Which way is best? Students' conceptions of optimal strategies for solving equations

Good problem solvers typically know many promising approaches to solving a problem and can identify some strategies that may be better than the rest. This study is an initial exploration into this capacity, with particular emphasis on the development of students ’ conceptions of what it means for a strategy to be the “best. ” 23 sixth graders were taught the basic operators of linear equation solving and then left to discover strategies on their own in three one-hour problem solving sessions. Students were regularly asked a series of questions designed to assess their developing conceptions of what it means for a strategy to be the best. Results indicate that many students developed quite sophisticated notions of best strategies, taking into account such criteria as length of solution and quickness of execution. Those with sophisticated conceptions were also stronger on measures of transfer equation solving, flexibility, and conceptual knowledge. The ability to distinguish between effective and ineffective strategies is one of the key competencies that is integral to good problem solving in mathematics (Owen & Sweller, 1989). Good problem solvers often know many promising approaches to solving a problem and can also identify some that may be better than the rest. This study examines this capacity, with a particular focus on the development of students ’ conceptions of what it means for a strategy to b