Chapter 6
Theoretical Considerations
Abstract
This chapter addresses several theoretical questions. The question of how each cognitive event facilitates learning is answered by considering the specific structure and presentation of each cognitive event, creating a framework that lists the individual steps for authoring a particular Guided Cognition homework question, and then using these steps to identify the cognitive processes most likely to be engaged when a student performs a Guided Cognition task. Then, we identified how that cognitive event might facilitate learning, and we have listed the cognitive processes that are most likely to be elicited by each cognitive event. In this chapter, we also explain the relation of cognitive events to various cognitive processes. Then we discuss how, on the surface, a particular cognitive event can appear very different for different content (for example, literature and mathematics) but can actually have very similar underlying cognitive processes that facilitate learning. The observable performance of the cognitive events defines the surface structure of students' study efforts. The elicited cognitive processes constitute the deep structure of students' study efforts. The surface-level expression of particular cognitive events may look different for literature and mathematics, but these cognitive events nevertheless are likely to elicit similar sets of learning-effective cognitive processes for each content area. Whether for literature or mathematics, engaging in these cognitive processes is hypothesized to make the studied content more meaningful and more memorable.
Keywords
Cognitive events; Cognitive processes; Question patterns or frames; Relation of cognitive events to cognitive processes; Surface structure and deep structure
Guided Cognition effects raise several theoretical questions. How do the content-focused cognitive events facilitate learning? What cognitive processes are likely to be elicited by each cognitive event? How are the cognitive events related to one another? Why does Guided Cognition-designed homework facilitate the learning of very different content such as literature and mathematics? This chapter addresses these questions.
How Does Each Cognitive Event Facilitate Learning?
The interesting results of Experiment 14 (Chapter 4) can be used to clarify how performing cognitive events facilitates learning. By doing the cognitive events in this mathematics experiment, students in the Guided Cognition Condition were guided to think about how to set up and solve story problems that involved multiplying or dividing fractions and mixed numbers, but these students did not have any additional calculation practice. Nevertheless, on an unexpected quiz given a few days later, and on another unexpected quiz given months later (Experiment 15), these Guided Cognition Condition students were better than the Traditional Condition students at solving story problems (which required interpretation and set up, and execution of the calculations), and they were also better at solving plain numerical problems (which required just execution of the calculations).
It may not be surprising that students who thought about story problems, even without working them, showed improvement in interpreting and working story problems. On the other hand, it is somewhat surprising to find that students who thought about story problems, without doing the calculations, also showed improvement in performing calculations for plain numerical problems. What are students learning from the various cognitive events that facilitates later problem solving for story problems and for numerical-only problems?
To answer this question, it is helpful to consider the specific structure and presentation of each cognitive event by creating a framework that lists the individual steps for authoring a particular Guided Cognition homework
question. Considering these steps makes it easier to identify the cognitive processes most likely to be engaged when a student performs a Guided Cognition task. Thus, we have provided a general pattern (or frame) for creating each of the four cognitive events in mathematics Experiment 14. Then, we have identified how that cognitive event might help students with subsequent interpretation of story problems and also with subsequent execution of the mechanics of story problems and of numerical-only problems. In addition, we have listed the cognitive processes that are most likely to be elicited by each cognitive event.
Frame for the Role Play Cognitive Event
Part A
Part B
The Role Play Cognitive Event Could Help With Subsequent:
Interpretation
- • Explaining how to do a specific type of problem enables a student to practice the interpretation of that type of problem and will facilitate subsequent memory for how to interpret such problems.
- • Role playing helps the student identify with and relate more closely to the interpretation: Imagining oneself actively involved in a situation creates a different and memorable perspective, and a closer association with unfamiliar concepts.
Execution
Cognitive Processes Likely Elicited by the Role Play Cognitive Event
Frame for the Relate to Prior Experience Cognitive Event
Part A
Part B
- • Ask the student to tell about a situation like the one in the Part A problem that the student has experienced, read about, or can imagine, where knowing how to perform the mathematics in the Part A problem can help determine an answer.
- • Have the student circle the types of numbers, terms, or other mathematics concepts that are part of the student's problem. (Name these in the instructions to the student.)
- • Tell the student not to work the student's example problem.
