University of North Carolina Wilmington



How to Teach Abstract or Higher-order Concept Knowledge

Martin Kozloff

2012

We’re going to teach kids abstract or higher-order concepts. A procedure that’s effective (that is, most kids learn from it) and efficient (that is, most kids learn fast and with hardly any mistakes) is pretty simple. But to design an effective and efficient procedure, you have to know the following.

What We Need to Know

1. What an abstract or higher-order concept is. (Kame’enui and Simmons, 1990).

2. How teaching the identified abstract concept fits in your curriculum.

3. What lessons look like.

4. We are working on the first phase of learning and teaching---the acquisition of knowledge—using explicit instruction. After acquisition, we will work on generalization to new examples, fluency, and integration of knowledge elements (e.g., concepts) into larger wholes, such as essays.

5. We must decide when to teach a concept with a synonym and examples, and when to teach a concept with a verbal definition and examples.

1. What an abstract or higher-order concept is.

There are two kinds of concepts: basic or sensory concepts and abstract or higher-order concepts (Kame’enui and Simmons, 1990). The thing about sensory concepts is that:

a. Their defining features (the sameness in certain features in all examples) are tangible; you can see, hear, smell, feel, or taste the features; and

b. Any example shows all of the defining features; the features are all right there in front of your face or ears or nose.

So, you can teach basic concepts just by showing and naming examples. “This is a triangle.” Or, “This is red.” Or, “This is straight.” And then you show contrasting examples (“This is red.”) with nonexamples (This is NOT red) that are the same in NONdefining features, but are DIFFERENT in the DEFINING features.

“This is red.” “This is not red.”

(1) Same in nondefining features: size, shape. (2) Named differently (red, not red). (3) So, the way they are the same logically CAN’T be why they are named differently. (4) Different in defining feature (color). (5) So, logically, the way they are different (color) MAKES the difference in how they are named.

However, with abstract concepts,

a. Some defining features are NOT tangible; they are themselves abstract; you can’t directly see, hear, smell, or feel then.

b. Each example may not show all of the defining features. For instance, any example of red (a basic concept) will show THE defining feature---redness. But every example of democracy (an abstract concept) may not show all the defining features at once.

For example, voting is a defining feature of democratic political systems (the concept). You might show an example of Athens in the fifth century BC (a democracy), but Athenians were NOT having a vote at the time. Maybe they were at war. So, basically, you can’t bring an example of an abstract concept into class and say, “Here’s (a democracy, a forest, a galaxy, plate tectonics, volcano).

Instead, to teach an abstract concept you have to either:

a. Give a synonym (a more common word) that means the same thing as the

new concept.

b. Give a verbal definition that TELLS the defining features. And then show examples that ALL

have the defining features (and call them the same thing---“This is a democracy.”) and

contrasting NONexamples that do NOT have the defining features (and call them

something different from the examples---“This is NOT a democracy”).

2. How teaching the identified abstract concept fits in your curriculum.

Your state’s and district’s standard course of study, scientific research, expert opinion, and your own expertise will help you to establish objectives (what students will DO) for a whole year or course. For instance, among many other objectives in a science curriculum,

“Students will:

a. Define ecosystem, desert, rainforest, ocean, and salt marsh.

b. Correctly identify examples and nonexamples of ecosystems, deserts, rainforests, ocean

and salt marshes.

c. Make a diagram of a model, with verbal explanation, of threats to salt marsh

ecosystems, and how salt marsh ecosystems deteriorate.

These final objectives will help you establish objectives for units, and unit objectives will help you establish objectives for each lesson. For instance, given the final science curriculum objectives, the UNIT on ecosystems, and therefore LESSONS in the unit, will have to teach the concepts identified above. It will also have to teach concepts such as convection cells, equilibrium, feedback loop, and acceleration.

3. What lessons look like. A lesson is a sequence of tasks.

a. Review and firm what was taught earlier; e.g., system, natural system, elements and

wholes, boundaries.

b. Teach new item; e.g., the concept, ecosystem. Model( lead ( test( correct errors or

verify correct answers.

c. Teach more.

d. Review and firm it all.

e. Integrate earlier and new knowledge into something larger, if possible; e.g., a diagram

of a model of ecosystem.

4. We are working on the first phase of learning and teaching---the acquisition of knowledge. We will use explicit instruction to ensure that most kids “get it” quickly and with few errors.

