Longitudinal Proof Project
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Hoyles, C & Küchemann, D, 2000, Year 8 Students' Proof Responses: Some Preliminary Findings from Four Groups, British Society for Research into Learning Mathematics, T Rowland (ed), 20, 3, pp.43-48.

Küchemann, D & Hoyles, C, 2001, Identifying Differences in Students' Evaluation of Mathematical Reasons, British Society for Research into Learning Mathematics, Proceedings, Vol 21,1 pp. 37-42

Küchemann, D & Hoyles, C, 2001, Tracing Development of Students' Algebraic Reasoning Over Time, 12th ICMI Study Conference, pp. 320-327.

Küchemann, D & Hoyles, C, 2001, Investigating factors that influence students' mathematical reasoning, Proceedings PME 25, Utrecht, Netherlands, Vol 3 pp 265-272.

Küchemann, D & Hoyles, C, 2002, The quality of students' reasons for the steps in a geometric calculation, British Society for Research into Learning Mathematics, Proceedings, 22,2. pp. 43-48.

Küchemann, D & Hoyles, C, 2002, Students' understanding of a logical implication and its converse, Proceedings PME 26, UEA, Norwich, Volume 3 pp 241-248.

Hoyles, C & Küchemann, D, 2002, Students' understanding of logical implication. Educational Studies in Mathematics, 51, 3, 193-223.

Küchemann, D & Hoyles, C, 2003, The Quality of Students' Explanations on a Non-standard Geometry Item. Proceedings of CERME 3, March 2003, Bellaria, Italy.

Küchemann, D, 2003, Angle in a circle: taking a point for a walk. Mathematics in School, March 2003.

Hoyles, C., Küchemann, D., Healy, L. and Yang, M., 2005, Students' Developing Knowledge in a Subject Discipline: Insights from combining Quantitative and Qualitative Methods. International Journal of Social Research Methodology, Vol. 8, No. 3, July 2005, pp225-238 ISSN 1364-5579

Hoyles, C & Küchemann, D, 2004, How students learn to reason mathematically: insights from a large-scale longitudinal survey, Paper submitted to AERA 2004

Küchemann, D & Hoyles, C, 2004, Year 10 students' proofs of a statement in number/algebra and their responses to related multiple choice items: longitudinal and cross-sectional comparisons. Proceedings of the British Society for Research into Learning Mathematics, 24,1, pp. 37 - 42.

Küchemann, D & Hoyles, C, 2005, Pupils' awareness of structure on two number/algebra questions, in M. Bosch (chief ed.) European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4), Sant Feliu de Guíxols, Spain, February 2005, pp 438 - 447. http://ermeweb.free.fr/CERME4/. Legal deposit B - 46971 - 2006, ISBN 84-611-3282-3.

Küchemann, D, 2005, Angle at the centre, transformed. Mathematics in School, March 2005, 34, 2, 13.

Küchemann, D & Hoyles, C, 2006, Influences on students' mathematical reasoning and patterns in its development: insights from a longitudinal study with particular reference to geometry. International Journal of Science and Mathematics Education, 4, 4, pp 581 - 608.
(ISSN 1571-0068 (Print) 1573-1774 (Online), DOI 10.1007/s10763-006-9039-6, Online Date Tuesday, August 29, 2006)

Hoyles, C & Küchemann, D, 2009 From computational to structural reasoning: tracking changes over time. Chapter in book on the learning and teaching of mathematical proof across the grades, edited by Despina Stylianou, Maria Blanton and Eric Knuth (first draft by 1 Sept 2005, revised draft by 1 Aug 2006, in press 2009)

Küchemann, D & Hoyles, C, 2006, Secondary school pupils' approaches to proof-related tasks in geometry. Proceedings of the British Society for Research into Learning Mathematics, 26, 1, pp. 53 - 58.

Küchemann, D 2006, Observations on the development of structural reasoning in a four-phase teaching sequence. Proceedings of the British Society for Research into Learning Mathematics, 26, 3, pp. 31 - 36.

Küchemann, D and Celia Hoyles, C. (2007) Changes in school students' observations and reasoning during a 4-phase teaching sequence, in L Bills, J Hodgen and H Povey (eds), Research in Mathematics Education, 9, pp 65 - 78.

Küchemann, D, 2007, Approaches to a circle-theorem task by a novice group of secondary school pupils. Proceedings of the British Society for Research into Learning Mathematics, 27, 1, pp. 42 - 47.

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