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Influences on Students' Mathematical Reasoning and Patterns in its Development: Insights from a Longitudinal Study with Particular Reference to Geometry

  • Dietmar KüchemannEmail author
  • Celia Hoyles
Article

Abstract

We report some findings of the Longitudinal Proof Project, which investigated patterns in high-attaining students' mathematical reasoning in algebra and in geometry and development in their reasoning, by analyses of students' responses to three annual proof tests. The paper focuses on students' responses to one non-standard geometry item. It reports how the distribution of responses to this item changed over time with some moderate progress that suggests a cognitive shift from perceptual to geometrical reasoning. However, we also note that many students made little or no progress and some regressed. Extracts from student interviews indicate that the source of this variation from the overall trend stems from the shift over the three years of the study to a more formal approach in the school geometry curriculum for high-attaining students, and the effects of this shift on what students interpreted as the didactical demands of the item.

Key words

geometry curriculum geometrical reasoning longitudinal analysis proof 

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Copyright information

© National Science Council, Taiwan 2006

Authors and Affiliations

  1. 1. Institute of EducationUniversity of LondonLondonUK

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