After acquisition, we will work on generalization to new examples and integration of knowledge elements into larger wholes. For examples, students might use earlier and new concepts and rules to diagram and describe relationships among parts of a salt marsh ecosystem.

5. When to teach a concept with a synonym and examples, and when to teach a concept with

a verbal definition and examples.

a. Use synonyms to teach concepts that are defined by FEW features, and so you can give the synonym definition quickly. For example, huge (very big), unalienable right (part of being human, can’t be taken away), monarchy (rule by one person).

b. Use verbal definitions plus examples and nonexamples to teach concepts that are defined by many features, and when these features are themselves NOT tangible objects. Political system, economics, galaxy, nebula, justice, democracy. These have so many features that you can’t find a synonym (one or two words) that means the same thing. You’d have to give a verbal definition that TELLS the features, followed by examples that SHOW the features.

Let’s see when she could use synonyms and when we should use verbal definitions plus examples. Here’s an introduction to solar systems from a science for kids website. Some words (concepts) can be defined with synonyms WHILE you and/or students read it. Other concepts are more complex, and are so important, that you would PRE-TEACH these with verbal definitions and examples. I’ve added synonyms, [in italicized brackets] below, as if I we reading the document to students for the first time. I’ve put in bold face concepts that I would pre-teach.

How did the solar system form? This is an important question, and one that is difficult for scientists to understand. After all, the creation of our Solar System took place billions of years before there were any people around to witness it. Our own evolution [changes over time in our species] is tied closely to the evolution of the Solar System. Thus, without understanding from where the Solar System came from, it is difficult to comprehend [understand] how mankind came to be. Scientists believe that the Solar System evolved [develop] from a giant cloud of dust and gas. They believe that this dust and gas began to collapse [parts got closer and closer, like squeezing a piece of paper into a small ball] under the weight of its own gravity. As it did so, the matter contained within this could begin moving in a giant circle, much like the water in a drain moves around the center of the drain in a circle.

At the center of this spinning cloud, a small star began to form. This star grew larger and larger as it collected more and more of the dust and gas that collapsed into it.

Further away from the center of this mass where the star was forming, there were smaller clumps of dust and gas that were also collapsing. The star in the center eventually ignited [caught flame] forming our Sun, while the smaller clumps became the planets, minor planets, moons, comets, and asteroids.

Once ignited, the Sun's powerful solar winds began to blow. These winds, which are made up of atomic particles being blown outward from the Sun, slowly pushed the remaining gas and dust out of the Solar System.

So, before we start reading or teaching from the document, we would teach the concepts: solar system, billions of years, gravity, matter, star, planets, minor planets, moons, comets, asteroids.

solar winds, atomic particles.

1. We would teach some of these concepts (atomic particle, billions, gravity, matter) much earlier, perhaps near the beginning of the science strand in our curriculum, because these concepts apply to just about everything ON the strand. However,

2. We would teach solar system, star, planet, minor planet, moon, comet, asteroid, and solar wind only a few lessons earlier (and review up to the current lesson) because it is only NOW that these concepts are relevant.

And we would do this teaching by:

1. Giving a verbal definition.

2. Making sure students SAY that definition and define each main concept IN it.

3. Giving an acquisition set of examples that show the features identified in the definition, and

nonexamples that don’t have the features identified in the definition.

4. Testing students by asking them either: (a) whether each instance is or is not an example,

with a follow-up question (“How do you know?”) that requires students to USE the definition to judge each instance; and/or (b) to identify each instance. “Is this a monarchy?.... How do you know?”

Okay, let’s begin.

Teaching Higher-order Concepts with Synonym Definitions Followed by Examples

The easiest way to teach the definition of a higher-order concept is with SYNONYMS.

Huge means real big.

Equal means the same.

Ignorant means lacking knowledge.

Using synonyms is fine for concepts or vocabulary words used in everyday life. Or for getting through a novel.

“Hey, Joe, what’s obtuse mean?”

“It means a block head, like you.”

Here are examples of teaching higher order concepts with synonyms.

Teaching the Concept—Practice--with Synonyms

Student talk is in italics.

Gain attention and frame task

Boys and girls. Here’s a new word [point to word on board.] practice.

What’s our new word? practice.

Spell practice. p r a c t I c e

What word? practice.

Yes, practice!

Model. Practice means to do something over and over to get better.

Test. What does practice mean?... doing something over and over to get better.

Verification. You got it. Practice means doing something over and over to get better.

More models. He sings a song over and over to get better at singing. He practices singing.

