Visual Learners and Designing Instruction

“I am a visual learner … I have to see it, and then I can understand.”

You’ve heard this, and you may have said this. What does it mean? Does it mean that graphical representations are best? Are they required?

The situation is not that simple, and is misleading at times. The issues deal with what a person actually sees in a graph, and how the brain processes information. In a clever study, Gagatsis and Elia conducted a study that showed two things … first, that multiple representations by themselves do not improve mathematical understanding; second, that the different modes of representations are not ‘equal’ in learning. (See http://dipmat.math.unipa.it/~grim/quad14_gagatsis.pdf)

Behind this, I believe, is how a human brain processes information. Experts seem to feel that there are separate ‘channels’ for phonological (word-like) and visual information. Some evidence indicates that the phonological channel has a higher priority in the processing; perhaps this is simply due to the native difference in the information — after all, a visual image is global when first processed while verbal information tends to have higher level of details. I would point out that an expert sees a very different set of information in a graph compared to a novice. See the ‘cognitive psychology’ books by Roger Bruning (2003, page 122 ), and by Bruce Goldstein (2005, pages 166 to 168).

A recent study by Aleven and others looked at the effectiveness of various graphical representations with fractions. They found that multiple graphical representations of the same concept AND switching between graphical and symbolic forms produced the best learning. If a student only sees one ‘view’ graphically, it is not as good; different views help the learner ‘see’ more information, similar to a ‘compare & contrast’ writing assignment. Learning was also improved when there was a routine switch from graphical to symbolic forms. (See http://www.learnlab.org/research/wiki/index.php/Sequencing_learning_with_multiple_representations_of_rational_numbers_(Aleven,_Rummel,_%26_Rau)

How should we use ‘visual’ displays with our students? Students like them (at least, compared to the symbolic forms). The bottom line is that students do not see the same visual information that we see … when they understand well, they will see much of what we see. When you see a graph of an exponential function over a small domain, you see the parts that are not shown — even though the shape of the graph does not necessarily imply this information. Students need to see the relationship in multiple graphical forms, as well as symbolic and numeric forms, to become more ‘expert’ — to have the understanding that is needed. When you see a graph of any relationship, you understanding the ‘approximating’ nature of the graph, and know to look at the numeric and symbolic forms for additional accuracy; again, students need scaffolding along this path of understanding.

In addition to graphs, we also tend to use a variety of visual aids with our students — whether it is a triangle image to represent part-whole work with fractions or percents or a table to summarize information. You may have noticed that some students are helped, and others confused, by these displays. To become mathematically literate, our students would be able to translate from these and to state some basic limitations of such a visualization; a tool used without knowing the limitations is a ticket for future difficulties.

It’s not enough to say that “graphical representations are good”; we need to design a learning experience that brings the student to a more complete understanding of all representations. Visual images might help students in the short-term, or might confuse; neither condition is good for the long-term. Having “different representations” is not just a “been there, done that” approach … we need to attend to the transitions between representations and to the native limitations of each. Good instruction makes explicit the connections between representations in an ‘iterative’ process.

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