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.

先前有关教师数学知识的工作有助于我们理解教师知识在教与学中的重要作用。但是，教师数学知识的一个方面很少受到关注：解决单词问题的战略能力。根据数学学习的最全面的特征之一（NRC，2001），我们认为教师的数学知识还包括战略能力，这包括制定有效的解决方案策略，对问题进行数学处理（即选择特定的策略和演示文稿）。将单词问题翻译成数学表达式），然后得出正确的答案（执行解决方案）来解决单词问题。通过研究美国350位四年级和五年级教师对四个多步分数词问题的回答，我们能够探索教师对单词问题的战略能力的体现。调查结果表明，教师的战略能力与他们是否制定有效的战略密切相关。此外，教师如何在数学上解决单词问题时如何处理已知数量和未知数量，这是其战略能力的重要指标。具有较强战略能力的教师比起具有较弱战略能力的教师，使用代数符号或图形表示，并且在解决方法中更频繁地处理未知数。