Wednesday, October 31, 2007

Change the Representation, Deepen the Learning

Can a second-grade student not yet formally taught the concept or mathematical processes of division identify one-tenth of a rectangle?

In Mind, Brain, and Education (June 2007), researcher Florence Mihaela Singer details how a change in representation can trigger the use of knowledge never formally studied and deepen the understanding of new knowledge. A change in representation is a change in the form of how material is viewed and considered. For example, rather than a rectangular grid from which students identify a tenth, a blank sheet of paper activates different thinking. The second-grade student cited as an example successfully identified one-tenth of a rectangle once the researcher changed the form, from a grid to a blank rectangle, with which the student was working. While the grid encouraged a focus on numeric elements (the number of squares in the grid), the blank rectangle allowed a focus on spatial relationships, and this shift enabled the child to accomplish the task.

Changing the representation of material provides a powerful means of deepening learning and constructing understanding. Even after students have processed new material, changing its representation forces a new focus on the material and increased processing of its important details and relationships. Consider the knowledge, insights, and wisdom conveyed in narrative forms—fables, parables, allegories. The change in representation imbues the information with memorable power through a shift in perspective from factual statement to narrative context.

Similar impact can occur when teachers force a change in representation of new instructional material. For example, imagine you have just taught a social studies unit on the American Civil War to middle school students. You have presented the facts—key issues, events, and personalities—and students have processed these in various but somewhat familiar ways. Perhaps they have created a timeline of the key events, explained the differing perspectives on critical issues, and associated specific individuals with issues and events. This is effective processing and will generate some understanding.

However, consider the potential of a change in representation. For example, you may engage students in exploring a change of scale: What if the entire Civil War had been fought within one house? Would the upstairs represent one side of the conflict and the downstairs the other? How would the important personalities be represented within a family? Where would the battlefields be located? How would the difference in perspectives have become evident? As students change the scale from a national to a familial conflict, every important detail of the instructional material must be revisited in depth to assign it the most rational role in the new representation. The new content gets processed deeply as the new, in this case imaginary, representation is explored and developed.

Teachers using the Architecture of Learning Instructional Design Model (see have a built in opportunity for such processing. The Elaboration Strand of both the Content and Combination Blueprints provide ideal opportunities for reprocessing new material through representational change.

For some students, such a change will make new material learnable. For others, the initial learning will deepen, increasing the value, meaning, and potential transfer of newly constructed understandings. All learners benefit from such activity.

Change the representation, deepen the learning.

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