She paints pictures over and over to get better at painting. She practices painting,

Test

She jumps rope over and over to get better at jumping rope. Tell me….she practices or not practices?... practices.

How do you know? She jumps rope over and over to get better.

Verification. Correct! To practice is to do something over and over to get better. And she jumps rope over and over to get better. So, she practices.

Test. They do NOT read books over and over to get better at reading. Tell me…they practice or not practice?... Not practice.

How do you know? Practice means to do something over and over to get better. They don’t do something over and over to get better. So, they don’t practice.

Verification.

Excellent! You said the definition of practice so you could tell if the kids practiced or did not practice reading!

Application

I’ll say a sentence with old words and then I’ll say that sentence with our new word.

She is writing her letters---a b c’s---over and over to get better and better at writing letters.

I’ll say that with our new word. She is PRACTICING writing her letters.

TEST. Your turn.

I’ll say a sentence with old words and then YOU’LL say that sentence with our new word.

He is riding his bike over and over to get better at riding his bike.

Say that with our new word?

He is practicing riding his bike.

Etc.

If you are reading stories with little kids, it’s easy to tell which words/concepts you could teach with synonyms. kitten = very young cat. garage = a building where you park cars. sofa = couch rodent = rats, mice

But some text will have some concepts that can be taught with synonyms and other concepts that should be taught with verbal definitions plus examples.

So, you have to decide when: (1) you can just give synonyms; versus (2) you need to give a more complete definition. Let’s practice.

Here’s the second paragraph of the Declaration of Independence. The objectives are:

1. Students will define a set of concepts (e.g., unalienable rights, just powers, consent of the

governed, despotism, and others); and

2. Students will identify the main rule statements, restate them as simple declarative

statements, and arrange these statements into the theory of representative

government. For example, this long sentence,…

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness…

…becomes this:

“All human beings are created equal.”

“All human beings have unalienable rights.”

“The unalienable rights if all human beings come from their Creator.”

“All human beings have the unalienable rights to life, liberty and the pursuit of happiness.”

Now, which concepts can be defined with synonyms WHILE you teach, and which should be defined EARLIER (pre-taught) with verbal definitions and examples? Which of these pre-taught concepts would you teach MUCH earlier because they are relevant throughout the course, and which could you teach a few days before you work on the declaration?

We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed.

That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

1. Which concepts could you teach with synonyms WHILE you and students reads the text? List

them.

2. Which concepts should you teach with verbal definitions and examples---BEFORE you work

on the text? Both:

a. Which should you teach MUCH earlier in the curriculum—because they are relevant to

most all of the curriculum? List them.

b. Which might you teach a few days earlier and then review before you started on the

Declaration? List them.

Here’s how I see it.

Let’s say you’re going to read the text it aloud while the class reads along. I would use [synonyms] to teach the concepts in brackets and italics WHILE we read the text. I would use verbal definitions to teach the concepts in bold face. I would teach some of these much earlier, because they are relevant throughout the curriculum, and I would teach others for a few days before we deal with the Declaration. Like this.

We hold these truths [rules of nature] to be self-evident [obvious to anyone], that all men [human beings] are created equal [equal in their rights], that they are endowed [provided, given] by their Creator [God] with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness [the right to pursue your own interests]. That to secure these rights, Governments are instituted among Men, deriving their just powers [not just plain power, but power that is considered just by the citizens] from the consent of the governed [rulers don’t take power; they are given power by those who consent TO be governed].

That whenever any Form of Government becomes destructive of these ends [to secure unalienable rights of the governed], it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles [rules of how the government will be organized and operated] and organizing its powers [such as different branches will have power to do different things, such as war and legislation] in such form, as to them shall seem most likely to effect their Safety and Happiness….But when a long train of abuses [acting against the unalienable right of the people]and usurpations [taking power not consenting to by the governed], pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.

So, I would teach the following concepts:

1. Rights, form of government (monarchy, aristocracy, democracy, republic), power, and

branches of government much earlier in the curriculum, and then review these right before

we worked on the Declaration. But I would teach the concepts

2. Declaration (as a form of argument), absolute despotism, and unalienable rights shortly

before working the document, because it is only NOW that they are relevant.

Whether much earlier or right before, I would concepts by:

1. Giving a verbal definition.

2. Making sure students SAY that definition and define each main concept IN it.

3. Giving an acquisition set of examples that show the features identified in the definition, and

nonexamples that don’t have the features identified in the definition.

