Algebra Students' Knowledge of Equivalence of Equations
This study examined algebra students' understanding of equivalent equations. Ninety-eight eighth- and ninth-grade students were presented with pairs of equations and asked to judge whether the equations in each pair were equivalent. The students were also asked to justify their answers. The responses fell into three major groups: computed solutions, judgments based on transformations of equations, and incorrect solutions. Most of the students consistently gave justifications from one group. Children who gave reasons based on transformations had a significantly higher rate of correct responses than the children who calculated solutions. In the incorrect group, the success rate was much lower than in the other two groups. Most students in the transformations group were able to transfer their knowledge to transformations not used in solving equations.