Talks

... for sixth formers (Years 12 and 13)

• Mathematical mystery tour

• Mathematical encounters of the third kind

• How to think logically

... for secondary schools  (Years 8, 9, 10 and 11)

• Mathematical mystery tour

... for secondary/tertiary maths teachers

• Developing algebraic fluency

• Developing skills of geometric proof

... for primary teachers and groups of parents

• Mathematical games and puzzles

 

Research Interests

• Mathematical Education
• Cognitive development

• Algebra
• Commutative rings

 

Publications

... relating to School Mathematics Teaching

• ‘Starting Points and End Points’, Mathematics in School, Vol. 31, No. 3, 23-26 (2002).

• ‘Hurdles and Strategies in the Teaching of Algebra’, Mathematics in School, Vol. 31, No. 1, 10-13 (2002).

• ‘Hurdles and Strategies in the Teaching of Algebra II’, Mathematics in School, Vol. 31, No. 4, 41-44 (2002).

• ‘Hurdles and Strategies in the Teaching of Algebra III’, Mathematics in School, Vol. 31, No. 5, 12-15 (2002).

• (with Nick Lord) ‘Hurdles and Strategies in the Teaching of Algebra IV’, Mathematics in School, Vol. 32, No. 2 (2003).

• A pocket map of algebraic manipulation, The Mathematical Association (1999).

• 'Structure in mathematics and mathematical thinking.' Mathematics Teaching No. 155, 6-10 (1996).

• (with Peter Saunders) ‘Superior sums that don’t add up to much’, The Guardian newspaper, (28th December 1994).
• ‘Is the proof in the practice?’, Mathematics in School, Vol.18, No.4, 9-13 (1989).

... in Mathematics Education

• ‘Reducing Mathematics to Human Size’, Research in Mathematics Education, Vol. 4, 115-126 (2002).

·        ‘Compressed units of mathematical thought’, Journal of Mathematical Behaviour, Vol.17, No.4, 401-404 (1999).

• (With David Tall), ‘Cognitive units, connections and mathematical proof’, Proceedings of the 21st International Conference for the Psychology of Mathematics Education, Vol.2, 41-48 (1997).

• ‘"To be or not to be": Pupils’ difficulties in negating statements.’ Proceedings of the Third British Congress on Mathematical Education, Part 1, 136-143 (1996).

• 'The impact of `meaning' on students' ability to negate statements.' Proceedings of the Nineteenth International Conference for the Psychology of Mathematics Education, Vol 2, 3-10 (1995).

... in Commutative Algebra

• ‘Commutative rings with operators (Galois theory and ramification)’, Proc. London Math. Soc. (3) 28 (1974), 274-290.

• ‘Distributive extensions of modules’, J. Algebra (2) 70 (1981), 303-315.

• ‘Multiplication modules’, J. Algebra (1) 71 (1981), 174-178.

... relating to University Mathematics Teaching

• ‘Why are proofs difficult?’, Mathematical Gazette, Vol. 84, No. 501, 415-422 (2000).

• (With Kahn P, Anderson J, Austin K, Jagger J and Chetwynd A) ‘The significanceof ideas in undergraduate mathematics; a case study of the views of lecturers and students’, Teaching Mathematics and its Applications, Vol.17, No. 2, 78-85 (1998).

• (with Johnston Anderson, Keith Austin and Janet Jagger) ‘Do third-year mathematics undergraduates know what they are supposed to know?’, Inter J. Math. Ed. in Sci. and Tech., Vol. 29, No. 3, 401-420 (1998).

• (With Anderson J, Austin K, Chetwynd A and Kahn P) ‘Supporting student learning’, Teaching Mathematics and its Applications, Vol. 19, No. 4, 166-172 (2000).

• (With Candia Morgan), ‘Theory and Practice in Undergraduate Mathematics Teaching: A Case Study’, Proceedings of the 20th International Conference for the Psychology of Mathematics Education, Vol.2, 43-50 (1996).

... of General Mathematical Interest

• ‘30 is curiouser than 24’, Mathematical Gazette, Vol. 85, No. 504, 461-462 (2001).

• (With John Silvester) ‘Circle theorems and a property of the (2,3,4) triangle’,  Mathematical Gazette, Vol. 85, No. 503, 312-316 (2001).

• ‘Less than 10p’, Mathematics in School, Vol.25, No.2, 28-29 (1996).

• ‘A thousand million leagues’, Mathematical Gazette, Vol.77, No.480, 329-336 (1993).

• (with Bill Chambers and John Silvester), ‘Guaranteeing the period of linear recurring sequences (mod 2^e)’, Institute of Electrical Engineers Proceedings-E, Vol.140, No.5, (1993), 243-245.

• ‘When is an example not an example?’, Mathematics Review, Vol.2, No.4, 20-22 (1992).

Other academic-related activities

• Council of the Mathematical Association

• Schools Committee of the London Mathematical Society

• QCA Algebra and Geometry Advisory Group

• Key Stage 3 Mathematics Test Review Group (to 2003)

• Royal Society/ JMC Working Group for the report Teaching and Learning Algebra pre-19 (September 1997)

• Royal Society/ JMC Working Group for the report Teaching and Learning of Geometry 11-19 (July 2001)

• LMS, RSS and IMA Committee for the report Tackling the Mathematics Problem (October 1995)