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

Authors: Küchemann, Dietmar¹; Hoyles, Celia²

Source: International Journal of Science and Mathematics Education, Volume 4, Number 4, December 2006 , pp. 581-608(28)

Publisher: Springer

Key:

- Free Content

- New Content

- Subscribed Content

- Free Trial Content

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.

Keywords: geometry curriculum; geometrical reasoning; longitudinal analysis; proof

Document Type: Research article

DOI: 10.1007/s10763-006-9039-6

Affiliations: 1: Email: d.kuchemann@ioe.ac.uk 2: Email: c.hoyles@ioe.ac.uk

The full text electronic article is available for purchase. You will be able to download the full text electronic article after payment.

$42.00 plus tax