Developing Students' Flexibility in Solving Linear Algebraic Equations
Kawel, Kathryn A.
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The present study extends research on students' flexibility in problem solving to explore the development of flexibility in algebra. 65 graduated sixth graders used the standard 4 operators (i.e., expand, combine, move, divide) to solve linear algebraic equations in either the control or alternative-ordering (AO) conditions after minimal, strictly procedural instruction. In order to encourage a flexible use of procedures, students in the AO condition were instructed to solve some equations twice using a different solution procedure each time. A post-test was given to all students after 3 consecutive days of problem solving. All students improved in problem-solving ability as evidenced by improved pre-test to post-test scores. Although most post-test measures were exploratory and found no differences between the conditions, the AO condition led to a higher level of flexibility on the post-test measure asking students to apply a particular operator in an atypical way on a line of an equation. The results of this study suggest the alternative-ordering task may be a sufficient manipulation to assess algebraic flexibility.