Reader in Mathematics Education

Director, Mathematics Education Research Centre

University of Warwick, CV4 7AL

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Publications in refereed journals

*Gray, E. (1991). An Analysis of Diverging Approaches to Simple Arithmetic: Preference and its Consequences. Educational Studies in Mathematics, 22, 551–574.

*Gray, E. & Tall, D.O., (1991). Duality, ambiguity & flexibility in successful mathematical thinking. Proceedings of XV International Conference for the Psychology of Mathematics Education, Vol. II, 72–79. Assisi :Italy.

Gray, E. (1993). Count-on: The parting of the ways in simple Arithmetic. In I. Hirabayashi, N. Hohda, K Shigematsu and Fou-Lai Lin (Eds.), Proceedings of XVII International Conference for the Psychology of Mathematics Education. Vol. I, 204–211. Tsukuba: Japan.

Gray, E. & Tall, D.O., (1993). Success and failure in mathematics: The flexible meaning of symbols as process and concept, Mathematics Teaching, 142, 6–10

Gray, E. (1994). Spectrums of performance in two digit addition and subtraction. In J. P. Ponte and J. F. Matos (Eds.), Proceedings of XVIII International Conference for the Psychology of Mathematics Education, Vol. III, 25–32. Lisbon: Portugal.

Gray, E. & Tall, D.O., (1994). Duality, ambiguity and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25, 2, 115–141.

Gray, E. & Tall, D.O., (1994). Reply to Werner Liedtke, Journal for Research in Mathematics Education, 25, 5, 539–540.

Gray, E. (1995a). Children and counting: A Response to MacLellan, Education 3–13, 23, 3, 36–40.

Gray, E. & Pinto, M., (1995). Difficulties teaching Mathematical Analysis to Non-Specialists. In L. Miera & D. Carraher (Eds), Proceedings of XIX International Conference for the Psychology of Mathematics Education., Vol. II, 18–25. Recife: Brazil.

Gray, E. & Pitta, D. (1996). Number Processing: Qualitative differences in thinking and the role of imagery. In L. Puig and A Guitiérrez (Eds.), Proceedings of XX International Conference for the Psychology of Mathematics Education, Vol.4, 155–162.Valencia: Spain.

Pitta, D. & Gray, E. (1996). Nouns, Adjectives and Images in Elementary Mathematics. In L. Puig and A Guitiérrez (Eds.), Proceedings of XX International Conference for the Psychology of Mathematics Education, Vol.3, 35–42.Valencia: Spain.

Gray, E. & Pitta. D. (1997). Emily and the supercalculator. In E. Pehkonen (Ed.), Proceedings of XXI International Conference for the Psychology of Mathematics Education, Vol.4, 17–25. Lahti: Finland.

Gray, E. & Pitta. D. (1997). In the Mind...What can imagery tell us about success and failure in arithmetic? In G.A. Makrides (Ed.), Proceedings of the First Mediterranean Conference on Mathematics , 29–41. Nicosia: Cyprus.

Gray, E. & Pitta, D. (1997c). Changing Emily’s Images. Mathematics Teaching, 161, 38–51.

*Gray, E., Pitta, D. & Tall, D.O. (1997). The nature of the object as an integral component of numerical processes. In E. Pehkonen (Ed.), Proceedings of XXI International Conference for the Psychology of Mathematics Education, Vol.1, 115–130. Lahti: Finland.

Gray, E. (1999). Spatial Strategies and visualisation. Proceedings of XXIII International Conference for the Psychology of Mathematics Education, Vol. 1, 235–243. Haifa: Israel.

*Gray, E. & Pitta, D. (1999a). Images and their frames of reference: A Perspective on Cognitive Development in Elementary Arithmetic. Proceedings of XXIII International Conference for the Psychology of Mathematics Education, Vol. 3, pp. 49–57. Haifa: Israel.

*Gray, E. & Pitta, D. (1999b). A perspective on mental arithmetic. Mathematics Teaching, 167, pp.12—15.

*Gray, E. & Pitta, D., Pinto, M., Tall, D.O. (1999). Knowledge construction and diverging thinking in elementary & advanced mathematics. Educational Studies in Mathematics. Vol 38, 1-3, 111–133

Bills, C. & Gray, E. (1999). Pupils images of teachers representations. Proceedings of XXIII International Conference for the Psychology of Mathematics Education., Vol. II, 113–121. Haifa: Israel.

Klapsinou, A. & Gray, E. (1999). The intricate balance between abstract and concrete in Linear Algebra. Proceedings of XXIII International Conference for the Psychology of Mathematics Education, Vol. III, 153–161. Haifa: Israel.

