Linda Jarvin, Yale University
Nicole M. McNeil, Yale University
Robert J. Sternberg, Yale University
(Authors contributed equally and are listed alphabetically)
Abstract: It is widely assumed that it is easier to solve math problems when they are presented in a practical (or concrete) way than when they are presented in an abstract way. This assumption has a large impact on our schools. Teachers are encouraged to develop lessons that "contextualize" math, so students can draw on their practical knowledge when solving problems. Teachers are also encouraged to use manipulatives during instruction because most people assume that it is beneficial to link math to real-world objects. Although many of these methods seem like they should help, it is unclear which of them (if any) truly facilitate students' understanding of math. Moreover, several scientists have even suggested that some methods to make problems more practical may hinder students' understanding.
We examined students' (grades 4-6) performance on math word problems in five experiments. The goal was to determine which of the following methods (if any) improve students' performance: (a) using familiar units (e.g., dollars and cents), (b) presenting problems orally, (c) providing manipulatives, (d) making students the protagonists of the problems, and (e) using problems that refer to tangible people and objects in the real world. Results demonstrate that some efforts to make problems more practical (e.g., oral presentation) improve students' performance, whereas some methods (e.g., providing manipulatives) may hinder performance. Findings suggest that the role of "practicality" in students' understanding of math problems is more complex than scientists and educators generally assume.