4. Testing students by asking them either: (a) whether each instance is or is not an example,

with a follow-up question (“How do you know?”) that requires students to USE the definition

to judge each instance; and/or (b) to identify each instance. “Is this a monarchy?.... How do

you know?”

Okay, here are

The Basics Of Teaching Higher-Order Concepts With Verbal Definitions And Examples

What does a good verbal definition look like? Genus and difference. Here’s a VERBAL definition of the higher-order concept—constitutional republic.

A constitutional republic is a state where the head of state and other officials are representatives of the people and must govern according to existing constitutional law that limits the government's power over citizens.

The definition has two parts: genus and difference.

Genus. A constitutional republic is a STATE (a political relationship between government and citizens).

The genus is the larger category or concept in which constitutional republic in located. The genus tells you what KIND of thing something is and what KINDS of things it isn’t. A constitutional republic is not a society. Not a geographic thing, like mountains. And not anything that other species do. However, constitutional republics are not the only kind of (not the only member of the class of) states. Other kinds of states are monarchies, democracies, and aristocracies. So a full definition has to tell the difference between constitutional republic states and other kinds of states. This is the difference part of a verbal definition.

Difference. …. where the head of state and other officials are representatives of the people and must govern according to existing constitutional law that limits the government's power over citizens.

The difference part of the definition tells the difference between constitutional republics (as ONE example of state) and OTHER kids of states, such as monarchies, democracies, and aristocracies.

A diagram of the verbal definition looks like this.

Political states [largest category]

Constitutional republics

Monarchies

Aristocracies

Democracies

Particular, individual examples of democracies, aristocracies, etc., are INSIDE each smaller circle.

Note: There is no such thing as a true definition. Rather, some definitions are better than other definitions; they are better at directing attention to the right events. So, definitions are better when:

1. They state the genus and the difference.

2. The difference part of the definition contains enough descriptors (features of the

thing defined) that it can easily be distinguished from other kinds of things in the

class (genus).

Here’s a poor definition.

Dogs are canines (genus) with four legs (difference).

The genus part is okay. Dogs ARE in the class of canines---along with wolves, foxes, and coyotes. But the difference part is so skimpy that you can’t USE this definition to distinguish dogs (as canines) and foxes, wolves, and coyotes (as canines) because all of them have four legs.

Here’s another poor definition.

Monarchy is a form of government (genus) in which one person rules (difference).

Yes, monarchy IS a form of government (or state) in which one person rules, but the difference (one person rules) does not tell enough to distinguish monarchies and other forms of government in which one person rules. Dictatorships are also rule by one person. So, if a student reads about a dictatorship, the student might WRONGLY judge it to be a monarchy. So, the difference portion should include more features of monarchies (in contrast to dictatorships). Here’s a more descriptive definition.

A monarchy is a form of government (genus) in which supreme power is absolutely or nominally lodged with an individual, who is the head of state [by virtue of hereditary ascension], often for life or until abdication…The person who heads a monarchy is called a monarch (difference).

Now look at a good definition of dictatorship. It is good because it is useful---it enables you to distinguish monarchy (rule by one person) from dictatorship (also rule by one person).

A dictatorship is defined as an autocratic [one ruler. MK] form of government in which the government [means the same as “supreme power is absolutely or nominally lodged with an individual”] is ruled by an individual, the dictator, without hereditary ascension.

3. All of the words have clear meaning; that is, the words in the definition clearly point to the events named.

Poor definitions.

A donut is a kind of pastry that is shaped like a donut. [Yes, but what is a

donut shaped like?]

Fear is an emotion that involves being afraid. [Fear and afraid mean the same

thing. So, the definition is just saying Fear is an emotion at involves fear.]

Here’s an example. Student talk is in italics.

Procedure for Teaching Higher-order Concept: Simile

Set up

1. Objective

The teacher presents examples and nonexamples of simile and asks, “Is this a simile?” When students answer, the teacher asks, “How do you know?” Students correctly identify similes and nonsimiles, and use the definition to explain their answer.

2. Frame.

Teacher. “New figure of speech. Simile. [writes on board.]

Spell simile.”

Class. s i m i l e .

Teacher. “What word?”

Class. s i m i l e .

Teacher. “Write it in your notebooks.” [Check to make sure they do this.]

Focused Instruction

3. Model—lead—test/check.

Teacher. “Listen. A simile is a figure of speech [genus] in which two unlike things are compared, using the words like or as [difference between similes, as figures of speech, and other figures of speech, such as metaphors.]” [Model]

The larger class [genus] of figures of speech

The class of metaphors. “His temper is volcanic.”

