Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

Abstract

Prior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid solution strategy, mathematizing the problem (i.e., choosing particular strategies and presentations to translate the word problem into mathematical expressions), and arriving at a correct answer (executing a solution) for a word problem. By examining the responses of 350 fourth- and fifth-grade teachers in the USA to four multistep fraction word problems, we were able to explore manifestations of teachers’ strategic competence for word problems. Findings indicate that teachers’ strategic competence was closely related to whether they devised a valid strategy. Further, how teachers dealt with known and unknown quantities in their mathematization of word problems was an important indicator of their strategic competence. Teachers with strong strategic competence used algebraic notations or pictorial representations and dealt with unknown quantities more frequently in their solution methods than did teachers with weak strategic competence. The results of this study provide evidence for the critical nature of strategic competence as another dimension needed to understand and describe teachers’ mathematical knowledge.