Two teachers worked with a teacher educator and developed math problem posing (MPP) tasks for teaching ratio and proportion in two grades, using a “solve-after-pose” design approach. Data collected included: (1) Problem-solving worksheets, (2) problem-posing worksheets, math diaries sheets, students’ interviews, and, teacher’s journals. For the sixth-grade class, the worksheets were randomly assigned worksheets so that students had a balance in four semantics types and four categories of number choices. After solving, the analysis was for strategies for success and common types of mistakes. Findings showed that after posing, students changed problem structure, number, objects, and contexts. In addition, there were differences in solving related to semantic structures and number choice in word problems. For the seventh-grade class, in addition to the solve-after-pose activity, students also did “easy-difficult posing”. Students of high and low ability in math were compared. The results showed that the high-group students could apply mathematics knowledge of different units in problem posing and skillfully use numbers that were more complicated but legitimate for a solution. In addition, high-group students considered the conditions, variables, and complexity in the calculation when posing easy-difficulty problems. Finally, the teachers suggested implications on how students actively learn ratio and proportion.

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Two Studies on Learning Ratio and Proportion Using Problem Posing: Transition from Grade Six to Grade Seven

  • Shuk-kwan S. Leung

摘要

Two teachers worked with a teacher educator and developed math problem posing (MPP) tasks for teaching ratio and proportion in two grades, using a “solve-after-pose” design approach. Data collected included: (1) Problem-solving worksheets, (2) problem-posing worksheets, math diaries sheets, students’ interviews, and, teacher’s journals. For the sixth-grade class, the worksheets were randomly assigned worksheets so that students had a balance in four semantics types and four categories of number choices. After solving, the analysis was for strategies for success and common types of mistakes. Findings showed that after posing, students changed problem structure, number, objects, and contexts. In addition, there were differences in solving related to semantic structures and number choice in word problems. For the seventh-grade class, in addition to the solve-after-pose activity, students also did “easy-difficult posing”. Students of high and low ability in math were compared. The results showed that the high-group students could apply mathematics knowledge of different units in problem posing and skillfully use numbers that were more complicated but legitimate for a solution. In addition, high-group students considered the conditions, variables, and complexity in the calculation when posing easy-difficulty problems. Finally, the teachers suggested implications on how students actively learn ratio and proportion.