The class of similes. “His temper is like a volcano.”

The class of hyperbole. “His breath comes straight from

hell.”

Teacher. “Listen again. A simile is a figure of speech in which two unlike things are compared, using the words like or as.” [Model]

Teacher/ “Say it with me. A simile is a figure of speech in which two Students unlike things are compared, using the words like or as. [Lead]

Teacher. “Your turn. Define simile.” [Test/check]

Students. A simile is a figure of speech in which two unlike things are compared, using the words like or as.

Teacher. “Yes, you said that perfectly!” [Verification]

Teacher. [Students know the verbal definition. Now the teacher uses examples and

nonexamples to display the defining features of the concept that are IN the examples and NOT in the nonexamples.]

“Listen. The air was hot as a stove. The air was hot as a stove. Are two things compared?” [The teacher ensure that students recall the details of the definition.]

Students. Yes.

Teacher. “What two things?” [The teacher makes sure students USE these features to

examine examples.]

Students. Air and stove.

Teacher. “Is like or as used to compare them?” [Ensuring students focus in another detail

of the definition.]

Students. Yes.

Teacher. “So, is ‘The air was hot as a stove’ a simile?” [Students use the definition to judge an possible example.]

Students. Yes.

Teacher. “Yes, The air was hot as a stove a simile?” [Verification]

Next, the teacher does exactly the same thing with a second example to firm up the features of the definition and students’ use of the definition to judge a possible example.

4. Then the teacher presents a NONexample so that students (comparing the two previous examples with the nonexample) can see the difference---the comparison of unlike things, using like or as—between the examples and the nonexample.]

Teacher. “Listen. The evening sun was red ruby. The evening sun was red ruby.”

Teacher. “Are two things compared?”

Students. Yes.

Teacher. “What two things.”

Students. Evening sun and red ruby.

Teacher. “Is like or as used to compare them?”

Students. No…. It said the evening sun WAS red ruby.

Teacher. “So, it compares unlike things, but it does NOT use like or as. So, is it a simile?”

Students. No.

Teacher. “Correct. It is NOT a simile. A simile compares unlike objects

AND uses like or as.” [Restates the definition to firm it.]

The teacher then juxtaposes a few more examples and nonexamples using the SAME WORDING as above.]

5. Error correction.

The teacher corrects errors immediately. For example.

Teacher. “Her eyes shined like diamonds. Simile?”

Students. A few students say No.

Teacher. “Her eyes shined like diamonds. Does it compare two things?” [Uses the

definition to help students make the judgment.]

Students. Yes.

Teacher. “What two things?”

Students. Her hair and diamonds.

Teacher. “Does it use LIKE or as?” [Uses the definition to help students make the

judgment.]

Students. Yes.

Teacher. “So, is it a simile?” [Has students make the judgment.]

Students. Yup!

Teacher. “Yup, it IS a simile.” [Verification]

[The teacher will return to this example later, to retest.]

6. Delayed acquisition test.

The teacher tests all the examples and nonexamples used.

Teacher. “The air was hot as a stove. Simile or not simile?”

Students. Simile.

Teacher. “How do you know?” [This requires students to use the definition to judge

examples and nonexamples.]

Students. Compares unlike things….Two unlike things…. Air and hot stove…. Uses as.

Teacher. “Correct!! A class full of geniuses!!”

Here’s another example.

Teaching a Higher-order Concept: Convection Cell

Here’s an example of teaching an abstract or higher-order concept: convection cell. Notice how every single statement from the teacher does something to (1) prepare the class to learn; and (2) communicate the concept. And every response from the class does something to communicate what they’ve learned or not learned. See explicit instruction. This is several tasks in a science lesson. [Explanation of what’s going on is in brackets. I put numbers in to show main parts of the instruction.] The procedure for teaching convection cells is longer than the procedure for teaching similes. Why? Because (1) there is a lot more background knowledge elements involved in convection cells that must be reviewed and integrated into the concept (e.g., system); (2) the concept of convections cells must be examined thoroughly (lots of examples) because they are have so many features and because examples vary widely (ocean, atmosphere, pot of boiling water)----while similes are defined by a few words.

Task 1. Set up [First, we make sure students (1) are paying attention, (2) have their materials ready, (3) are told the objectives, and are (4) firm on any pre-skills/background knowledge needed.]

