Department of Education

John H. Mason

Honorary Research Fellow

College Affiliation: Linacre College

Having taught mathematics ever since he was 15, John Mason was retired as Professor Emeritus from the Open University in 2009 where he had worked for 39.5 years. He continues an active interest in and concern for the teaching of mathematics in schools in each and every phase, from kindergarten to university.

He conducts numerous workshops for teachers in the UK and abroad, leads seminars, and presents plenary lectures, always stressing the dimension of lived-experience rather than theoretical stance.


His principal focus is thinking about mathematical problems, and supporting others who wish to foster and sustain their own thinking and the thinking of others.  Other interests include the study of how authors have expressed to students their awareness of generality, especially in textbooks on the boundary between arithmetic and algebra, and ways of working on and with mental imagery in teaching mathematics.

He is perhaps best known for being the principal author of Thinking Mathematically (with a new augmented edition published in 2009), joint author of Mathematics as a Constructive Enterprise: learner generated examples with his wife, Prof. Anne Watson, for his uncompromisingly experiential stance to research methods in Researching Your Own Practice Using the Discipline of Noticing and for his contribution to practical suggestions for teachers such as Questions & Prompts for Mathematical Thinking, and Thinkers, both written with colleagues.


See for full list


  • Mason, J. (2014). Uniqueness of Patterns Generated by Repetition. Maths Gazette. 98(541) p1-7.


  • Mason, J. & Davis, B. (2013). The Importance of Teachers’ Mathematical Awareness for In-The-Moment Pedagogy. CJSMTE 13(2) p182-197.
  • Sandefur, J. Mason, J. Stylianides, G. & Watson, A. (2013). Generating and Using Examples in The Proving Process. Educational Studies in Mathematics 83 (3) p323-340.
  • Mason, J. (2013). Working with the Whole Psyche: nurturing reflective learners. In B. Kaur (Ed.) Nurturing Reflective learners in Mathematics. Yearbook 2013 Association of Mathematics educators. Singapore: World Scientific & AME.
  • Monaghan, J. & Mason, J. (2013). Exploring the notion ‘cultural affordance’ with regard to mathematics software. In C. Smith(Ed) Proceedings of the British Society for
Research into Learning Mathematics. 32(3) p132-138. ISSN 1463-6840
  • Mason, J. (2013). Exchange as a (the?) core idea in school mathematics. In C. Smith(Ed) Proceedings of the British Society for
Research into Learning Mathematics. 32(3) p126-131. ISSN 1463-6840
  • Mason, J. (2013). Phenomenal Mathematics
 as a Source of Pedagogic Strategies for Learning from E-Screens. In M. Inprasitha (Ed.) Proceedings of the 6th East Asia Regional Conference on Mathematics Education (EARCOME6) Phuket, Thailand. p2-12.
  • Sandefur, J. & Mason, J. (2013). Circular Inclusion. College Math Journal. 44(3) p193-201.


  • Mason, J. (2012). What is Arithmetic? In M. van Zanten (Ed.) Opbrengstgericht Onderwijs – Rekenen! – Wiskiunde?. Proceedings of the 30th PANAMA Conference. Utrecht: Fisme, Universiteit Utrecht. P11-24
  • Mason, J. (2012). Undersøgelser som en made at studere matematik på. Matematik i skolen. 14 (4) p60-66.
  • Ryve, A. Nilsson, P. & Mason, J. (2012). Establishing Mathematics for Teaching Within Classroom Interactions in Teacher Education. Educational Studies in Mathematics. 81 (1) p1-14.
  • Mason, J. (2012). You Can Lead a Horse to Water…: Issues in Deepening Learning Through Deepening Teaching. In S. Hegedus & J. Roschelle (Eds.) Democratizing Access to Important Mathematics through Dynamic Representations: Contributions and Visions from the SimCalc Research Program. Berlin: Springer-Verlag. ISBN 978-94-007-5695-3
  • Mason, J. (2012). Having Good Ideas Come-to-Mind: contemporary Pólya-based advice for students of mathematics. In M. Badger, C. Sangwin & T. Hawkes (Eds.) with R. Burn, J. Mason & S. Pope (contributors). Teaching Problem-Solving in Undergraduate Mathematics. Loughborough: National HE STEM Centre.
  • Jones, C. & Mason, J. (2012). Experiential Learning. Mathematics Teaching 229 p17-20.
  • Mason, J. (2012). 3-D Proofs of 2-D Theorems. Mathematics Teaching 229 p38-41.
  • Mason, J. (2012). On Knowing in Mathematics. CULMS 5 p29-39.
  • Scataglini-Belghitar, G. & Mason, J. (2012). Establishing Appropriate Conditions: students learning to apply a theorem. IJSME 10(4) p927-953. DOI: 10.1007/s10763-011-9305-0. (


