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This study investigated exemplary middle school mathematics teachers’ knowledge of students’ thinking with algebraic word problem solving and how they used this knowledge and understanding in their planning and teaching of students to solve algebraic word problems.
Initially, a questionnaire was distributed to nine teachers to gather their interpretation of students’ thinking with particular algebraic word problems. From the analysis, four teachers participated in follow-up interviews and classroom observation to identify two teachers with the clearest strength in understanding students’ mathematical thinking with algebraic word problems and the ability to clearly describe how they used this knowledge for planning to teach units in this area. Upon identification, extended classroom observations led to the development of in-depth cases where teachers were asked to describe their thinking about their planning through stimulated recall interviews.
While these two teachers demonstrated a clear understanding of students’ solution strategies for algebraic word problems, they each displayed unique ways of using their understandings in planning and teaching. In planning and teaching their lessons, they carefully chose problems amenable to multiple approaches and solutions. They relied on outlines from their previous teaching experience which they modified mentally in relying on students’ mathematical thinking. They noted their attention to student strategies enabled them to plan their lessons effectively. They used questioning to extract students’ thinking and worked to support students in taking risks. Their consistent strategies included: (1) extending time to help students unpack the algebraic word problems; (2) using students’ ideas to describe solution strategies; (3) relying on questioning to gather students’ ideas; (4) using students’ strategies to summarize the lessons. While these points suggest a student-centered instructional approach, the two teachers differed in this respect with one teacher using primarily a teacher-leaded whole class questioning approach and the other teacher using a student-centered questioning in small group work. Both approaches appeared to engage students in successfully working with the problems.
Because knowledge of students’ mathematical thinking helps teachers prepare and teach their lessons, teacher preparation programs are encouraged to provide multiple experiences in analyzing student thinking with word problems in preparation for designing their lessons. |
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