PDF Worked Examples. Provide a comprehensive review of the worked ...

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Worked Examples. a. Provide a comprehensive review of the worked examples literature. b. There are at least two ways to look at worked examples. In one view. by providing steps of complex procedures, the cognitive load of the overall task is reduced. You might say that the process was scaffolded. Another way to look at this is to say that the worked example provides a means by which the declarative knowledge can be proceduralized. Discuss these two views in such as way that you reflect deep understanding of cognitive load theory, Anderson's notion of proceduralization, and the unified learning model.

Worked Examples: Proceduralization, Cognitive Load Theory, and the Unified Learning Model

Worked Examples

The learning process is very structured, and it is important to understand the psychological events that occur during learning. We are all equipped with two memory systems: working memory and long-term memory (Clark, Nguyen, & Sweller, 2006). All information must first be processed through working memory; this is where learning occurs. Long-term memory is equivalent to storage. Once information is processed through working memory, it will hopefully be moved to long-term memory for later retrieval. However, working memory has limits on both capacity and duration of holding information. This capacity can be increased through the use of worked examples and practice. The amount of tasks that the working memory attends to during learning is termed cognitive load. Long-term memory does not have the same capacity limits as working memory. As more information is stored in long-term memory, there are greater opportunities for meaningful schema development, which in turn increases working memory capacity. Schemas can also be developed by worked examples and practice without exhausting cognitive load.

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Worked examples are a common method of teaching problem-solving skills. They are schematic presentations of information without imposing on cognitive load (Cooper & Sweller 1987; Mwango & Sweller, 1998; Sweller & Cooper, 1985; Tarmizi & Sweller, 1988; Ward & Sweller, 1990; Zhu & Simon 1987). Typically, worked examples are commonly used in mathematic subjects to demonstrate how problems are solved step by step. The goal is placed on understanding the how and why of each step of a problem, not solving the problem. This allows students the opportunity to reflect on and fully understand each step of the problem before moving to the next. Worked examples provide a systematic approach to problem solving, rather than a general search strategy which increases cognitive load because the learner attends to not only the process of solving the problem, but the solution as well (Sweller & Cooper, 1985). General search strategies, such as trial and error, are not effective because relationships are not formed, causing the learner to not fully grasp why certain steps are taken. General search strategies do not accommodate schema acquisition; therefore, more strain is placed on cognitive load. Proceduralization, cognitive load theory, and the unified learning model all have important implications on worked examples.

Proceduralization

John Anderson's ACT theory provides a framework for cognitive skill development (Anderson, 1982; Anderson, 1987). It is a structured, goal-oriented framework in which productions are shaped. These productions are "condition-action pairs that specify that if a certain state occurs working memory, then particular...actions should take place" (Anderson, 1987, p. 193). Productions are a series of mental steps the learner takes to accomplish a certain skill.

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There are three stages to the ACT framework: declarative, knowledge compilation, and procedural learning. Learners must first receive information and instructions about a skill to be learned. Without this initial mediation, learners cannot be successful in skill acquisition and subsequent development. These declarative facts are essential for production development which in turn develops skills. Anderson (1982) points out the importance of general problem-solving skills and prior knowledge to the declarative stage, "general interpretative procedures with no domain-specific knowledge can be applied to some facts about the domain and produce coherent and domain-appropriate behavior" (p.375). This automated process assists in using skills interpretatively, or skill transference, while not placing additional strains on working memory. Having enough working memory available is vital in the successful demonstration of a skill.

Declarative knowledge can have a negative effect on behavior (Anderson, 1982). If obtained knowledge is incorrect or not processed correctly, an incorrect procedure can be performed. This can hamper the learning process because it is more difficult to correct mistakes because of an additional extraneous load than to introduce a new correct procedure. Instead, the instructor should redirect attention to the correct behavior to reduce overall cognitive load. This is also the reason why information must first be introduced declaratively: it is easier to correct factual errors than behavioral errors.

Knowledge compilation is the second stage of skill acquisition, and it focuses on making information retrieval more efficient. Two major phenomena occur during the stage, composition and proceduralization (Anderson 1982). Composition results in the formation of schemas, or the collapse of adjacent and goal-similar productions into a new single production. The new production has the same goal as the latest collapsed production. In other words, composition results in the combination of multiple steps into an efficient single step. Composition increases

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speed in which a skill is demonstrated. At this point, some declarative information is still in working memory. Proceduralization, on the other hand, results in productions becoming automated. Supporting declarative information is no longer needed in working memory to accomplish the production. New productions are built and schemas are collapsed. Proceduralization is essential in freeing up working memory, thus increasing working memory capacity.

Research on the Einstellung Effect suggests that proceduralization has a greater influence on success of transference than composition (Anderson, 1982). This occurs because proceduralization decreases the load on working memory. Research also found that learners must understand the declarative information before proceduralization will occur; proceduralization does not occur without understanding.

Procedural learning results from the actual application of productions (Anderson, 1982). Anderson also refers to this stage as "tuning," which is similar to fine-tuning a skill. Research shows that experts use fewer moves to accomplish a skill set than novices. They have developed more compositions, and proceduralization occurs more readily. Novices use more generalized and less effective strategies, such as trial and error, to accomplish similar skills. In earlier works, Anderson and other researchers identified three processes that have a positive impact on procedural learning: generalization, discrimination, and strengthening.

Generalization results from the learner broadening the rules of production applications. Some productions are more generic, thus they are applicable in more situations. This can have a positive effect on transference. Anderson (1982) suggests that it takes at least two examples to

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make a solid generalization; therefore, learning the relationship between rules or productions is critical in forming generalizations.

Discrimination occurs when the learner applies the procedures in only the correct situation (Anderson, 1982). Declarative knowledge about both correct and incorrect application and corrective feedback is required. Action discrimination and condition discrimination production are formed during this process. Action discrimination is the learning of a new production, while condition discrimination restricts the old production. The condition discrimination does not replace the original production; instead, all three co-exist for a greater comprehension. Whereas generalization allows for the generic application of some productions, discrimination results in production specificity.

The frequency of which production is applied in order to eliminate error is termed strengthening (Anderson, 1982). Strengthening is necessary during procedural learning to correct the errors that can be made with generalization, discrimination, or incorrect declarative information. Strengthening also occurs by incorporating correct new productions into the learning process.

Anderson's ACT theory of skill acquisition focuses on structural relationships (Anderson, 1982). Without understanding these relationships, learners cannot develop appropriate compositions, generalizations, and discriminations to assist in decreasing the number of procedures required to accomplish a skill. Furthermore, proceduralization and strengthening will not take place and speed of skill will not decrease. There are limits to the number of productions a learner can handle at one time, and these processes work together to decrease the load on working memory, increasing its capacity. This allows for subsequent improvement.

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