Beyond a Relational Understanding of Fractions: Elements of Instruction that Contribute to Preservice Teachers' Knowledge and Motivation

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This study was undertaken in order to better understand preservice elementary teachers' knowledge of and motivations toward fractions before and after taking a course designed to promote relational understanding, as well as what teaching practices might be related to student outcomes. Students in five sections of the course were given a fraction assessment and a motivation questionnaire at the beginning and end of the semester, and observations were made of the nine days when fractions were taught. Students' knowledge of basic concepts improved, as did their computational skill and ability to solve word problems. However, their tendency to use inefficient algorithms did not change. Error patterns at the beginning of the semester revealed misconceptions about fractions, but errors at the end of the semester were largely reflective of low skill. Value and self-concept of ability increased while anxiety decreased, but these changes differed somewhat by instructor. In particular, having students explain their thinking instead of listen to lecture tended to have increased benefits for anxiety.