## Emeritus Professor Derek Holton

**Office:**

**Phone:**

**Email:**dholton@maths.otago.ac.nz

** Retired April 2009 but continuing links with the Department **

### Research Interests

Graph theory and mathematics education.

### Supervision

- Julie Anderson MSc - The impact of the Intermediate Number Project (INP) on teacher classroom practice
- Wong Sew Ling MSc - The use of calculators in the teaching and learning of Intermediate school mathematics
- Palani Veloo (jointly with Canterbury University) PhD - The effect of representation and representation plus writing instruction on Mathematical thinking and effect of Year 5 and 6 pupils
- Robert Lewis PhD - Assessment in mathematics education
- Chris Linsell PhD - Activity based maths programmes

### Recent publications (since 1998)

#### Books:

- Derek Holton - Problems to Ponder, Mathematical Association, London, 1998.
- Derek Holton in collaboration with Charles Lovitt - Lighting Mathematical Fires, Curriculum Corporation, Carlton, Victoria, Australia, 1998.
- Peter Hilton, Derek Holton and Jean Pedersen - Mathematical Vistas: From a Room with Many Windows, Springer, New York, 2002.
- Marilyn Watson, Derek Holton and Sally Andrew - Children with Autism: Suggestions for Teaching in the Inclusive Classroom, Donald Beasley Institute, Dunedin, 1998.
- Derek Holton, Anthony Neyland, Jim Neyland and Bronwen Thomas - Teaching Problem Solving: An introduction for primary and junior secondary teachers, Kingsham Press, Chichester, West Sussex, U.K., 1999
- Derek Holton and Bronwen Thomas - Teaching Problem Solving in Mathematics: Years 1-8, published for Ministry of Education by Learning Media Ltd, Wellington, 1999.
- Derek Holton - Problem Solving: Answers and Teachers' Notes in Figure It Out Series, published for the Ministry of Education by Learning Media Ltd, Wellington, 2001.

#### Editor of Conference Proceedings, etc.

- Derek Holton (editor) Special Issue, International Journal of Mathematical Education in Science and Technology, 31(1), 2000.
- Holton, Derek (editor), The Teaching and Learning of Mathematics at Undergraduate Level: An ICMI Study, Kluwer Academic, 2001.

#### Chapters in Books:

- Daniel, C.M. and Holton, D. Opportunities for Talented Mathematics Students in New Zealand. In Developing Mathematically Promising Students. L.J. Sheffield (ed), The National Council of Teachers of Mathematics, USA, 192-194 (1999).
- Derek Holton - A Perspective on Able Mathematical Children in New Zealand in Exploring Issues in Mathematics Education. Proceedings of a Research Seminar on Mathematics Education (Year 0-6 Students) held at the Ministry of Education on 12 June 1998. Research and Curriculum Divisions, Ministry of Education, (1999).
- Derek Holton and Gill Thomas. Mathematical Interactions and Their Influence on Learning in Perspectives on Practice and Meaning in Mathematics and Science Classrooms. David Clarke (ed), Kluwer Academic Publishers, The Netherlands, 75-104 (2001)
- Afzal Ahmed, Derek Holton and Honor Williams. Developing Active Learners in Effective Learning and Teaching in Mathematics and Its Applications. Peter Kahn and Joseph Kyle (eds), published in association with the Institute for Learning and Teaching and The Times Higher Education Supplement, pp34-48 (2002).

