Developing Students' Flexibility in Solving Linear Algebraic Equations
Kawel, Kathryn A.
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.
vii, 53 p.
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