1. “Boys and girls.” [Gain attention and focus] “Okay, great. Your eyes are on me and you’re sitting up nice and tall, ready to learn. What a great class I have!!”

“Please open (your text book to chapter 12, science lesson 12 on your computer) for today’s lesson. Also, open your guided notes to lesson 12.”

2. “New concept: convection cell. We’ll USE the concept of convection cell in our study tomorrow of weather and ocean current. Look at your guided notes to see what we studied earlier, what we’re studying today, and what we’ll study next. Now we’ll review background knowledge. Second, you’ll learn what convection cells are. You’ll tell the definition of convection cell and identify examples. [Objectives] And third, we’ll do an experiment on convection cells.”

3. “First, let’s review.” [Firm up pre-skills. Also see compound.]

3a. “The concept, fluid. Read the definition with me in your guided notes. [Students read with the teacher to increase their attention and involvement.] A fluid is a continuous (not broken into parts), amorphous substance (amorphous means without a specific form) whose molecules move freely past one another and that has the tendency to assume the shape of its container.”

[Teacher gave a quick definition of continuous and amorphous. If these concepts were brand new or tough, the teacher would have defined them before saying the sentence.]

“So, water is a fluid. [Uses water as an example of fluid because water will be the fluid in one of the examples of convection cell.] It is continuous and amorphous. Its molecules move freely past one another. And in its liquid state, it conforms to the shape of its container. Give me an example of how water conforms to the shape of its container.” [Test/check. If students generalize to a new example, they must know the concept so far.]

Bathtub….sink…swimming pool…..ocean.

“Excellent. Yes, those examples show how water is a fluid. Its molecules move past one another. It is continuous. And it conforms to the shape of its container.” [Teacher verifies the correct answer by repeating the answer.]

“Oxygen is a gas. It is continuous and amorphous. Its molecules move freely past one another. And it conforms to the shape of its container. Give me an example of how oxygen conforms to the shape of its container.” [Another example of fluid. Test/check. If students generalize to a new example, they must know the concept so far.]

Fills a room…Fills a refrigerator…Fills a tank.

“Yup. Great examples. The gas, oxygen, is a fluid. Its molecules move past one another. It is continuous. And it conforms to the shape of its container. [Teacher verifies the correct answer by repeating the answer.]

3b. Next. Here’s a rule from yesterday. Check your guided notes….. As a substance becomes cooler, it becomes more dense. As a substance becomes warmer, it becomes less dense. [Have students read that rule with you.] So, if you heat water, will it become more or less dense?” [Test/check students’ using the rule about heat and density to make a deduction.]

Less dense.

“Correct. As the water is heated, it becomes less dense.” [Verification]

“If you let the water sit there in the pot, it will cool. Will it become more or less dense?” [Test/check students’ using the rule about heat and density to make a deduction.]

More dense.

“That is correct. As a substance cools, it becomes more dense.” [Verification]

3c. “Another rule. Among objects (solid or fluid) that are the same size or volume, the denser objects are heavier than the less dense objects. [Have students read that rule with you.]

So, there are two containers that each contain one cubic foot of oxygen. The oxygen in container A is more dense than the oxygen in container B. Which container has heavier oxygen? [Test/check students using the rule about density-weight to make a deduction.]

Container A.

“How do you know?” [Follow up question to check reasoning. Did students use the rule or were they guessing?]

If it’s more dense, it’s heavier.

“Correct. If it’s more dense, it’s heavier. Good use of the rule.” [Verification.]

“How about water. You have two containers of water, and each container has one gallon of water. One of the gallons weighs more than the other. And one of the gallons is more dense than the other. Which container has denser water?” [Another test/check of students using the density-weight rule to make a deduction.]

The heavier one.

“How do you know?” [Follow up question to check reasoning. Did students use the rule or were they guessing?]

If it’s denser, it’s heavier.

“And which one is cooler?” [Test/check students using the density-weight rule to make a deduction.]

The denser one.

“How do you know.” [Follow up question to check reasoning. Did students use the rule or were they guessing?]

If it’s cooler, it’s denser.

“Yes, you got it. If it’s hotter, it’s less dense, and if it’s less dense, it lighter.” [Summarize the rules before going on.]

___________________________________________________________________________

The Set-up part is done. Now we move to new material.

