Proof Materials Project

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.