Supporting Learners as Problem-Solvers

Theories abound about how human memory functions, but sometimes the theories are too abstract for us to be able to see how they might be relevant in the day-to-day world of the classroom.

Our knowledge of how the memory functions is growing rapidly however, and some recent contributions from researchers at Miami University and the University of Texas at Arlington do seem to have some obvious implications for learning and teaching.

One consistent research finding about our use of memory has been that our ability to reason appears to be independent of our ability to recall particular facts. Wolfe, Reyna, and Brainerd believe that this indicates that humans may have a memory for the underlying structure of concepts, which may be independent of our memory for particular facts. They refer to these two types of memory as “gist” memory and “verbatim” memory respectively.

These researchers tested this hypothesis using concepts of geological time. All participants in the study were given a list of dates of geological events. One group was simply told to study the chronology of events. The second group was told to generate an analogy between geological time and a familiar quantity, while maintaining accurate relationships between events.

It was found that participants in the “generate analogy” group tended to construct one of two potential types of analogy. They were therefore further divided into groups based on the kind of analogy they created. The two groups thus formed were:

1. Unit conversion analogies, where units in one scale were converted to units in another scale. For example, converting 100 million years to US$100.

2. Metaphoric analogies, where one whole entity was transformed onto the scale of another whole entity. For example, comparing the age of the earth with a single year. (Note: the researchers considered the metaphoric analogies to be the only true analogies.)

There were thus three conditions: study group, metaphoric analogy group and unit conversion group. Participants were later asked to perform three tasks, which assessed their understanding of the relationships between events in geological time:

1. Cued recall: participants were given events in a table, and they had to write the appropriate age of the event.

2. Time line task: participants were given a list of events and asked to place them on a time line.

3. Question asking: participants were told to ask any questions they had about natural history, based on what they had learned.

What were the results?

• Participants from the study group recalled the age of events far better than other groups.

• Participants who generated metaphoric analogies placed events onto a time line with much greater accuracy (with respect to the relative age of events) than other groups.

• The total number of questions asked did not differ significantly between groups, but there were differences in the types of questions asked. The metaphoric analogy group tended to ask more questions related to geological and evolutionary processes and more questions that projected into the future.

• Overall, the researchers claim that there is some degree of independence between “gist” memory and “verbatim” memory. Participants who studied the chronology using a rote memorization strategy performed well on the cued recall task, but poorly on the time line task, which required a deeper understanding of the scalar aspects of geological time. In contrast, participants who developed metaphoric analogies performed better on the time line task, but less well on the cued recall task.

What might these results mean?

Overall, it seems that generating a metaphoric analogy allowed participants to create a representation of the underlying scalar aspects of geological time. This is significant because a good deal of research suggests that when people perform reasoning tasks, they prefer to work with gist representations.

David Jonassen, from the Center for the Study of Problem Solving at the University of Missouri has some ideas that may help explain why gist representations are so important for reasoning. Dr. Jonassen posits that there are three kinds of knowledge:

• Declarative knowledge, our knowledge of facts, events, and idea (“knowing that...”);

• Procedural knowledge, our knowledge as it is applied to real situations (“knowing how...”); and

• Structural knowledge, of how concepts, facts, and ideas are interrelated.

Dr. Jonassen believes that structural knowledge mediates the translation of declarative knowledge into procedural knowledge: “It is not enough to know that. In order to know how, you must know why.” The thinkers and problem solvers we hope to produce in our classrooms need an understanding of how things are connected, and it makes sense that analogies would provide a good means of gaining this structural knowledge.

Examining the similarities and differences between the underlying structure of two situations or ideas can lead to an extraction of the underlying structures and patterns.

One implication of this study then, would seem to be that we should be very clear about the situations in which we expect our students to make use of their learning. Only by being clear about this can we make rational decisions about whether we should be implementing activities that are likely to lead to a verbatim representation of the knowledge or those which are more likely to lead to a gist representation.

Given the finding that most problem solving depends more on gist representations, there are probably only very limited situations where verbatim representations of knowledge are the most appropriate. A further implication seems to be that the use of analogy could be a powerful learning strategy for the formation of these gist representations.

Reference

Wolfe, C., Reyna, V., & Brainerd, C. (2005) “Fuzzy-Trace Theory: Implications for Transfer in Teaching and Learning.” In: Mestre, J. (Ed.) Transfer of Learning from a Modern Multidisciplinary Perspective. Information Age Publishing: Greenwich, Connecticut.

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