___________________________________________________________________________

Task 2. Initial Instruction (Acquisition) of New Concept

1. “Now for our new concept: convection cell. Follow in your guided notes.” [Gain attention and focus]

2. “Here’s the definition. A convection cell [SUBJECT] is a loop of moving fluid (such as air, or water, or even molten rock) [GENUS] in which the motion from the bottom to the top of the cell, and from the top of the cell back to the bottom of the cell, results from differences in density caused by differences in temperature [DIFFERENCES].”

[Verbal definition Notice that the first part---“A convection cell is a loop of moving fluid”---is the GENUS part of the definition. It places things that are convection cells INSIDE the larger class (genus) of things that are loops of moving fluid. Other things that are loops of moving fluid would be water and air churning behind a propeller; water going down the drain; water stirred in a pot; and water or gas circulating through pipes. So, the next part of the definition (the DIFFERENCE) tells how convection cells are different from other things that are in the same genus of loops of moving fluid. “….in which the motion from the bottom to the top of the cell, and from the top of the cell back to the bottom of the cell, results from differences in density caused by differences in temperature.” This is DIFFERENT from a loop of water going down the drain, or air swirling behind a propeller.]

“Read that definition with me…” [Lead. Students map their behavior onto the teacher’s model. Correct any errors by repeating the model and lead.]

“Now read that definition yourself.” [Test/check to ensure they can do it independently. Correct any errors by repeating the definition and retesting. Why is the teacher doing so much—model, lead, test, correct errors, repeat? Because this definition is a pre-skill for achieving the objective. If they don’t know the concept---convection cell—they can’t identify examples and can’t do experiments on them.]

3. [Now the teacher shows examples that reveal clearly the features that define convection cells. The examples are different in the irrelevant/nondefining features, such as where the cell is and what the fluid is. But they are the same in the DEFINING features---loop of fluid, heating and cooling. As students examine and compare examples, they identify how they are the same. When they then contrast examples and nonexamples, they see how nonexamples are MISSING the festures that all the examples SHARE. This way, the learning mechanism figures out (induces) the SAMENESS in examples that defines convection cell IN GENERAL. Please see induction.]

“This is a convection cell. Notice the motion from the bottom to the top of the cell, and from the top of the cell back to the bottom of the cell, results from differences in density caused by differences in temperature.” [Teacher labels the example and then identifies features in the example that match the definition. This shows students WHY an example IS an example. But the teacher is also teaching a more GENERAL skill---namely, “Examine things; identify their features; see if the features match the definition.” This teaches students to USE definitions to guide their attention and inspection.]

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“This is a convection cell. Notice the motion from the bottom to the top of the cell, and from the top of the cell back to the bottom of the cell, results from differences in density caused by differences in temperature.”

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“Here’s another convection cell. Use the definition and our rules about temperature, weight, and density, to tell how it works.” [The students have just seen several examples of convection cells. The teacher used the definition to help them to examine the examples. Now the teacher goes a step further---use the rules (reviewed earlier) to explain what is happening. Notice that THIS example is a lot like the previous one. So, having students generalize to this new example should be easy.]

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Heat makes the water less dense….Less dense fluid is lighter than more dense fluid…..Lighter fluid rises….. When warm fluid is at the top, it cools….Cooler fluid becomes more dense…Denser fluid is heavier….Heavier fluid falls….Then it gets hot again, becomes more dense, becomes lighter, and rises…. [Correct any errors.]

“Yes, you told how this convection cells works, and you used the rules and heat, density, and weight.” [Verification.]

“And here’s another example. It’s water in the ocean. But it’s still a convection cell because hotter and lighter fluid moves from the bottom to the top of the cell, and from the top of the cell (where it cools and becomes denser and heavier) back to the bottom of the cell.” [Teacher helps students to generalize the definition to a new and rather different example.]

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Here’s another convection cell. In the one before, a volcano heated the fluid (water) from the bottom. In this one, the sun heats the ground, which heats a different fluid---air. The kind of fluid and the source of heat are different, but they are convection cells because hotter and lighter fluid moves from the bottom to the top of the cell, and from the top of the cell (where is cools and becomes denser and heavier) back to the bottom of the cell.” [Teacher helps students to generalize the definition to a new and rather different example. Teacher points out irrelevant differences but sameness in defining features.]

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“This is a convection cell in the earth itself. The fluid is liquid rock, or magma, heated by the hot earth’s core. Tell me what happens as the magma rises.” [Test/check students using the definition and the rules to explain what is happening in the example.]

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It cools….Get’s less dense…Gets lighter…Rises above the denser magma….Gets to the surface and cools…Gets heavier…Gets more dense…Flows back down….