The Relate to Prior Experience Cognitive Event Could Help With Subsequent:
Interpretation
- • Authoring an example problem helps the student analyze the structure of the given problem.
- • Relating a problem to prior experience activates the student's prior knowledge and creates a stronger context for understanding.
- • Associations to prior knowledge help the student recall information about this type of problem.
Execution
Cognitive Processes Likely Elicited by the Relate to Prior Experience Cognitive Event
Frame for the Divergent Thinking Cognitive Event
Part A
- • Present a story problem that can be solved using more than one method or procedure, such as with more than one order of steps, more than one way to perform the calculations, etc.
- • Show the student two ways to solve the problem.
- • Ask the student to explain which way might be preferred because of fewer steps, easier calculations, etc.
- • Provide a hint to help the student understand the difference between the two procedures.
- • Tell the student to answer the question by thinking about how to solve the problem, but not to execute the calculations of the problem.
Part B
The Divergent Thinking Cognitive Event Could Help With Subsequent:
Interpretation
- • Divergent thinking helps prevent mechanization by encouraging students to think about the order of operations.
- • Divergent thinking helps students represent the physical properties that constrain the procedures.
- • Divergent thinking encourages students to review and evaluate mathematical procedures.
Execution
Cognitive Processes Likely Elicited by the Divergent Thinking Cognitive Event
Frame for the Visualize and Illustrate Cognitive Event
Part A
Part B
The Visualize and Illustrate Cognitive Event Could Help With Subsequent:
Interpretation
- • Visualizing helps the student practice selecting the important terms and values so that the problem can be accurately represented.
- • Visualizing and illustrating helps the student create a mental model that can transfer to similar materials.
- • Visualizing and illustrating combines visual memory and motor performance to reinforce memory and understanding.
Execution
Cognitive Processes Likely Elicited by the Visualize and Illustrate Cognitive Event
The above analysis of what students may be learning from each cognitive event provides some insight into why students improve, not only in solving story problems, but also in solving plain numerical problems without any additional calculation practice. In addition, enumerating the cognitive processes that are most likely activated by each cognitive event reveals that there is substantial overlap in the cognitive processes that are likely triggered by the various cognitive events. That finding is explored further in the next section.
The Relation of Cognitive Events to Cognitive Processes
On the surface, the various cognitive events seem quite different from one another, but how different are they? Recall that the performance of cognitive events is directly observable in the homework completed by students. In contrast, cognitive processes are generally inferred from observing what the students do. For example, for the cognitive event visualize and illustrate, we can directly observe the illustration made by the student, but we must infer that to make that illustration the student mentally visualized a scene or an object and engaged in several cognitive processes to do so. For the cognitive event role play, we can directly observe the student speaking in the first person (I …), but we must infer that the student is actually imagining himself or herself in a situation and again, engaging in several cognitive processes to do so. We can look at a list of cognitive processes, and for each cognitive event, we can infer that certain ones are likely to be elicited.
We performed an extensive logical analysis of this sort, and the results are shown in Table 6.1. In the table, check marks indicate the cognitive processes that are most likely to be elicited by the content-focused cognitive events used in our experiments. This table may not be comprehensive, and some relationships may be debatable, but the table provides an example of how theoretical cognitive processes can be mapped to observable cognitive events.
An overview of the table reveals two interesting findings. The first is that Guided Cognition design is effective, in part, because performing a particular cognitive event likely elicits several cognitive processes that collectively increase comprehension and retention, thereby improving subsequent performance.
The second finding is that, although each type of cognitive event is distinct at the observable level, there is a substantial overlap in the cognitive processes that the various cognitive events are likely to elicit. Similarities in these underlying processes help explain why each cognitive event has been found to be effective in facilitating learning via Guided Cognition homework questions and tasks (see Experiments 10 and 11). For practical education applications, the overlap in elicited processes by the various cognitive events is a good outcome because it provides a great deal of surface-level variety for constructing effective homework.