*Tall, D.O., Gray, E., M.,Bin Ali, M., Crowley, L.,DeMarois, P., McGowen, M., Pitta, D.,Pinto, M., Thomas, M., Yusof,Y., (2000). Symbols and the Bifurcation between Procedural and Conceptual Thinking. The Canadian Journal of Science, Mathematics and Technology Education, 1, pp. 80–104.

Tall, D.O., Davis, G., Thomas, M., Gray, E., & Simpson, A. (2000). What is the object of the encapsulation of a process. Journal of Mathematical Behavior, 18, 2, 1–19.

*Gray, E., Pitta, D & Tall. D.O. (2000). Objects, Actions and Images: A perspective on Early Number Development. Journal of Mathematical Behavior, 18,4, 1–19.

BOOK CHAPTERS

Gray, E. (1991b). The primary mathematics textbook, intermediary in the cycle of change. In Pimm D. & Love E. (Eds.), Teaching and learning school mathematics, 122–136. London: Hodder and Stoughton.

Gray, E. (1997). Compressing the counting process: developing a flexible interpretation of symbols. In I. Thompson (Ed.), Teaching and Learning Early Number, 63–72. OUP: Buckingham, UK.

Gray, E. & Pitta, D. (1999c). Changing Emily’s Images. In A. Pinel (Ed.), Teaching, Learning and Primary Mathematics, 56–60. Association of Teachers of Mathematics: Derby.

Gray, E. & Pitta, D. (1999d). Beyond the Physical Actions: A perspective on cognitive development in arithmetic. In A. Gagatsis (Ed.), A multidimensional approach to learning in mathematics and sciences, 93–106. Intercollege Press: Cyprus.

OTHER PUBLICATIONS

Gray, E. (1988). ‘O God - Its Take Away’ : An examination of the strategies that below average children use to solve basic subtraction problems, Proceedings of BSRLM Conference, University of Warwick, May 1988, 27–29

Gray, E. (1988). Slower learning children and their range of risk in basic addition calculations. Proceedings of BSRLM Conference, University of London Institute of Education, November, 1987, 9

Gray, E. (1989). Counting and Creativity, Proceedings of BSRLM Conference, Brighton Polytechnic, May 1989, 13–14

Gray, E. (1990). New Technology in Primary Mathematics, Micromath, 6, (2), 45–46

Gray, E. & Tall, D.O., (1992a). Success and failure in mathematics: Procept and procedure. 1. A primary perspective: Workshop on Mathematics Education and Computers, Taipei National University, 209–215.

Gray, E. & Tall, D.O., (1992b). Success and failure in mathematics: Procept and procedure. 2. Secondary mathematics: Workshop on Mathematics Education and Computers, Taipei National University, 216–221

Gray, E. (1995b). Tackling the problems: An explanation for success and failure. In M. Hejeny and J. Novotná (Eds.), Proceedings of the Third International Symposium Elementary Math Teaching, 2–8. Prague: Czech Republic.

Gray, E. (1995c). Trying to get it right: A perspective on counting. In Gates (Ed.), Proceedings of the Joint Conference of the British Society for Research into Learning Mathematics and the Association of Mathematics Education Tutors, 36–40. Northampton: UK.

Gray, E. (1997). Misguided notions of mathematical development. In M. Hejeny and J. Novotná (Eds.), Proceedings of the Third International Symposium on Elementary Math Teaching, 51–53. Prague: Czech Republic.

Gray, E. (with Demetra Pitta) (1997). Evaluating children’s mental structures in elementary arithmetic. In M. Hejeny and J. Novotná (Eds.), Proceedings of the Third International Symposium on Elementary Math Teaching, 33–37. Prague: Czech Republic.

Gray, E. (with A. Klapsinou) (1998). Subsidising Definitions in a Linear Algebra Course. In W. Barker (Ed.), Proceedings of the Samos International Conference on the Teaching of Mathematics. 182–185. John Wiley:

Gray, E. & Pitta, D. (1998) The "Graphic Calculator" as a means of developing mathematics concepts. Proceedings of the Second Pancyprian Conference of Mathematics Education, pp. 60–68. Limassol: Cyprus.

Gray, E. (with A. Klapsinou) (1999). Definitions and processes: Two contrasting approaches to the teaching and learning of linear algebra.

Gray E. & Pitta Pantazi, D (2000) Descriptive and relational images: A framework for understanding numerical achievement. (Cyprus).