#### Papers:

- Robert Aldred, Carl Berendsen, Derek Holton, Andrew Lonie and Martin Stearne - Research into matching extensions: A class exercise. Bulletin of the ICA, 22 (1998), pp 41-51.
- Aldred, R E L, Holton, D A and Porteous M J and Plummer, M D - Two results on matching extensions with prescribed and proscribed edge sets. Discrete Maths, Bulletin of the ICA, 22, 1998, pp 41-51.
- Derek Holton and Robert E. L. Aldred - Planar Graphs, Regular Graphs, Bipartite Graphs and Hamiltonicity. Australasian Journal of Combinatorics 20 (1999), pp 111-131.
- Aldred, R E L, Bau, S, Holton, D A, and McKay Breandan D - Cycles through 23 vertices in 3-connected cubic planar graphs. Graphs and Combinatorics 15 (1999), pp 373-376.
- Derek Holton and Robert E. L. Aldred - Planar Graphs, Regular Graphs, Bipartite Graphs and Hamiltonicity: Corrigendum. Australasian Journal of Combinatorics 21 (1999), p 311.
- R E L Aldred, Sheng Bau, D A Holton and B D McKay - Non-Hamiltonian 3-Connected Cubic Planar Graphs. Siam Journal of Discrete Mathematics, 13(1), (2000), pp. 25-32.
- Albert, M.H., Holton, D.A. and Nowakowski, R.J. - The ultimate categorical matching in a graph. Discrete Mathematics, 232(1), (2001), pp1-10
- Michael Albert, R E L Aldred, Derek Holton - On 3*-connected graphs. Australasian Journal of Combinatorics 24 (2001), pp 193-207.
- M H Albert, M D Atkinson, C C Handley, D A Holton and W Stromquist - On Packing Densities of Permutations. The Electronic Journal of Combinatorics R5, 9(1), (2002), pp
- Derek Holton - A First Lecture in Graph Theory. Teaching Mathematics and Its Applications 21(3), (2002), pp 105-119.
- R.E.L. Aldred, D.A. Holton, Dingjun Lou, Akira Saito * M-alternating paths in n-extendable bipartite graphs. Discrete Maths, 269 (2003) 1-11.
- Derek Holton and Jim Neyland - Mathematics Problem Solving: A Theoretical Perspective. The Mathematics Educator, 3(1), (1998), pp 1-25.
- Derek Holton, Teaching versus Lecturing: Some Thoughts on the Teaching of Mathematics at Tertiary Level, Teaching Mathematics and Its Applications, Vol. 17, No. 2, 1998, pp 49-54.
- Warwick Evans, Jean Flower and Derek Holton, Peer Tutoring in First Year Undergraduate Mathematics, in International Conference on the Teaching of Mathematics, University of Aegean, Samos, Greece, 1998, J. Wiley & Sons, Chichester, (1998), pp101-104.
- Derek Holton, Jim Neyland - Mathematical Problem Solving: A Teaching Strategy. The Mathematics Educator, 3(2), (1998), pp 1-25.
- Derek Holton - Matters for debate: Problem-solving? No. Mathematics? Yes! The Mathematical Gazette, England, July 1999, pp 1-6.
- Derek Holton, Julie Anderson, Bronwen Thomas and David Fletcher - Mathematical problem solving in support of the curriculum? International Journal of Mathematical Education in Science and Technology 30(3), (1999), pp 351-371.
- Derek Holton - A Perspective on Able Mathematical Children in New Zealand in Exploring Issues in Mathematics Education, Proceedings of a Research Seminar on Mathematics Education (Year 0-6 Students) held at the Ministry of Education on 12 June 1998. Research & Curriculum Divisions, Ministry of Education, Wellington, 1999.
- Sik Hung Ng, Margaret-Ellen Pipe, Bruce Beath, Derek Holton - Framing the Problem: effects of wording on children's statistical inferences. Educational Psychology, 19(4), 1999, pp 489-499.
- Derek Holton, Chair, ICMI Study on the Teaching and Learning of Mathematics at University Level, Foreword to Special Issue, International Journal of Mathematical Education in Science and Technology, 31(1), 2000, pp 1-2.
- Warwick Evans, Jean Flower and Derek Holton - Peer tutoring in first-year undergraduate mathematics. International Journal of Mathematical Education in Science and Technology 32(2), (2001), pp 161-173.
- Derek Holton, Afzal Ahmad, Honor Williams and Christine Hill - On the Importance of Mathematical Play. International Journal of Mathematical Education in Science and Technology 32(3), (2001), pp 401-415.
- Kian-Sam Hong, Kwok-Wing Lai, Derek Holton and Tet-Loke Liau - Reliability and validity of the Malay language version of the attitudes towards statistics. Journal of Science and Mathematics Education in Southeast Asia 24(2), (2001), pp1-6.
- Kian-Sam Hong, Kwok-Wing Lai, Derek Holton and Tet-Loke Liau - Applicability of Learning Style Scales in a Malaysian Context. Science Education International, 13(4), (2002), pp 9-13.
- Hong, K.S., Lai, K.W., and Holton, D. - Assessing the factorial structures and the reliability of the Malay Language version of the Computer Self-Efficacy Scale. Malaysian Journal of Education Technology, 2(1), (2002), pp 7-16.
- Kian-Sam Hong, Kwok-Wing Lai and Derek Holton - Students' Satisfaction and Perceived Learning with a Web-based Course. Educational Technology & Society, 1 (2003), pp.
- Derek Holton - Six circles: almost the complete story. Teaching Mathematics and Its Applications, 22(1) (2003), pp 21- 35.