Surface Structure and Deep Structure of Cognitive Events
The overlap of cognitive processes elicited by different cognitive events makes it easier to understand why different cognitive events can similarly facilitate learning. However, it is more difficult to understand how a particular cognitive event can facilitate learning in two distinct content areas where the cognitive event is expressed in very different ways. For example, a student considering divergent motives for a character's actions and a student considering two ways to work a mathematics problem are both thinking divergently. In literature, a student is considering relationships among characters in a story, whereas in mathematics, a student is thinking about alternative procedures for solving a problem. In these content areas, the surface structures appear different in their specific instructions, distinct operations, and unique results; however, the specifically formatted cognitive event that is incorporated into each Guided Cognition homework question may engage the same underlying cognitive processes. These processes
operate at a deeper structural level to provide a foundation for effective learning of widely different subjects. The relationship of the different surface structures of a singular cognitive event and the common deep structure (the cognitive processes) that these surface structures elicit is illustrated in Figure 6.1.
Table 6.1
Support for the idea that similar learning-effective cognitive processes can be elicited by cognitive events that are expressed differently for different subjects is provided by reviewing experiments with 7th-grade students (reported in Chapters 3 and 4). In Experiments 8 and 9, respectively, average-ability and advanced-ability 7th-grade middle school students studied a novel in literature class. Students answered either Traditional or Guided Cognition homework questions about the novel, and 4
days later, they were given an unexpected quiz. In Experiment 8, the average-ability students who were assigned Guided Cognition homework performed 8.1 percentage points better on this delayed quiz, compared to average-ability students who were assigned Traditional homework. Similarly, in Experiment 9, the advanced-ability students who performed Guided Cognition homework performed 9.7 percentage points better on the delayed quiz about the novel's content, compared to advanced-ability students who were assigned Traditional homework.
In Experiment 14, average-ability 7th-grade middle school mathematics students studied multiplying and dividing fractions and mixed numbers. Students were assigned Traditional or Guided Cognition homework. All students solved the same story problems, but those in the Guided Cognition Condition engaged in cognitive events that encouraged further thinking about the problems without including any additional calculation practice. A few days later, all students were given an unexpected review activity (quiz) that included story problems and plain numerical problems. Students who were in the Guided Cognition homework condition performed 9.1 percentage points better on story problems and 7.3 percentage points better on plain numerical problems compared to students who were in the Traditional homework condition.
So, whether for learning literature or mathematics, the Guided Cognition-designed homework helped students perform almost a letter grade better, assuming letter grades are 10 points apart. The theoretical explanation for these results is that although on the surface the literature and mathematics students in these experiments were completing very different tasks for the same cognitive events, students in each content area were able to learn more effectively because they were engaged in a similar set of learning-effective cognitive processes.
This idea can be further illustrated by comparing examples of the role play cognitive event frames used to author homework in the two content domains:
The Frame for the Role Play Cognitive Event as Used in Literature Homework
Pretend you are __________. Speaking in the first person as __________ (I...), tell or explain __________.
The Frame for the Role Play Cognitive Event as Used in Mathematics Homework
Part A
Part B
Comparing these frames shows very different tasks for literature and mathematics, even though those tasks are based on the fundamental requirement of role playing. Table 6.1 presents a logical analysis that relates cognitive events to cognitive processes and indicates why Guided Cognition homework facilitates learning in these very different content domains. This analysis suggests that the underlying deep structures (i.e., the sets of elicited cognitive processes for a cognitive event) can be similar even though the surface structures (i.e., the performed cognitive events) appear very different. For the role play cognitive event, whether a student is speaking as a character in a story, or speaking as a person who is explaining how to work a mathematics problem, it is likely that many or all of the six cognitive processes checked in the role play column would be elicited. As another example, the long list of cognitive processes that are indicated for the
relate to prior experience cognitive event may be elicited by a student who is discussing literature and also may be elicited by a student who is thinking about a mathematics problem.
So to summarize, well-defined frames can be used to design homework that includes specific cognitive events. As illustrated in Figure 6.1, the observable performance of the cognitive events defines the surface structure of students' study efforts. The elicited cognitive processes constitute the deep structure of students' study efforts. The surface-level expression of particular cognitive events may look different for literature and mathematics, but these cognitive events nevertheless are likely to elicit similar sets of learning-effective cognitive processes for each content area. Whether for literature or mathematics, engaging in these cognitive processes is hypothesized to make the studied content more meaningful and more memorable.
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