logic in science) initially demanding of working memory, become automatic with practice. Those processes must become automatic in order for students to advance their thinking to the next level. The great philosopher, Alfred North Whitehead captured this phenomenon in this comment: “It is a profoundly erroneous truism, repeated by all copybooks and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.”
Practice makes memory long lasting
Why learn things in high school that we will soon forget? A certain amount of truth exists in the student complaint “We’re never gonna use this stuff.” So if what we teach students will simply vanish, why the heck do we teach it?
Well, the truth lies somewhere between the two extremes. We all remember a little of the things we learned in high school and college. Certainly we know much less now than we did right after we finished the classes we took—but we know more than we did before we took them. Researchers have examined student memory more formally and have drawn the same conclusion: we forget much (but not all) of what we have learned, and the forgetting occurs rapidly.
In one study of students who get A’s compared with B and below students three years after the class, the A students remembered more overall, which does not seem surprising—they probably knew more to start with. But they forgot just like other students did, and at the same rate. So apparently studying hard doesn’t protect against forgetting. But something else does protect against forgetting: continued practice. For example, a student who gets a C in their first algebra course but goes on to take several more math courses will remember their algebra, whereas a student who gets an A in their algebra course but doesn’t take more math will forget it. That happens because taking more math courses guarantees that you will continue to think about and practice basic algebra. If you practice algebra enough, you will effectively never forget it. [Note how this and the FICSS study results support each other.] Other studies have shown exactly the same results with different subject matter, such as Spanish studies as a foreign language.
Do these results occur because you study more, or because you stretch the study out over time? Does it matter how you space out your studying? Studying something for two hours works better than studying for one, but how should distribute those 120 minutes? Should you study for 120 minutes in a row? Or for 60 minutes one day and then 60 minutes the next? How about 30 minutes each week for four weeks?
People commonly call doing a lot of studying just before a test cramming. If you pack lots of studying into a short period, you’ll do okay on an immediate test, but you will forget the material quickly. If, on the other hand, you study in several sessions with delays between them, you may not do quite as well on the immediate test but, unlike the crammer, you’ll remember the material longer after the test.
So, it makes sense that spreading out your studying would produce better memory than cramming, but we need to make explicit two important implications of the spacing effect. (1) You can get away with less practice if you space it out than if you bunch it together. But spacing practice has another benefit. Practice, as we’ve used the term, means continuing to work at something that you have already mastered. That sounds kind of boring, even though it brings cognitive benefits. So, (2) this practice will work more easily for the teacher and student in keeping it interesting if you space it out over time.
Practice improves transfer
As discussed earlier, challenges exist in getting what you already know to transfer to new situations. It occurs, but rarely. What can we do to increase the odds? What factors make a student more likely to say, “Hey, I’ve seen problems like this before and I remember how to solve them!”?
It turns out that many factors contribute to successful transfer, but a few of them seem especially important. First, transfer will more likely occur when the surface structure of the new problem has similarity to the surface structure of problems seen before. For example, a coin collector will more likely recognize that they can work a problem involving fractions if they see the problem framed in terms of money exchange rather than if they see a mathematically equivalent problem framed as one of calculating the efficiency of an engine.
Practice serves as another significant contributor to good transfer. Working lots of problems of a particular type makes it more likely that you will recognize the underlying structure of the problem, even if you haven’t seen this particular version of the problem before. Researchers think a couple of reasons explain this. First, practice makes it more likely that you will really understand the problem in the first place and that you will remember it later. If you don’t understand and remember the principle, not much hope exists for it to transfer to a new situation!
Second, we often use contextual information not only for understanding individual words with several possible meanings, but also for understanding relationships of different things in what we read. Your mind stores functional relationships between concepts just as it stores the meaning of individual words. The first time someone tells you that eye can refer to the center of a hurricane, you don’t have any trouble understanding it; but that doesn’t mean that the next time you encounter eye the correct meaning will pop into mind. More likely, you will feel puzzled and need to work out from the context what it means. To interpret eye automatically the right way, you will need to see it a few more times—in short, you will need to practice it. The same holds true of deep structures. You might understand a deep structure the first time you see it, but that doesn’t mean you will recognize it automatically when you encounter it again. In sum, practice helps transfer because practice makes deep structure more obvious.
Classroom implications
This chapter started with two obvious reasons to practice: to gain minimum competence (as when a teenager practices driving with a manual shift until they can reliably use it) and to gain proficiency (as when a golfer practices putts to improve their accuracy). We then suggested three more reasons to continue practicing mental skills, even when no obvious improvements in our abilities occur. Such practice yields three benefits: (1) it can help mental process become automatic and thereby enable further learning; (2) it makes memory long lasting; and (3) it increases the likelihood that learning will transfer to new situations. The downside of this sort of practice seems pretty obvious: People tend to get pretty bored practicing something they don’t seem to get better at! Some ideas about how we can reap some benefits of practice while minimizing the costs follow.
• What should students practice? We cannot practice everything extensively. We simply don’t have time, but fortunately we don’t need to practice everything. If practice makes mental processes automatic, we can then ask, Which processes need to become automatic? Retrieving number facts from memory seems a good candidate, as does retrieving letter sounds from memory. A chemistry teacher may decide that his students need to have basic facts about the periodic table at their fingertips. A physics teacher may decide that her students need to quickly retrieve certain equations from memory. In general, the processes that need to become automatic probably serve as the building blocks of skills that will provide the most benefit in the short and long term if they become automatic. The things one does again and again serve as the building blocks in a subject area, and they serve as the prerequisites for more advanced work.
• Space out the practice. Do not think that all of the practice with a particular concept or skill needs to occur within a short span of time or even within a particular unit. In fact, good reasons exist to space out practice. Memory becomes more enduring with spaced out practice, and practicing the same skills again and again often becomes boring. It works better to offer some change. Students will get more practice thinking through how to apply what they know as an additional benefit of spacing. If you bunch all of the practice of a skill together, students will know that every problem they encounter serves as a variant of the practiced skill. But if you sometimes include material from a week, a month, or three months ago, students must think more carefully about how to tackle the problem, and about what knowledge and skills they have that might apply. Then too, remember that your students will encounter other teachers. An English teacher might think it very important for their students to understand the use of imagery in poetry, but students will acquire the knowledge and skills necessary to appreciate imagery over years of instruction.
• Fold practice into more advanced skills. You may target a basic skill as one that students need to practice to the point of mastery, but that does not mean that students cannot also practice it in the context of more advanced skills. For example, students may need to practice retrieving sounds in response to printed letters, but why not put that practice into the context of interesting reading—insofar as possible without overloading working memory? A competent bridge player needs to count the points in a hand as a guide to bidding, but a bridge instructor should not have their students do nothing but count points until they could do so automatically. Automaticity takes lots of practice. The smart way involves distributing the practice not only across time but also across activities. Think of as many creative ways as you can to practice the really crucial skills, but remember that students can still get practice in the basics while they work on more advanced skills.
Question 6: What can we do to get students to think like scientists, historians and mathematicians?
