I said in my last post that I would talk about role of mental representation in comprehension. Before I get into that topic, however, I need to discuss a somewhat related idea I have been thinking about quite bit as I have worked with some of my students, namely, the importance of structuring lessons to allow students to verify their answers and their thinking.
The following story about my son provides a nice example of the importance of what I am calling verification. One day when my wife went to pick my son up from kindergarten (nine years ago) he wanted to read to her a story that the class had read together that day. The reading of the story was done not by showing the students how to “sound out” the words, but through repetition and predictability of the text. My son apparently read the whole story correctly, except that he read some small function word incorrectly, perhaps “in” for “on” Some of the other students who heard him read the story corrected him immediately. However, because he had simply memorized the text pattern rather than learned how to translate the letters into sounds, he became upset. Moreover, there was no really good way to repair the error so that he understood the mistake: I suspect in his mind, it was not an error of translation, but an error of memory.
This sort of thing happens countless times with our students, and those of us who work especially with struggling students see that such instructions ends up teaching students to guess constantly and to approach their work un-strategically, confident that it will never entirely be fully understandable to them. The problem of such mis-understanding in education is quite large: Howard Gardner has an interesting book called The Unschooled Mind that discusses a significant body of research that demonstrates that even students with high achievement in typical measures of academic performance have persistent and fundamental misunderstandings about what they seem to have learned.
As I’ve worked with students, the curricula that I find the most effective as well as enjoyable to use are those that are founded upon sense-making and require students to prove their answers in terms and with explanations that make sense to them. This can be as simple as having a student verify a number fact by counting on his fingers, and demonstrating that his subtraction calculation was correct by using base-ten blocks or some similar physical representation.
Much of this can be built into a curriculum systematically. But one of the great arts of teaching, it seems to me, is to figure out how to help a student assimilate new information and new experiences within the terms of his own understanding.