  • Mason, J. (2011). Learning From Acting On Objects. In A. Oldknow & C. Knights (Eds.). Mathematics Education with Digital Technology. Education & Digital Technology. p84-100. London: Continuum.
  • Mason, J. (2011). Trabahano com Padrões. In P. Palhares, A. Gomez & A. Amaral (Eds.). Complementos de Matemática para professors do Ensino Básico. p215-234.
  • Mason, J. (2011). Mean-Invariant Polynomial Intersections: a case study in generalization Technology, Knowledge and Learning Journal 16 (2) p183-192. DOI: 10.1007/s10758-011-9185-y
  • Mason, J. (2011). Classifying & Characterising: provoking awareness of the use of a natural power in mathematics and mathematics pedagogy. In O. Zazlavsky & P. Sullivan (Eds.) Constructing Knowledge for Teaching Secondary Mathematics. p39-56. Springer: London.
  • Scataglini-Belghitar, G. & Mason, J. Teaching Takes Place In Time, while Learning Takes Place Over time: maturation of mathematicians seen as phase transitions in Te Ara Mokoroa (the long abiding path of knowledge). In J. Hannah (Ed.) Delta Communications.
  • Mason, J. (2011). A Generalization of the Parabolic Chord Property. The College Mathematics Journal 42 (4) p326-328.
  • Sinclair, N. Watson, A. Zazkis, R. & Mason, J. (2011). The Structuring of Personal Example Spaces. Journal of Mathematical Behavior 30 (4) p291-303.
  • Mason, J. (2011). Att ta vara på barns förmågor (Making use of children’s powers to think mathematically). In B. Bergius, G. Emanuelsson, L. Emmanuelsson & R. Ryding (Eds.) Nämnaren TEMA 8. Trondheim: Nationellt Centrum för Matematikutbildning p13-20.
  • Mason, J. (2011). Envisioning What Is Possible in the Teaching and Learning of Algebra. In Jinfa Cai & Eric Knuth (Eds). Early Algebraization: a global dialogue from multiple perspectives. Advances in Mathematics Education, Springer p557-578.
  • Mason, J. (2011). Mathematics Education: theory, practice & memories over 50 years. For the Learning of Mathematics 30 (3) p3-9.
  • Mason, J. (2011). Phenomenology of Example Construction. ZDM 43 (2) p195-204. DOI 10.1007/s11858-010-0297-y
  • Mason, J. (2011). Noticing: roots and branches. In M. Sherin & R. Philips. Mathematics Teacher Noticing:  Seeing Through Teachers’ Eyes. p.35-50. Mahwah: Erlbaum.


  • Mason, J. & DeGeest, E. (2010). How an Experientially Presented Labelled-Framework Approach to Professional Development at a Distance Can Influence Teachers’ Practice. In M. Pinto & T. Kawasaki (Eds.) Proceedings of the 34th International Conference on the Psychology of Mathematics Education. Belo Horizonte: PME Vol 3 p273-280.
  • Mason, J. (2010). de definitions en Définition. Losanges 9 p2-5.
  • Mason, J. (2010). Attention and Intention in Learning About Teaching Through Teaching. In R. Leikin & R. Zazkis (Eds.) Learning Through Teaching Mathematics: development of teachers’ knowledge and expertise in practice. p23-47. New York: Springer.
  • Mason, J. (2010). Mathematics Education: theories, practice, and memories over fifty years. In B. Davis & S. Lerman (Eds.) Mathematical Action & Structures of Noticing: studies on John Mason’s contribution to mathematics education. Rotterdam: Sense.


  • Molina, M. & Mason, J. (2009). Justifications-on-Demand as a Device to Promote Shifts of Attention Associated With Relational Thinking in Elementary Arithmetic. Canadian Journal for Science Mathematics and Technology Education. 9 (4) p224-242.
  • Mason, J. Stephens, M. & Watson, A. (2009). Appreciating Mathematical Structure for All. Mathematics Education Research Journal 21 (2) p10-32.
  • Mason, J. & Klymchuk, S. (2009). Counter Examples in Calculus. London: Imperial College Press.
  • Mason, J. & Houssart, J. (Eds.) (2009). Listening Figures. Stoke on Trent: Trentham.
  • Mason, J. Watson, A. (2009). The Menousa. For The Learning of Mathematics 29 (2) p33-38.
  • contributor to Burn, B. (2009). Coming to Know: the introduction of new concepts in undergraduate mathematics. Birmingham: MSOR, University of Birmingham.
  • 2009    Mason, J. (2009). Teaching as Disciplined Enquiry. Teachers and Teaching: theory and practice 15 (2-3) p205–223.
  • Houssart, J. & Mason, J. (Eds.) (2009). Listening Counts. Stoke on Trent: Trentham.
  • Mason, J. (2009). A Study of the Movement of Attention: The Case of a Reconstructed Calculation. In C. Bergson (Ed). Proceedings of MADIF 6.
  • Mason, J. (2009). From Assenting to Asserting. In O. Skvovemose, P. Valero & O. Christensen (Eds.). University Science and Mathematics Education in Transition. p17-40. Springer, Berlin.