Answer: We can’t. Students cannot cognitively do what trained and experienced scientists, mathematicians and historians do.
Critical principle 6: Cognition early in training differs fundamentally from cognition late in training.
Students do not only know less than experts; their memory also organizes it differently. Expert scientists did not think like experts-in-training when they started out. They thought like novices. In truth, no one thinks like a scientist or a historian without a great deal of training and experience. This conclusion doesn’t mean that students should never try to write a poem or conduct a scientific experiment; but teachers and administrators should have a clear idea of what such assignments will—and will not—do for students.
Traditionally, we find science classes structured as follows: (1) at home you read a textbook that explains some principle of biology, chemistry, or physics; (2) the next day the teacher explains the principle; (3) with a partner you conduct a laboratory exercise meant to illustrate the principle; and (4) that night you complete a problem set in order to practice applying the principle.
These activities don’t give students any practice in what scientists actually do. For example, scientists don’t know the outcome of an experiment before they do it—they do the experiment to find out what will happen, and they must interpret the results, which often surprises them or produces a self-contradictory result. Meanwhile, as traditionally done high schoolers know that laboratory exercises have predictable outcomes, so they likely focus much less on what the lab illustrates than on whether they “did it right”. Likewise, historians don’t read and memorize textbooks—they work with original sources (birth certificates, diaries, contemporary newspaper accounts, and the like) to construct sensible narrative interpretations of historical events. If we don’t give students practice in doing the things that historians and scientists actually do, in what sense do we teach them history and science? But even if we change the ways we teach, can we realistically teach them to think like historians and scientists?
Probably not. Real scientists have expertise. They have worked at science for forty hours (likely many more) each week for years. It turns out that those years of practice make a qualitative, not quantitative, difference in the way they think compared to how a well-informed amateur thinks. Thinking like a historian, a scientist, or a mathematician proves a very tall order indeed. What do expert thinkers do and how do they do it?
What do scientists, mathematicians and other experts do?
Obviously, what experts do depends on their field of expertise. Still we find important similarities among experts, not only in scholarly fields such as history, math, literature, and science, but also in applied fields such as medicine, banking, auto repair, and construction, and in recreational pursuits such as chess, bridge, and tennis.
Bombarded with information such as data from their own examination, results of multiple tests, the facts, and so forth, experience makes experts more sensitive to subtle cues that others miss. Experts have a lot of background knowledge about their field, but it takes more than knowledge to become an expert. Experts-in-training often know as much (or nearly as much) as experts. But the expert can access the right information from memory with great speed and accuracy—information that the more junior expert-in-training has in their memory but just don’t think of.
Expertise extends even to the types of mistakes that they make. When experts fail, they do so gracefully. When they don’t get the right answer, the wrong answer usually comes pretty close. Finally, experts show better transfer to similar domains than novices do. For example, a historian can analyze documents outside their area of expertise and still come up with a reasonable analysis. The analysis will take longer and will not have quite the detail as it would for material in their own area, but it will appear much more like an expert’s analysis that a novice’s.
Compared to novices, experts can better single out important details, produce sensible solutions, and transfer their knowledge to similar domains. We see these abilities in doctors, writers, mathematicians, chess players—and teachers.
What does an expert’s mental toolbox contain?
How do experts do what they do? What problem-solving abilities or specialized knowledge to they have access to? And how can we make sure that students have whatever it takes? We have discussed two ways of getting around of getting around the limitations of working memory, background knowledge and practice. Experts use both too, but their extensive experience makes these strategies even more effective.
Experts have lots of background knowledge in their area of expertise, but the expert brain has another advantage over the brains of the rest of us. They don’t just have lots of information in long-term memory; they also have that information in memory organized differently from the information in a novice’s long-term memory.
Experts don’t think in terms of surface features, as novices do; they think in terms of functions or deep structure, in terms of functional units. We can generalize by saying that experts think abstractly. They sort problems on the basis of the principles important to their solution.
The second way to get around the limited size of working memory involves practicing procedures so many times that they become automatic. That way the procedures don’t take space in working memory. Tie your shoes a few hundred times and you don’t need to think about it; your fingers just fly through the routine without any direction from thought processes that would crowd working memory. Experts have automatized many of the routine, frequently used procedures that early in their training required careful thought.
So experts save room in working memory through acquiring extensive, functional background knowledge; they do this by making mental procedures automatic. What do they do with that extra space in working memory? One of the things they do involves talking to themselves. What sort of conversation does an expert have with him or herself? Often they talk about a problem in progress, and they do so at an abstract level. The physics expert says things like “This is probably an energy conservation problem, and I need to show the transfer of potentially stored energy into kinetically stored energy.”
Interestingly, the expert can draw implications from this self-talk. The physics expert just mentioned has already drawn a hypothesis about the nature of the problem, and as they continue reading, they will evaluate the validity of their hypothesis. “Now I feel really sure, because we will squash the spring and that will store more energy potentially.” Thus experts do not just narrate what they do. They also generate hypotheses, and so test their own understanding and think through the implications of possible solutions in progress. Talking to yourself demands working memory, however, so novices will much less likely do it. If they do talk to themselves, what they say predictably occurs at a shallower level than what experts say. When novices talk to themselves, they narrate what they do, and what they say does not have the beneficial self-testing properties that expert talk has.
How can we get students to think like experts?
Experts see problems and situation in their chosen field functionally rather than at the surface level. Sounds great. How can we teach students to do this? Unfortunately, we don’t have an exactly cheering answer to this question. It should seem obvious that offering novices advice such as “talk to yourself” or “think functionally” won’t work. Experts do those things, but only because their mental toolbox enables them to do so. The only path to expertise as far as anyone know involves long, focused practice.
Research on expertise fairly consistently shows one surprising finding. The great minds of science did not get distinguished as exceptionally brilliant as measured by IQ tests. For sure, they qualified as very smart, but not the standouts that their stature in their fields might suggest. What did prove singular involved their capacity for sustained work. Great scientists almost always qualify as workaholics. Each of us knows our limit; at some point we need to stop working and watch a stupid television program, read People magazine, or something similar. Great scientists have incredible persistence, and their threshold for mental exhaustion runs very high. Thomas Alva Edison, famous for inventing or greatly improving the light bulb, the fluoroscope (an early version of the x-ray machine), the phonograph, and motion pictures, also had fame for his work habits. He sometimes worked 100-hour work weeks, and he often took cat naps in his laboratory rather than sleep at home. Small wonder exists that he said “genius is 1 percent inspiration and 99 percent perspiration.”
Another implication of the importance of practice relates to the idea that we can’t achieve expertise until we put in our hours. A number of researchers have endorsed what has become known as the “ten-year rule”: one can’t become an expert in any field in less than ten years, whether physics, chess, golf, mathematics, or teaching. Some have argued that the rule fits prodigies such as Mozart, who began composing at age five, because they usually had imitative early output and did not get recognized by their peers as exceptional. So, even if we allow for a few prodigies every century, the ten-year rule holds up pretty well.
