On learning the relationship between quantitative properties and symbolic representations

Third International Conference of the Learning Sciences
Moore, J. L., & Schwartz, D.

Many students do not understand what representational problems a particular notation solves, thus limiting their ability to use the notation, as well as their understanding of the problem situation it applies to. Forty-six undergraduates completed a lesson designed to help them understand variance and its notation. Students in the invention group were asked to create a procedure for calculating the variance of contrasting distributions of numbers; students in the procedural group were presented with a procedure for calculating variance and asked to practice it on the numbers. Results indicate that invention students learned to reflect on the quantitative properties of distributions, and to evaluate statistical procedures in terms of their ability to differentiate those properties. Students in the procedural condition tended to evaluate a procedure simply in terms of whether or not it was like the "correct" procedure. We plan to extend this instructional method to facilitate classroom conversations and as a platform for a complementary intelligent instructional system.