The development of flexibility in equation solving

This paper explores the development of students’ knowledge of mathematical procedures. Students’ tendency to develop rote knowledge of procedures has been widely commented on. An alternative, more flexible endpoint for the development of procedural knowledge is explored here, where students choose to deviate from established solving patterns on particular problems for greater efficiency. Students with no prior knowledge of formal linear equation solving techniques were taught the basic transformations of this domain. After instruction, students engaged in problem-solving sessions in two conditions. Treatment students completed the “alternative ordering task,” where they were asked to re-solve a previously completed problem but using a different ordering of transformations. Those completing alternative ordering tasks demonstrated greater flexibility.