Nothing magical about a decade exists; it just seems to take that long to learn the background knowledge and to develop the automaticity that we’ve talked about here. Indeed, research has shown that those who have less time for practice take longer than a decade, and in fields where one has less to learn—short-distance sprinting or weightlifting, for example—one can achieve greatness with only a few years of practice. In most fields, however, ten years serves as a good rule of thumb. And study and practice do not end once one achieves expert status. The work must continue if one wishes to maintain their expert status.
Classroom implications
Experts do not simply think better than novices in their chosen field; experts actually think in ways qualitatively different. As novices, our students do not have expertise. How should that impact our teaching?
• Students can comprehend, not create new knowledge in a field. Experienced mathematicians, historians and scientists differ from novices. They have worked in their field for years and the knowledge and experiences they have accumulated enables them to think in ways not open to the rest of us. Thus, trying to get your students to think like them does not serve as a realistic goal. Getting your students to understand some science, math and history—a worthy goal indeed—works as a very different goal compared with getting them to think like scientists, mathematicians or historians.
Drawing a distinction between understanding knowledge and creating significant contributions to a field may help. Experts create significant contributions to a field. For example, scientists create and test theories of natural phenomena, historians create narrative interpretations of historical events, and mathematicians create proofs and descriptions of complex patterns. Experts not only understand their field, they add to it.
A more modest and realistic goal for students involves their constructing a firm knowledge foundation. A student may not construct a new scientific theory, but they can develop a deep understanding of existing theory. A student may not write a new narrative of historical fact, but they can follow and understand a narrative that someone else has written.
• Activities appropriate for experts may at times work appropriately for students, but not because they will do much for students cognitively. A key difference between the expert and the well-informed amateur lies in the expert’s ability to create new knowledge versus the amateur’s ability to understand concepts that others have created. Well, what happens if you ask students to create new knowledge? Most likely, they won’t do it very well because doing that requires a lot of background knowledge and experience that they don’t have.
But a teacher might have some very good other reasons for asking students to do these things. For example, a teacher might ask their students to interpret the results of a laboratory experiment not with the expectation that this teaches them to think like scientists, but instead to highlight a particular phenomenon or to draw their attention to the need for close observation of an experiment’s outcome.
Assignments that demand creativity may also motivate students. A music class may well emphasize practice and proper technique, but it may also encourage students to compose their own works simply because the students would find it fun and interesting. Does such practice prove necessary or useful in order for students to think like musicians? Probably not. Beginning students normally do not have the cognitive equipment in place to compose, but that doesn’t mean they won’t have a great time doing so, and that may provide reason enough.
The same holds true for science fairs. Judging a lot of science fairs reveals mostly terrible student projects. The students usually try to answer lousy questions not fundamental to the field. Because of the poor experiment design and failure to sensibly analyze data, the students don’t appear to have learned much about scientific methods. But some students really enjoy and feel proud of what they have done, and their interest in science or engineering has gotten a big boost. So although the scientifically creative aspect of the project usually flops, science fairs seem good bets for practice and motivation.
Bottom line: posing to students challenges that demand creating something new will normally lie beyond their reach—but that doesn’t mean that you should never pose such tasks. Just keep in mind what the student will or will not get out of it.
• Don’t expect novices to learn by doing what experts do. When considering how to help students gain a skill, it seems natural to encourage them to emulate someone who already knows how to do what you want them to do. Thus, if you want students to learn how to read a map, find someone who reads maps well and start training the students in the methods the good map reader uses. As logical as this technique sounds, it can backfire because significant differences exist between how experts and novices think.
For example, how should we teach reading? Expert readers make fewer eye movements than unskilled readers do. So one could say that the better way to read involves recognizing entire words, and that we should teach that method from the start because good readers read that way.
One should view such arguments with suspicion. Even though expert readers can take in a whole word at a time, they did not necessarily start off reading that way. Expert tennis players spend most of their time during a match thinking about strategy and trying to anticipate what their opponents will do. But we shouldn’t tell novices to think about strategy; novices need to think about footwork and about the basics of their strokes.
Whenever you see an expert doing something differently from the way a non-expert does it, the expert may well have once done it the ways the novice does it, and doing so may serve as a necessary step on the way to expertise. Ralph Waldo Emerson put it more artfully: “Every artist was first an amateur.”
Question 7: How should a teacher adjust their teaching to different types of learners?
Answer: They shouldn’t. No one has found consistent evidence supporting a theory describing such a difference.
Critical principle 7: Children have far more similarities than differences in how they think and learn.
Note that this claim does not say all children are alike, nor that teachers should treat children as interchangeable. Naturally some kids like math whereas others do better at English. Some children exhibit shyness and other an outgoing nature. Teachers interact with each student differently, just as they interact with friends differently; but teachers should know that, as far as scientists can determine, we do not have categorically different types of learners.
Styles and abilities
Students obviously have differences, and some teachers hope that they might use these differences to reach students. For example, a teacher might take a student’s strength and use it to remedy a weakness. A second possibility involves the idea that a teacher might take advantage of student’s different ways of learning. Clearly, these exciting possibilities imply more work for the teacher. Would it be worth it? Before discussing that, we need to clarify the differences between cognitive abilities and cognitive style.
Cognitive ability refers to capacity for or success in certain types of thought. In contrast, cognitive styles work as biases or tendencies to think in a particular way, for example to think sequentially (of one thing at a time) or holistically (of all of the parts simultaneously). Abilities involve how we deal with content and they reflect the level of what we know or can do. Styles involve how we prefer to think and learn. We consider having more ability better than having less, but we do not consider one style better than another. One style might work more effectively for a particular problem, but all styles have equal usefulness overall, by definition. (If they didn’t, we would classify them as abilities, not styles.) To use a sports analogy, we might say that two football players have equal ability even if they have different styles on the field. For example, one might take many risks while the other behaves more conservatively.
Cognitive styles
A cognitive styles theory must have the following three features: (1) it should consistently attribute to a person the same style, (2) it should show that people with different styles think and learn differently, and (3) it should show that people with different styles do not, on average, differ in ability. At this point we do not have a theory with these characteristics. That does not mean that cognitive styles don’t exist—they certainly might. But after decades of trying, psychologists have not found them. Regarding this, let’s consider the hypothesis of visual, auditory, and kinesthetic learners.
Visual, auditory, and kinesthetic learners
The visual-auditory-kinesthesia hypothesis holds that everyone can take in new information through any of the three senses, but most of us have a preferred sense. When learning something new, visual types like to see diagrams, or even just to see in print the words the teacher says. Auditory types prefer descriptions, usually verbal, to which they can listen. Kinesthetic learners like to manipulate objects physically; they move their bodies in order to learn.
People do differ in their visual and auditory memory abilities. But cognitive scientists have also shown that we do not store all of our memories as sights or sounds. We also store memories in terms of what they mean to us. For example, if a friend tells you a bit of gossip about a coworker who someone saw come out of an adult bookshop, you might retain the visual and auditory details of the story (for example, how the person telling the story looked and sounded), but you might remember only the content of the story (adult bookshop) without remembering any of the auditory or visual aspects of the telling. Meaning has a life of its own, independent of sensory details.