“Perfect. You used the definition and rules to explain the loop of moving fluid.” [Verification]

4. [Now juxtapose examples used earlier, with nonexamples. Make sure the juxtaposed examples and nonexamples are similar in NONdefining features (e.g., fluid, container), but are different in the DEFINING features (heat, density), so that the differences that MAKE the difference (heat, density) are easily seen. “This is a convection cell because it has…..?.....This is NOT a convection cell because it does not have….”]

[pic] [pic]

“This is a convection cell. “This is NOT a convection cell.

Hotter, less dense, a lighter There is no difference in temper-

fluid rises, cools, and then ature in the fluid, and therefore

falls.” it is all the same density and weight,

and therefore there is no loop of moving fluid.”

[pic] [pic]

“This is a convection cell. “This is NOT a convection cell.

Hotter, less dense, lighter There is no difference is temper-

fluid rises, cools, and then ature in the fluid under the ice.

falls.” And therefore, it is all the same density and weight,

And therefore there is no loop of moving fluid.”

5. [Now give a delayed acquisition test of (1) the rules about heat, density, weight, and motion of a fluid, and (2) all of the examples and nonexamples in the acquisition set---above. This is where you assess whether students met the objective. ]

5a. “Boys and girls, tell the definition of convection cell. Check your guided notes….Okay, go!” [Choral response. Test/check the definition first. It is LOGICALLY prior to examples of the concept or rules about how convection cells work.]

A loop of moving fluid…air, or water, molten rock….the motion from the bottom to the top of the cell, and from the top of the cell back to the bottom of the cell, results from differences in density….caused by differences in temperature.

[Verify correct answers. “Yes….!” Correct any errors, and have the group repeat until they are firm.]

[Now ask SEVERAL individual students, especially students who made errors or who need some success.]

“Individual turns. Define convection cell. Luis?”

[Verify correct answers. “Yes….!” Correct any errors and repeat until firm.]

5b. “Everybody. Tell me the rules about heat, density, weight, and motion…. Go!” [Now, test/check rules, which logically follow the definition of convection cell.]

When the fluid is hotter it is denser…When it’s denser, it rises….When it’s cooler it’s less dense….When it’s cooler, it falls.

[Verify correct answers. “Yes….!” Correct any errors and repeat until firm.]

“Individual turns. Tell me the rules about heat, density, weight, and motion. Debbie?”

[Verify correct answers. “Yes….!” Correct any errors and repeat until firm.]

5c. [Now show each example and nonexample, and test. Examples and nonexamples logically follow checking the definition and then the rules.]

“Is this a convection cell?”

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Yes.

“How do you know?”

Fluid loop….hotter on the bottom….less dense….lighter….water rises….cools at the top….denser and heavier….fluid falls.

“Correct! Excellent use of the rules and definition.”

“Is this a convection cell?” [Nonexample]

[pic]

No.

“How do you know?”

Frozen…No heat differences….No part is denser or heavier….No motion.

“Correct again. There are no heat differences. So, no part is more dense or heavy. And so there is no motion.”

[Repeat acquisition test with several more examples and nonexamples. Verify correct answer and correct all errors and repeat.]

6. [Now help students to EXPAND their knowledge by GENERALIZING it to new examples.]

“Here’s a bathtub with hot water running in it. Is IT a convection cell? Think about it using the words, heat, density, weight, and movement up or down.” [Hints/reminders of how they answered questions like this earlier.]

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Yes.

“How do you know?”

Hot water goes to the bottom, but is less dense and lighter than the cooler water in the tub….The hot water rises….The water at the top cools….Gets less dense….Gets lighter and falls.

“Wow! You used the definition of convection cell and all the rules!!” [Verification.]

“How about this one? The water has been sitting in the tub all day.” [A second generalization example.]

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Not a convection cell. Fluid is the same all over….No part is hotter or colder…Same density and weight. No motion.

“You are soooo smart!”

[You could give more generalization examples and nonexamples to the whole group and to individual students.]

Task 3. Application and Integration.

[Now you could APPLY the knowledge with projects that INTEGRATE this new knowledge AND prior knowledge of measurement and data collection.]

“Boys and girls. You are SOLID on convection cells. Let’s do some projects on convection cells, using glass beakers that we will heat from the bottom, blue dye that we can use to see motion, and thermometers to measure temperature in different parts of the fluid. We’ll use water and oil to see IF it takes higher or lower temperature to produce motion. We will make videos showing motion and heat.”

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