Across cultures and curricula, it is commonly observed that many beginning learners of formal algebra revert to familiar methods rooted in arithmetic reasoning to solve algebra problems. Though a prevalent cause for frustration in teachers trying to get students to practice and master letter-symbolic algebra, some have argued that such displays of “flexibility” in strategy choice should not be discouraged. Some even found children to be more successful in solving algebra problems when they use arithmetic methods (e.g., Nathan and Koedinger, 2000a). Are arithmetic methods more effective than algebraic methods in solving algebra word problems? Are students truly being “flexible” when they use arithmetic methods in situations calling for algebraic methods? Is it a case of flexibility or inflexibility when students persist in using arithmetic methods when they are no longer appropriate or effective? Are students’ strategy choices and their resulting success in solving algebra word problems contingent upon their cognitive capabilities and their understanding of algebra? We examined these questions by giving 157 Secondary 2 students a set of algebra word problems under specific instructions to use letter-symbolic algebra, as well as tests of their algebraic knowledge, intellectual ability, working memory, and inhibitory ability. Results revealed that(i) despite the specific instructions, a substantial number of students persisted in using arithmetic methods, suggesting a reluctance or inability to use letter-symbolic algebra; (ii)students were not more successful in solving algebra word problems when they used arithmetic methods; (iii) algebraic knowledge, intellectual ability, working memory, and inhibitory abilities contribute in both unique and overlapping ways to both strategy choice and success in solving algebra word problems. Copyright © 2009 Authors.
|Publication status||Published - Jun 2009|