So, it proves true that some people have especially good visual or auditory memories. In that sense, we have visual and auditory learners. But the key prediction of the hypothesis does not involve that. The key prediction involves the idea that students will learn better when instruction matches the cognitive style. In other words, suppose Anne prefers an auditory style while Victor prefers a visual style. Suppose further that you give Anne and Victor two lists of new vocabulary words to learn. To learn the first list, they listen to a tape of the words and definitions several times; to learn the second list, they view a slide show of pictures depicting the words. The theory predicts that Anne should learn more words on the first list than on the second whereas Victor should learn more words of the second list than on the first. Psychologists have conducted dozens of studies along these lines, including studies using materials more like those used in classrooms. Overall these studies do not support the hypothesis. Matching the student’s preferred learning mode does not give that student any edge in learning.
How can that happen? Why doesn’t Anne learn better with an auditory presentation, given that she prefers the auditory mode? Because the test does not test auditory information! Auditory information consists of the particular sound of the voice on the tape, but the test tests the meaning of the words. Anne’s edge in auditory memory doesn’t help her in situations where meaning has importance. Similarly, Victor might better recognize the visual details of the pictures used to depict the words on the slides, but again, the test does not test that ability.
The situation described in this experiment probably matches most school lessons. Most of the time students need to remember what things mean, not what they sound, look, or feel like. Sure, sometimes that information counts; someone with a good visual memory will have an edge in memorizing the particular shapes of countries on a map, for example, and someone with a good auditory memory will better get the accent right in a foreign language. But the vast majority of schooling concerns itself with what things mean, not with what they look like, sound like, or how they feel.
So does that mean that the visual-auditory-kinesthetic hypothesis works correctly some small proportion of the time, such as when students learn foreign language accents or countries on a map? Not really, because the point of the hypothesis involves the idea that we can present the same material in different ways to match each student’s strength. So, visual learners presumably should view shapes of countries while auditory learners should listen to descriptions.
If the visual-auditory-kinesthetic hypothesis does not fit, why does it seem so right? About 90 percent of teachers believe we have students predominantly visual, auditory, or kinesthetic learners. Probably several factors contribute to the hypothesis’ plausibility. First, it has become commonly accepted wisdom—one of those alleged “facts” that everyone figures must hold true because everyone believes it. (And the beliefs of people around us have powerful effects in shaping our own beliefs.)
Another important factor relates to the idea that something similar to the hypothesis does prove true. People do differ in their visual and auditory memories. For example, maybe you have watched in wonder as a student has painted a vivid picture of an experience from a class field trip and thought, “Wow, Lacy is obviously a visual learner.” Lacy may well have a really good visual memory, but that doesn’t mean she qualifies as a “visual learner” in the sense that the hypothesis implies.
A final reason the visual-auditory-kinesthetic hypothesis seems right involves a psychological phenomenon called confirmation bias. Once we believe something, we unconsciously interpret ambiguous situations as consistent with what we already believe. The great novelist Tolstoy put it this way:
“I know that most men, including those at ease with problems of the greatest complexity, can seldom accept the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have proudly taught to others, and which they have woven, thread by thread, into the fabrics of their life.”
For example, many people believe that all sorts of interesting things happen during a full moon: the murder rate goes up, emergency room admissions increase as do calls to police and fire department, and more babies come into the world, among other things. Actually, researchers have exhaustively examined this hypothesis and found it wrong. Why do people believe it? One factor involves the confirmation bias. When a full moon occurs and nurses have a busy delivery room, the nurse notices and remembers it. When they have a busy delivery room and no full moon, they don’t take note of it.
We’ve gone into a lot of detail about the visual-auditory-kinesthetic hypothesis because so many people believe it, even though psychologists know it does not work. What we have said about this theory goes for all of the other cognitive style hypotheses as well. That we have mixed evidence concerning them serves as about the best that we can say about any of them. Now, what about abilities, and how should we think about differences in them among students?
Abilities and multiple intelligences
The different abilities (or “intelligences”, if you like) do not interchange. We have to learn mathematical concepts and skills mathematically, and skill in music, for example, will not help us do this. Writing a poem about the arc that a golf club should take will not help your golf swing. These abilities do not completely remain insulated from one another, but they remain separate enough that you can’t take one skill you do well and leverage it to bolster a weakness.
Some people have suggested that we might at least get students interested in subject matter by appealing to their strength. To get the science whiz reading for pleasure, don’t hand her a book of Emily Dickenson’s poetry; give her the memoirs of physicist Richard Feynman. That seems a sensible idea, if not terribly startling. But this will take you only so far, much like trying to appeal to a student’s individual interests, a point taken up in Chapter One.
(See pages 122-125 in the book for a more detailed discussion of the history and evidence related to these issues.)
Conclusions
Everyone can appreciate that students differ from one another. What can (or should) teachers do about that? One would hope we could use those differences to improve instruction, and researchers have suggested two basic methods, one based on difference in cognitive style. From this view, if one matches the method of instruction to the preferred cognitive style of the child, learning presumably will occur more easily. Unfortunately, no one has described a set of styles based on good evidence.
We find the second way that teachers might take advantage of differences among students rooted in differences in abilities. If a student lacks in one cognitive ability, presumably one could use a cognitive strength to make up for or at least bolster the cognitive weakness. Unfortunately, good evidence suggests that this sort of substitution does not occur. To state the situation clearly, students definitely do differ in their cognitive abilities; the error lies in the substitution idea.
Classroom implications
We do not suggest here that teachers should not differentiate instruction. We hope that they will. But when they do, they should know that scientists cannot offer any help. It would prove wonderful if scientists had identified categories of students along with varieties of instruction best suited to each category, but after a great deal of effort, they have not found such types, and many researchers think that such types don’t exist. Teachers need to treat students differently on the basis of their experience with each student and remain alert for what works for that student. When differentiating among students, craft knowledge trumps science. That said, consider these positive thoughts for your classroom:
• Think in terms of content, not in terms of students. Learning style theories don’t help much when applied to students, but they may help when applied to content. Consider the visual-auditory-kinesthetic distinction. You might want students to experience material in one or another modality depending on what you want them to get out of the lesson; students should see a diagram of Fort Knox, they should hear the national anthem of Turkmenistan, and they should wear the cheche turban the Saharan tribes use to protect themselves from the sun and wind.
• Change grabs attention. Change during a lesson invigorates students and refocuses their attention. If the teacher has been doing a lot of talking, something visual (a video or a map) offers a welcome change. If the students’ work has demanded a lot of logical, deductive thinking, perhaps they should do another task that calls for thoughtful, measured responses. Rather than individualizing the required mental processes for each student, give all of them practice in all of these processes, and view the transitions as an opportunity for each student to start fresh and refocus their mental energies.
• We can value all children, even if they don’t seem “smart in some way”. You have probably heard someone say, “Every student is intelligent in some way,” or ask students to identify “What kind of smart are you?” Teachers probably say this in an effort to communicate an egalitarian attitude to students: everyone can do something well. But we should feel leery of this attitude for a couple of reasons. First, it implies that intelligence brings value—and that a lack of intelligence means less or no value. But every person exists uniquely, and no one knows enough to judge the global value or worth of any person in the universe, whether intelligent or not. One would have to know all things in order to make such a judgment.
