Seeing Language Learning inside the Math: Cognitive Analysis Yields Transfer

Achieving and understanding effective transfer of learning requires a careful analysis of the hidden knowledge and skills to be transferred. We present an experiment that tests a subtle prediction of such an analysis. It concluded that a critical difficulty in students’ learning to translate algebra story problems into symbolic expressions is in learning the grammar of such expressions. We hypothesized that exercises requiring students to substitute one algebraic expression into another would enhance students’ algebraic grammar knowledge. This hypothesis led to a counter-intuitive prediction that learning to symbolize story problems could be better enhanced through practice on dissimilar looking substitution exercises than through practice on more similar looking story problems. We report on an experimental comparison involving 303 middle school students that supports this prediction. We discuss how having learners externalize a uniform abstract form and get interactive feedback on it may be important factors in enhancing transfer.