#### General:

Holton, D.A. - University of Otago, Department of Mathematics and Statistics, 1988 to 1990, Problem Solving Series:

- No. 1 How To
- No. 2 Combinatorics 1
- No. 3 Number Theory
- No. 4 Graph Theory
- No. 5 Geometry 1
- No. 6 Proof
- No. 7 Geometry 2
- No. 8 IMO Questions 1
- No. 9 Combinatorics 2
- No. 10 Geometry 3
- No. 11 Number Theory 2
- No. 12 Inequalities
- No. 13 Combinatorics 3
- No. 14 IMO Questions 2
- No. 15 Creating Problems

Holton, D.A. - University of Otago, Department of Mathematics and Statistics, 1991, Cluster Mathematics Series:

- No. 1 Seven Problems
- No. 2 Geometry From a New Angle
- No. 3 Investigations
- No. 4 Public Key Cryptography
- No. 5 Seven Geometry Problems
- No. 6 Two More Investigations
- No. 7 Problems from the Past
- No. 8 December Problems 1987-1989
- No. 9 Chaos
- No. 10 December Problems 1990-1992

Neyland, J. (Ed)

- Holton, Derek - International Mathematical Olympiads. New Zealand Association of Mathematics Teachers, 3(1), (1998), pp 13-18.
- Holton, Derek - What is Mathematics? EQ Australia published by Curriculum Corporation, Literacy and Numeracy, (1998), pp 8-10.
- Holton, Derek - Chessboard Problem I. The New Zealand Mathematics Magazine, 35 (2), (1998), pp 32-33.
- Holton, Derek - Chessboard Problem II. The New Zealand Mathematics Magazine, 35 (3), (1998), pp 34-40.
- Holton, Derek - Teaching versus Lecturing - Some thoughts on the teaching of mathematics at tertiary level. Teaching Mathematics and Its Applications, 17 (2), 1998.
- Holton, Derek and Zulauf, A. - Chessboard Problems III. The New Zealand Mathematics Magazine, 36 (2), (1999), pp 53-56.
- Holton, Derek and Zulauf, A. - Chessboard Problems IV. The New Zealand Mathematics Magazine, 36 (3), (1999), pp 41-46.
- Holton, Derek - Problem-solving? No. Mathematics? Yes! The Mathematical Gazette, 83, (1999), pp 245-250.
- Holton, D. and Fletcher, D. - Qwerty Revisited. Mathematical Medley, 26(2), (1999), pp 73-79.
- Holton, Derek and Zulauf, A. - Chessboard Problems V. The New Zealand Mathematics Magazine, 37 (1), (2000), pp 36-41.
- Holton, Derek and Zulauf, A. - Chessboard Problems VI. The New Zealand Mathematics Magazine, 37 (2), (2000), pp 41-46.
- Holton, Derek - Maths needs the mana we bestow on our rugby. NZ Herald, Monday 11 September 2000.
- Holton, Derek - A worried man, maths and NZ societal values. Otago Daily Times, Tuesday October 3, 2000.
- Holton, Derek - Education success question of priorities. Otago Daily Times, Wednesday October 4 2000.
- Holton, Derek and Zulauf, A. - Chessboard Problems VII. The New Zealand Mathematics Magazine, 37 (3), (2000), pp 45-52.
- Holton, Derek and Zulauf, A. - Chessboard Problems VIII. The New Zealand Mathematics Magazine, 38 (1), (2001), pp 49-53.
- Holton, Derek and Zulauf, A. - Chessboard Problems IX. The New Zealand Mathematics Magazine, 38 (2), (2001), pp 48-52.
- Holton, Derek and Zulauf, A. - Chessboard Problems X. The New Zealand Mathematics Magazine, 38 (3), (2001), pp 65-70.
- Holton, Derek and Zulauf, A. - Chessboard Problems XI. The New Zealand Mathematics Magazine, 39 (1), (2002), pp 94-102
- Holton, Derek and Zulauf, A. - Chessboard Problems XII. The New Zealand Mathematics Magazine, 39 (2), (2002), pp 66-72.
- Holton, Derek and Zulauf, A. - Chessboard Problems XIII. The New Zealand Mathematics Magazine, 39 (3), (2002), pp 82-91.
- Derek Holton, Joe Morrison, and Gill Thomas - www.nzmaths.co.nz. Computers in New Zealand Schools, 14 (1) (2002), pp 23-26.
- Holton, Derek and Zulauf, A. - Chessboard Problems XIV. The New Zealand Mathematics Magazine, 40 (1), (2003), pp 60-67.