Second, it does not necessarily hold true that every child has some kind of intelligence. The exact percentage of children classified as “smart” would depend on how many intelligences you define and whether “smart” means “top 10 percent” or “top 50 percent”, and so on. It doesn’t really matter much—you will always have some kids not especially gifted in any of the intelligences thus classified. Certainly, telling kids that they have a skill they don’t possess seldom works. (If you briefly fool a child, their peers will usually happily bring reality crashing down on their head.)
Third, it never helps to tell a child that they “are smart”. Doing so makes them less smart. Really. (See Question 8 below.)
• Don’t worry—and save your money. If you have felt nagging guilt that you have not evaluated each of your students to assess their cognitive style, or if you think you know their styles and have not adjusted your teaching to them, don’t worry about it. We have no reason to think that doing these things will help. And if you thought of buying a book or inviting someone in for a professional development session on one of these topics, save your money.
If “cognitive styles” and “multiple intelligences” don’t help to characterize how children differ, what might work better? Why do some children seem to breeze through mathematics while other struggle? Why do some children love history, or geography? Background knowledge serves as an important determinant of what we find interesting; for example, problems or puzzles that seem difficult but not impossible pique our interest. Background knowledge serves as an important determinant of our success in school. Cognitive processes such as analyzing, synthesizing, and critiquing cannot operate alone. They need background knowledge to make them work.
Still, background knowledge does not account for all differences between students. Evidence supports the idea that some students simply think and behave in cleaver ways. The next section relates to how we can maximize the potential of all students regarding the degree of their cleverness.
Question 8: How can we optimize school for students who don’t have the raw intelligence that other students have?
Answer: Westerners tend to view intelligence as a fixed, unchangeable attribute. But if a student fails a test or does not understand a concept, neither we nor they should conclude that they cannot learn the material. They just have not worked hard enough yet. This attribution helps students because it tells students that they have control over their intelligence. No doubt exists that one can change intelligence. [Note how this relates to Martin Seligman’s learned helplessness theory.]
Critical principle 8: Children do differ in intelligence and sustained, hard work can change intelligence.
What do we mean by intelligence? Although we might make many finer distinctions, the overall idea that some people reason well and catch on to new ideas quickly captures most of what we mean when we say “intelligence”. We should note two things about this definition. First, it does not include abilities in music, athletics, or other fields that Gardner included in his theory of multiple intelligences. As described in chapter seven, most researchers consider those abilities just as important as those considered aspects of intelligence, but calling them intelligences rather than talents muddies the waters of communication and does not advance the science. Second, the definition actually seems to include just one intelligence referred to as g (for general).
No one knows exactly what g consists of. People suggest that it might relate to speed or the capacity of working memory, or even that it reflects how quickly the neurons in our brain fire. Knowing what underlies g does not prove important for our purposes; it does have importance to know the reality of g, which tends to predict success in school.
What makes people intelligent?
At this point, the importance of hard work and practice to cognitive task expertise should have become clear. Perhaps people we consider intelligent have had lots of practice (probably from a very young age) doing the kinds of tasks that define intelligence. Perhaps for whatever reasons they have received exposure to lots of complex ideas and explanations of those ideas, have had many opportunities to reason in a supportive environment, and so on.
The other main view involves the idea that intelligence comes genetically from one’s parents. According to this view, some people come into the world smart and although they might further develop this ability through practice, they will remain pretty smart even if they do little or nothing to develop their intelligence.
At this point we have two possible answers to the question Where does intelligence come from? and both answers fall at extreme ends of the possibilities: all nature (genetics) or all nurture (experience). Whenever people raise the question, Does nature or nurture account for intelligence? the answer usually boils down to both, almost always with the difficulty of specifying more specifically how genes and experiences interact. But a significant shift in researchers’ points of view has occurred in the last twenty years. It has moved from thinking “both, but probably mostly genetic” to “both, but probably mostly environmental”.
Why might the effects of genetics actually prove fairly modest? Because of past misattribution to genetics. It may often work like this: The genetic effects often look large because the effect of genetics involves making a person likely to seek out particular environments. For example, suppose identical twins get separated at birth and adopted into different families. Their genes make them unusually tall at a young age, and they continue to grow. Because each twin has unusually great height, each tends to do well in informal basketball games around the neighborhood. For that reason, each asks their parents to put up a net at home. The skills of each naturally improve with practice, and each gets recruited for their junior high basketball team. More practice leads to still better knowledge and skill, and by the end of high school each twin plays quite well—not a future professional, perhaps, but still better than 98 percent of the population, let’s say.
Notice what has happened. As identical twins raised apart, if a researcher tracked them down and administered a basketball skill test, they would find both quite good, and because they did not get raised together the researcher would probably conclude, wrongly, that this demonstrates a genetic effect. But their genes made them tall, not good at basketball. Having great height then nudged them toward environments that included a lot of basketball practice from an early age. Practice—an environmental effect—made them good at basketball, not their genes. Genetic effects can make you seek out or select different environments with different practice contingencies.
Now think of how this might apply to intelligence. Maybe genetics has had some small effect on your intelligence. Maybe it has made you slightly quicker to understand things, or made your memory a little bit better, or made you more persistent on cognitive tasks, or simply made you more curious. Your parents or other important people in your environment noticed this and encouraged your interest. They may not have even had any awareness of their encouraging you. They might have talked to you more, or about more interesting subjects, or read to you more, or used a broader vocabulary. Over time as you got older, you saw yourself more and more as one of the “smart kids”. You made friends with other smart kinds, and entered into friendly but quite real competition for the highest grades. Then too, maybe genetics subtly pushed you away from other endeavors. You may have done things a little more slowly or clumsily physically than others. That encouraged you to avoid situations that might develop your athletic skills (such as pickup basketball games) and instead stay inside and read (which would strongly practice vocabulary, intellectual focusing, and reasoning skills).
The key idea here involves the fact that genetics and the environment interact. Small differences in genetic inheritance can steer people to seek different experiences in their environments, and these differences in environmental experiences, especially over the long term, have large cognitive consequences. For this reason, we should not assume that twins raised in different households have experienced significantly different environments. The fact that they have the same genes may well have encouraged them to seek out environments similar in important ways.
How does all of this matter? Because how we treat students, and what they think of themselves, depends on how we and they understand about the nature of intelligence. If intelligence consisted mainly of a matter of one’s genetic inheritance, then not much point would exist in trying to make kids smarter. In that case, we would try to get students to do the best they could given the genetically determined intelligence they have. We’d also think seriously about trying to steer the not-so-smart kids toward intellectually undemanding tracks in schools, figuring they have a destiny for low-level jobs anyway. But intelligence does not work that way. Intelligence has malleability. It can improve.
Great! So how do we improve intelligence and skills? The first step involves convincing our students that they can improve their intelligence.
