The effect of analogies on learning to solve algebraic equations

A total of 236 seventh grade students who had never been taught algebraic equations before, attending 10 Chilean schools of varying socio-economic status, were randomly divided into two groups at each school. The students in one group watched a 15-minute video teaching them how to solve five different first-degree linear equations using a traditional symbolic strategy, while in the other group, the students watched a 15-minute video teaching them how to solve the same equations using four analogies for solving an equation: a two-pan balance for the equals sign, a box for a variable, candies for numbers, and guessing the number of candies inside a box. The students were then tested on 12 equation solving problems, all of them written, using only symbolic notation. The group that watched the analogies video performed significantly better. Students with a below-average mathematics GPA who watched the analogies video did as well as students with an above-average GPA who watched the symbolic strategy video. Students who watched the analogies video also reached a better conceptual understanding, were better at making generalizations, did significantly better on reasoning problems involving equations, and had a better affective reaction.