  • Mason, J. (2008). Joined-Up Reflections (part 2). Mathematics Teaching 211 p40-42.
  • Mason, J. (2008). Joined-Up Reflections (part 1). Mathematics Teaching 210 p42-44.
  • Goldenberg, P. & Mason, J. (2008). Spreading Light on and with Example Spaces. Educational Studies in Mathematics. 69 (2) p183-194.
  • Mason, J. (2008). Notes from a Session entitled: learning a mathematical topic: what does it mean and how can it be facilitated. MSOR 8 (3) p15-20
  • Mason, J. (2008). Thinking Algebraically and Geometrically. The Scottish Mathematical Council Journal 37 p43-45.
  • Mason, J. (2008). Phenomenal Mathematics. Plenary presentation. Proceedings of the 11th RUME Conference. San Diego.
  • Mason, J. (2008). PCK and Beyond. In P. Sullivan, & T. Wood, (Eds.) In International handbook of mathematics teacher education: Vol.1. Knowledge and beliefs in mathematics teaching and teaching development (p301-322). Rotterdam, the Netherlands: Sense Publishers.
  • Mason, J. (2008). Being Mathematical With & In Front of Learners: Attention, Awareness, and Attitude as sources of Differences between Teacher Educators, Teachers & Learners. In T. Wood (Series Ed.) & B. Jaworski (Vol. Ed.), International handbook of mathematics teacher education: Vol.4. The Mathematics Teacher Educator as a Developing Professional. Rotterdam, the Netherlands: Sense Publishers, p31-56.
  • Molina, M., Castro, E., & Mason, J. (2008). Elementary school students´ approaches to solving true/false number sentences. Revista de Investigación en Didáctica de la Matemática PNA 2(2), 75-86.
  • Mason, J. (2008) Flanking Triangles. Mathematics In Schools. 37 (1) p28-29.
  • Mason, J. & Watson, A. (2008). Mathematics as a Constructive Activity: exploiting  dimensions of possible variation.  In M. Carlson & C. Rasmussen (Eds.) Making the Connection: Research and Practice in Undergraduate Mathematics, Washington: MAA. p189-202.
  • Mason, J. (2008). From Concept Images to Pedagogic Structure for a Mathematical Topic. In C. Rasmussen & M. Carlson (Eds.) Making the connection: research into practice in undergraduate mathematics education. MAA Notes. Washington: Mathematical Association of America. p253-272.
  • Mason, J. (2008). Making Use of Children’s Powers to Produce Algebraic Thinking. In J. Kaput, D. Carraher & M. Blanton (Eds.) Algebra in the Early Grades. Lawrence Erlbaum. New York. p57-94.
  • Mason, J. (2008). Distinctive Ontogeny: ontological musings inspired by two discerning gentlemen of distinction(s), David Tall & Eddie Gray. Mediterranean Journal of Mathematics Education Vol 7 (2) p23-40.

Research topics

  • The role and structure of attention and intention in teaching,learning and doing mathematics
  • The Expression of Generality in Mathematics Textbooks
  • The Design and Use of Pedagogically Effective Tasks for Mathematics Learning
  • The Design and Use of Applets for plenary use in teaching mathematics

Current research projects

  • Learning to prove through constructing personal narratives (SSHRC Insight grant with Prof. Gila Hanna, University of Toronto)
  • Advisory panel for “Developing and trialling exemplar tasks that promote early number fluencies, strategies and number sense in Foundation Phase teaching in South Africa” (With Dr. Nicki Roberts)
  • Advisory panel for ” Strategies for ProfessionalDevelopment: Elementary In-service Teachers, Mathematical Abilities and Mathematics Classroom; University of Chile (with Prof. Patricio Felmer)
  • Advisory Panel for “The Role and Use of Examples in Learning to Prove” (with Amy Ellis, NRC-USA)
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