How beliefs about intelligence matter
Consider two hypothetical students. Felicia seems very concerned about whether she appears intelligent. When given a choice of tasks, she picks the easiest one to make sure that she succeeds. When confronted with a challenging task, she quits after the first setback, usually protesting loudly that she feels tired, or offering some other excuse. Molly, in contrast, doesn’t seem bothered by failure. Given a choice, she picks tasks new to her and seems to enjoy learning from them, even if she finds them frustrating. When she finds a task difficult, Molly doesn’t withdraw, she persists, trying a new strategy.
What accounts for the differences between the Mollys and Felicias in classrooms? Of course, many factors come into play, but one important one involves what they believe about intelligence. Students like Felicia may consider intelligence fixed, determined at birth; and because it cannot change, she feels very concerned that she get the “right label”, so she picks easy tasks. Or she may believe that the system has pigeon-holed her as “dumb”, so she sees no point in trying any more. Felicia’s beliefs about intelligence really paint her into a corner. She may think that smart people don’t have to work hard to succeed—they succeed through their superior intelligence. Therefore she sees working hard as a sign of “being dumb”. Thus, even though she may consider it important to appear smart, she won’t allow herself to work hard to make sure she succeeds because she thinks hard work makes her look dumb!
Molly, conversely, views intelligence as changeable. She thinks she gets smarter by learning new things. Thus, she does not find failure nearly so threatening, because she doesn’t believe it says anything permanent about her abilities. When Molly fails, she figures she didn’t work hard enough, hasn’t developed the needed skills, or hasn’t learned about this particular topic yet. Thus, Molly thinks she has control of her success or failure because she can always work harder if she fails. Molly sees nothing embarrassing in admitting ignorance or in getting a wrong answer. Therefore she has no motivation to pick easy tasks; instead will more likely pick challenging tasks, because she might learn from them. Molly also does not consider working hard a sign of stupidity—on the contrary, she considers hard work a sign of one trying to get smarter.
It looks like Molly will much more likely succeed in school, compared with Felicia, and good evidence suggests the truth of that. Students who believe that they can improve their intelligence with hard work get higher grades than students who believe that intelligence remains an unchangeable trait.
Any teacher would rather have a room full of Mollys than a room full of Felicias. Where do students get their ideas about intelligence and ability? Children’s understandings of intelligence have different aspects. Many factors contribute, but we have studied one factor in particular: how we praise children.
In a classic study on the effect of praise, the experimenters asked fifth graders to work on some problems in which they needed to find patterns among visual figures. The children would solve most of the first set of easy problems. The experimenters praised their success, telling them, “Wow, you did very well on these problems. You got (x number of problems) right. You got a really high score.” They told some, “You must be smart at these problems.” In other words, they praised these students for their ability. They told others, “You must have worked hard at these problems,” thus these students received praise for their effort. A different experimenter then interviewed each student to learn what the students thought about intelligence. The results showed that those who had received praise for their ability (“you’re smart”) were more likely to describe a fixed view of intelligence than those praised for their effort (“you worked hard”), who more often described a changeable view of intelligence. Many studies have shown similar effects, including studies of children as young as four years old.
Naturally a single experience with an experimenter whom a child doesn’t know will not shape their beliefs about intelligence forever, but a minor difference in praise—making it about ability or effort—did affect these children’s beliefs at least for the duration of the experiment. One can reasonably guess that what they hear from parents, teachers, and peers, and by how they see these people act, shape students’ beliefs for the long term.
What seems especially interesting about this work involves its concern with praise. How can it hurt to tell a student that they “are smart”? By praising a child’s intelligence, we let them know that they solved the problems correctly because they “are smart”, not because they worked hard. Then, the student can easily conclude that getting problems wrong serves as a sign of their “being dumb”. They tend to lose the connection between persistent, hard work and success.
Classroom implications
Slow students have the same potential as bright students, but they probably differ in what they know, in their motivation, in their persistence in the face of academic setbacks, and in their self-image as students. These students potentially can catch up, but one must acknowledge their position (far behind), and that catching up will take enormous effort. How can we help? To help slow learners catch up, we must first assure that they believe that they can improve; next we must persuade them that doing that work will pay off in ways worthwhile to them.
• Praise effort, not ability. Encourage your students to think of their intelligence as under their control, and especially that they can develop their intelligence through hard work. Therefore, you should praise process rather than ability. In addition to praising effort (if appropriate), you might praise a student for persistence in the face of challenges, or for taking responsibility for their work. Avoid insincere praise, however. Dishonest praise produces destructive results. If you tell a student, “Wow, you really worked hard on this project!” when the student knows good and well that they didn’t, you lose credibility as well as encouraging the student unrealistically to expect positive consequences for little work.
• Tell them that hard work pays off. Praising process rather than ability sends the unspoken message that the student has control of their intelligence. You can make this message explicit as well. Tell your students how hard famous scientists, inventors, authors, and other “geniuses” must work in order to “be smart”; but even more important, make that lesson apply to the work your students do. If some students in your school brag about not studying, explode that myth; tell them that most students who do well in school work at all levels work quite hard. In the world of work, most people who do well work hard.
You may not find it easy to persuade some students of this. A student on the football team and devotes a great deal of time to practice and little time to academics may attribute his poor grades to “I’m just a dumb jock.” Ask if the team (band, choir, etc.) has players with a lot of natural ability, but who just don’t work very hard. (Yes.) Ask if the other players respect players like this. (Of course not. They think these people idiots because they have talent they are not developing.) Don’t they respect these players because they are the best? (They are not the best. They are good, but lots of other people are better.) Academics works the same way. Most people have to work really hard at it. A few can get by without working very hard, but not many. And few people like or respect them very much. [Herein lies perhaps the biggest problem we face: a massive culture that deeply believes, “I should not have to do any academic work, and I will not.” Actually, this ends up helping those willing to work by greatly reducing the competition for colleges and jobs!]
• Treat failure as a natural part of learning. If you want to increase your knowledge, skills and intelligence, you have to challenge yourself. That means taking on tasks a bit beyond your reach—and that means you may very well fail sometimes, at least the first time around. Fear of failure can become a significant obstacle to tackling this sort of challenging work. We need to learn to consider this kind of failure as natural and not a big deal. When we do something stupid, we need to remember that “The only people who don’t make mistakes are the ones who never do anything.” To get things done, you have to learn to accept mistakes and failure. Michael Jordan put it this way: “I’ve missed more than nine thousand shots in my career. I’ve lost almost three hundred games. Twenty-six times I’ve been trusted to take the game-winning shot and missed. I’ve failed over and over and over again in my life. And that is why I succeed.” (He keeps working at it despite the failures!) [See Learned Helplessness y Peterson, Maier and Seligman re: this.]
Create a classroom atmosphere in which you and students consider failure, while not desirable, neither embarrassing nor wholly negative. Failure means you will soon learn something. You will find out something you did not understand of didn’t know how to do. Most important teachers need to model this attitude with their words and behaviors for their students. When you fail—and who doesn’t?—let them see you take a positive, learning attitude.
• Value study skills. Make a list of all of the things that you ask students to do at home. Consider which of these things have other tasks embedded in them and ask yourself whether the slower students really know how to do them. For older students, if you announce a quiz you assume that they will study for it. Do your older students really know how to study? Do they know how to assess the importance of different things they’ve read, heard and seen? Do your slower students know some simple tricks to help with planning and organizing their time? Do they know how long they should study for a test? (They probably need to study much longer than they think. At the college level, low-performing students often protest their low grades by saying, “But I studied for three or four hours for this test!” Meanwhile, the high-scoring students study about twenty hours, five or six times longer. [These students don’t just develop familiarity with the material. They actually practice it in order to develop automatic thinking processes that free working memory to do other, higher level tasks.]
These concerns prove especially important for students just starting to receive serious homework assignments—probably around the seventh grade. A period of adjustment occurs for most students when homework involves more than “bring in three rocks from you yard or the park”, turning into “read Chapter Four and answer the even numbered questions at the back.” All students must learn new skills as homework becomes more demanding—emotional skills of self-discipline, time management, and resourcefulness (for example, knowing what to do when they feel stumped). Students already behind will have that much more trouble doing work on their own at home, and they may learn these skills more slowly. Do not take for granted that your students have these skills, even if you believe that they should have acquired them in previous grades.
• The long-term goal involves catching up. You need to think realistically about what it will take for students to catch up. The more we know, the easier we find it to learn new things; the less we know, the harder. Thus, if your slower students know less than your brighter students, they simply can’t work at the same pace as the more knowledgeable students; doing only that, they will continue to fall behind! To catch up, the slower students must work harder than the brighter. [But many of them do not have the emotional skills for working harder on academic tasks. Asking them to do anything academically that they don’t especially feel like doing at the moment asks way too much. In many cases, asking them to use common social courtesy skills, such as talking one-at-a-time, asks too much. In that case, you need to teach the needed social and emotional skills.]
You might think of this situation as analogous to dieting. People usually find it overwhelmingly difficult to maintain their willpower for the extended period necessary to reach a target weight. The problem with diets involves their requiring people to make difficult choices again and again, and each time we make the best choice we don’t get rewarded with the instant weight loss that we believe we deserve! So, when a dieter makes a wrong choice or two, they have a tendency to consider their self a failure, and then to give up the diet altogether. A great deal of research shows that the most successful diets do not fall under the popularly understood definition of diet. Rather, they involve lifestyle changes that the person strongly believes they can live with every day for the years, for the rest of their life—for example, switching from regular milk to skim milk, or from dairy mild to soy milk, or walking the dog instead of just letting it out in the morning, or regularly drinking black coffee instead of lattes.
When thinking about helping slower students catch up, it will probably work best to set interim achievable, concrete goals. These goals might include such strategies as devoting a fixed time every day to homework, reading a weekly news magazine, or watching one educational DVD on science each week. Needless to say, enlisting parents in such efforts, if possible, will help enormously.
• Show students that you have confidence in them. If you ask people “Who was the most important teacher in your life?” most people have a ready answer. Interestingly, the reason that one teacher made a strong impression almost always relates to emotions. People never give reasons like “She taught me a lot of math.” Instead, people say things like “She helped me believe in myself” or “He taught me to love knowledge.” In addition, people consistently say that their most important teacher set high standards and believed that the student could meet those standards.
Communicating that confidence to your students involves praise: probably the least expensive, most common, most practical and arguably the most powerful reinforcer. Feel wary of praising second-rate work in your slower students. Suppose you have a student who usually fails to complete their work. Then, they manage to submit a project on time, although not done very well. You may feel tempted to praise the student—after all, submitting something on time improves over the past performance. But consider the message that praising a mediocre project sends. You say “good job”, but it really means “Good job for someone like you.” The student probably does not have so much naivety to really consider the project all that great. By globally praising substandard work, you send the message that you have lower expectations for this student. It will work much better to say, “I appreciate that you finished the project on time. Good work there! And I thought that you had an interesting opening paragraph. I also think that you could have done a better job of organizing it. Let’s talk about how you could do that.”
Question 9: What about the teacher’s thinking?
Answer: The teacher’s thinking works in the same ways that the students’ do.
Critical principle 9: Like any complex cognitive skill, we must consciously practice it to improve it.
Teaching involves cognitive skills and to think effectively we need sufficient room in working memory, which has limited space. We also need the right factual and procedural knowledge in long-term memory. Let’s consider how this relates to teaching.
Teaching as a cognitive skill
Teaching places great demands on working memory. It seems just as evident that factual knowledge proves important to teaching. Similarly, pedagogical content knowledge proves important. For a teacher, just knowing algebra really well does not prove sufficient. You have to have knowledge particular to teaching algebra. If pedagogical content knowledge did not have importance, then anyone who understood algebra could teach it well, and we know that it does not work that way.
OK, if teaching works as a cognitive skill just like any other, how can you apply what you’ve learned here to your teaching? How can you increase (1) space in working memory, (2) your relevant factual knowledge, and (3) your relevant procedural knowledge? Recall from Chapter Five It proves virtually impossible to become proficient at a mental task without extended, focused practice. Your best bet for improving your teaching involves practicing teaching.
The importance of practice
Practice and experience do not amount to the same thing. Getting experience means you have simply engaged in the activity. Practice refers to trying to improve your performance. For example, even though a person may have driven to 30 years, they may not be a very good or safe driver. They may have done a lot of driving—but not a lot of practice, working to get better at driving. This commonly happens. People get “good enough” at a skill and then stop trying to improve. Perhaps you know someone who speaks English as a second language, and even though they have lived here for 30 years they still speak English so badly that others have great difficulty understanding them. They speak it well enough to get by, but no better.
The same principle holds true for teachers. A great deal of data show that teachers improve during their first five years in the field, as measured by student learning. After five years, however, the curve goes flat, and a teacher with twenty years experience teaches, on average, no better or worse than a teacher with ten. It appears that most teachers work on their teaching until it moves above some threshold and they feel satisfied with their proficiency. One can easily criticize such teachers and think indignantly, “They should always strive to improve!” Certainly we would all like to think that we always seek to better ourselves, but we also need to think realistically. Practice takes much time and energy. It takes a great deal of work, and very likely work that infringes on time that one might spend with family or in other pursuits. But if you have read this far, you probably have yourself prepared to do some hard work.
First, we need to define practice. Practice involves more than just engaging in the activity; you have to work at improving. First, practice involves getting feedback from knowledgeable people. Without feedback, you don’t know what changes will make you a better golfer, dancer or teacher.
Yes, teachers get feedback from their students. You can tell if they do well or poorly, but that sort of feedback does not give sufficient specificity. For example, you student’s bored expressions tell you about listening issues, but they don’t tell you what you might do differently. Also, you probably miss more going on in your classroom than you think you do. As you busily teach, you don’t have the luxury of simply watching and reflecting on what you see happening. Also, you cannot impartially observe your own behavior. Though some of us see ourselves in a harsher light than appropriate, most of us interpret our world in a way that makes us look favorable to ourselves. (Social psychologists call this the self-serving bias. When things go well, it happens because of our skills and hard work. When things go poorly, bad luck caused it, or someone else made a mistake.) For these reasons, it usually helps greatly to see your class through someone else’s eyes.
In addition to requiring feedback, practice usually means investing time in activities not directly involved with the target task, but done for the sake of improving that task. For example, aspiring chess players don’t just play lots of chess games. They also spend considerable time studying and memorizing chess openings and analyzing the matches that other experts have played. Athletes of all sorts do weight and cardiovascular training to improve their endurance in their sport.
To summarize, if you want to get better as a teacher, you cannot feel satisfied simply to gain experience as the years pass. You must also practice, and practice means: (1) consciously working at improvement, (2) seeking feedback on your teaching, and (3) undertaking activities for the sake of improvement, even if they don’t directly contribute to your job. Of course, you could do these things in lots of ways. The next section describes one method.
A method for getting and getting feedback
1) Identify a teacher (or two) with whom you would like to work
2) Video tape yourself and watch the tapes alone
3) With your partner, watch the tapes of other teachers
4) With your partner, watch and comment on each other’s tapes
5) Bring it back to the classroom and follow up
(See pages 152-156 in the book for details.)
Consciously working at improving: self-management
We can easily resolve to do something. Following through proves much more difficult. Planning and scheduling needed activities on your calendar will probably help greatly in getting you out of your autopilot mode. Remember that you don’t need to do everything at once. You cannot realistically expect to go from your present level to “great” in a year or two. Set priorities. Think in terms of the long term and decide on what you most importantly need to work on, then set and focus on concrete, manageable steps to move you toward your goal over time.
Smaller steps
The video tape program laid out takes much time. You can start smaller. Here you find some ways you can work on your teaching that take less time.
• Keep a teaching diary or journal. Make notes that include what you intended to do and how it actually went. Did the lesson basically work? If not, what thoughts do you have about it? What changes do you need to make? By keeping these notes with the lesson, you can quickly and easily review them before you do the lesson again. However you manage your notes, take a little time to read past entries. Look for patterns in the kinds of lessons that went well and which didn’t. Look for situations that frustrated you, for moments of teaching that really keep you going, and so on.
A lot of people start a diary or journal and then find it difficult to stick with it. A few tips might help. First, find a time of day when you can write, making it a time you will likely maintain. (For example, a morning person might find writing just before bed would not work well at all.) Making notes during and/or immediately after the lesson—and then keeping the notes with the lesson—may work well. Getting into the habit of writing something each day (or each lesson), even if only “Today was an average day” will surely help. Do think in terms of developing a regular habit, but avoid thinking in all-or-none terms about the amount of time or length. The consistency of pulling out the dairy or journal and writing something will help make it a habit. An excellent rule of thumb suggests that if you will do something consistently with no exceptions for three weeks, you will have developed an automatic habit that you will no longer need to think about. Marking it on your calendar, especially for the first three weeks, will probably help greatly. On the other hand, remember that you do this solely for you. Don’t worry about the quality of the writing, don’t feel guilty if you don’t write much, and don’t beat yourself up if you miss days, or even weeks. If you do miss some time, don’t try to catch up. You will never remember all that happened and the thought of all that work will tend to stop you from starting again. Finally, criticize and praise yourself honestly; do feel free to dwell on moments that you feel proud about!
• Start a discussion group with fellow teachers. Get a group of teachers together for meetings, say, once every two weeks. Make one purpose to give and receive social support. You can grumble about problems, share successes, and so forth. Then one of your goals involves feeling connected and supported. Another purpose, certainly not completely independent of the first, can relate to using the meetings as a forum to bring up problems you have and get ideas for solutions from the group. It will probably help greatly to decide clearly from the start as a group whether you want your group to serve only the first function, only the second, or both. If different people have different ideas about the purpose, hurt feelings will more likely occur. If especially goal oriented, everyone might read a journal article or book for discussion.
• Observe. What makes students in your age group tick? What motivates them? How do they talk to one another? What passions do they have? You probably know your students pretty well in the classroom, but do you think your students “are themselves” when in your classroom? Would you find it useful to see them acting in ways not contrived for the classroom or when surrounded by a different group of children?
Find a location where you can observe children in the age group you teach. To observe preschoolers, go to a park; to watch teenagers, go to the food court at the mall. You will probably have to go to a different neighborhood or even a different town, because this exercise won’t work if they recognize you. Just watch the kids. Don’t go with a specific plan or agenda. Just watch. Initially, you will probably get bored. You’ll think, “Right. I’ve seen this before.” But if you keep watching, really watching, you will start to notice things you hadn’t noticed before. You’ll notice more subtle cues about social interactions, aspects of personality, and how students think. Allow yourself the time and space simply to observe , and you will see remarkable—and useful—things.
(Summary table on last page.)
Summary Table
(You may find that it works best to read this table vertically from top to bottom under each heading.)
| |Cognitive principles |Required knowledge about students |Most important classroom implications |
|1 |People naturally have curiosity, but |What lies just beyond what my students |Take the time necessary to develop the questions that lead to |
| |they do not naturally think well. |know and can do? |the material-to-learn as well as the answers. This develops |
| | | |and maintains interest, curiosity, and motivation. |
|2 |Factual knowledge precedes skill. |What do my students know about this topic?|One cannot possibly think well on a topic in the absence of |
| | | |factual knowledge about the topic. |
|3 |Memory exists as the residue of |What will my students really think about |What serves as the best barometer of every lesson plan? The |
| |thought. |during this lesson? |answer to this question: “What will my students actually think|
| | | |about with this lesson plan.” |
|4 |We understand new things in the context|What do my students already know that will|Always make deep knowledge your spoken and unspoken goal, but |
| |of things we already know. |serve as a toehold in understanding this |recognize that shallow knowledge will come first. |
| | |new material? | |
|5 |Proficiency requires conscious, focused|How can I get students to practice this |Think carefully and selectively about which specific material |
| |practice. (Not just repetition.) |without getting bored? |students really need at their fingertips. Have them practice |
| | | |that often and over a long period of time. |
|6 |Cognition differs fundamentally early |How do my students differ from experts? |Strive for deep understanding in your students, not their |
| |in training compared with late. | |creating new knowledge. |
|7 |Children have more similarities than |We do not need knowledge of students’ |Let lesson content drive decisions about how to teach, not |
| |differences in learning. |learning styles. |student differences. |
|8 |Intelligence can change through |What do my students believe about |Always talk about successes and failures in terms of effort, |
| |sustained, hard work. |intelligence? Do they know that effort |not ability. |
| | |changes intelligence and that effort | |
| | |predicts success much better than | |
| | |intelligence does? | |
|9 |Like any complex cognitive skill, one |What aspects of my teaching work well for |Improvement requires more than just experience; it also |
| |must consciously practice teaching in |my students, and what parts need |requires conscious effort and feedback. |
| |order to improve it. |improvement? | |
-----------------------
Long-Term Memory
(factual and procedural knowledge)
Working Memory
(site of awareness and thinking)
Environment
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