Department of Education

John H. Mason

Honorary Research Fellow

College Affiliation: Linacre College

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.

Research

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.

Publications

See http://www.pmtheta.com/jhm-publications.html for full list

2019
  • 2019 Mason, J. (2019). Evolution of a Task Domain. Digital Experiences in Mathematics Education. p1-21.
    http://link.springer.com/article/10.1007/s40751-018-0046-3
2018
  • 2018 Mason, J. (2018). Commentary – Doing is not the same as thinking or construing. In A. Kajander & E. Chernoff (Eds.). Teaching and Learning Secondary School Mathematics: Canadian perspectives in an international context. Springer DOI 978-3-319-92390-1_39
  • 2018 Mason, J. Watson, A. Venkat, H. & Askew, M. (2018). Multiple Formats for Multiplication.Mathematics Teaching262 p21-22.
  • 2018 Mason, J. (2018) Making Distinctions: a phenomenological Exploration in Mathematics Education. In P. Ernest (Ed.). The Philosophy of Mathematics Education Today. ICME-13 Monographs. Springer.
  • 2018 Mason, J. (2018). Educating Awareness Through Mediated Action.In D. Hewitt, A. Coles & J. Ingram (Eds.). On Teaching and Learning Mathematics with Awareness. p71-76. Derby: ATM.
  • 2018 Mason, J. (2018). Tensions between Teacher and Student Attention. Wikiletter. maths4maryams.org/mathed/wikiletter/
  • ​2018 Mason, J. (2018). Reflecting on values emerging from practice and the value of reflecting on practice. In D. Rowe & A. Watson (Eds.). Faith and Experience in Education: essays from Quaker perspectives. p63-91. London: Trentham Books.
  • 2018 Mason, J. (2018). Combining Geometrical Transformations: a meta-mathematical narrative. In R. Zazkis & P. Herbst (Eds) Scripting approaches in mathematics education: Mathematical dialogues in research and practice. p21-52. Switzerland: Springer International.
  • 2018 Watson, A. & Mason, J. (2018). A tale of two digital games: How discussion can augment personal narratives.
    In R. Zazkis & P. Herbst (Eds) Scripting approaches in mathematics education: Mathematical dialogues in research and practice. p73-88. Springer Publishers.
  • 2018 Mason, J. (2018). Making Distinctions: a phenomenological exploration in mathematics education. In P. Ernest, (Ed). Philosophy of Mathematics Education Today. Springer.
  • ​2018 Mason, J. (2018). How Early is Too Early for Thinking Algebraically?. In C. Kieran (ed.) Teaching and Learning Algebraic Thinking with 5- to 12-Year Olds: the global evolution of an emerging field of research and practice. ICME13 Springer.
  • 2018 Mason, J. (2018). Scoping Generality: an essential component of mathematical thinking by and for all. In M. Stein. (Ed.) A Life’s Time for Mathematics Education and Problem Solving: festschrift on the occasion of Andras Ambrus’ 75th birthday. Münster: WTM.​
2017
  • 2017 Mason, J. (2017). Structuring Structural Awareness: a commentary on chapter 13. In M. Bussi & X. Sun. Building the Foundation: whole numbers in the primary grades (ICME Study 23). New York: Springer.
  • 2017 Mason, J. & Metz, M. (in press). Digging Beneath Dual Systems Theory and the Bicameral Brain: abductions about the human psyche from experience in mathematical problem solving. In U. Eligio (Ed.). Understanding Emotions in Mathematical Thinking and Learning. Cambridge: Elsevier/Academic Press.
  • 2017 Mason, J. (2017). Introduction to Part II: Variation as a Pedagogical Perspective for Classroom Instruction in China. In R. Huang & Y. Lee. Teaching and Learning Mathematics through Variation: Confucian heritage meets western theories. Rotterdam: Sense. p107-p109.
  • 2017 Mason, J. (2017). Issues in Variation Theory and How It Could Inform Pedagogical Choices. In R. Huang & Y. Lee. (Eds.). Teaching and Learning Mathematics through Variation: Confucian heritage meets western theories. Rotterdam: Sense p407-p438.
2016
  • 2016 Mason, J. (2016). Rising Above a Cause-and-Effect Stance in Mathematics Education Research. JMTE 19(4) p297-300. http://rdcu.be/npTf
  • 2016 Mason, J. (2016). When is a Problem? “When” is Actually the Problem! In P. Felmer, E. Pehkonen & J. Kilpatrick (Eds.). Posing and Solving Mathematical problems: advances and new perspectives. Switzerland: Springer. p263-285.
  • 2016 Mason, J. (2016). Reaction: Problem Posing and Solving Today. In P. Felmer, E. Pehkonen & K. Kilpatrick (Eds.). Posing and Solving Mathematical problems: advances and new perspectives. Switzerland: Springer. p109-113.
  • 2016 Mason, J. (2016). Perception, interpretation and decision making: understanding gaps between competence and performance—a commentary. In S. Blömeke & J. Star (Eds.) Perception, Interpretation and Decision Making: understanding the missing link between competence and performance. ZDM, 48 (1-2) p219-226.
  • 2016 Mason, J. (2016). Pedagogical Mathematics for Student Exploration of Threshold Concepts. In R. Göller, R. Biehler, R. Hochmuth, H-G. Rück (Eds). Didactics of Mathematics in Higher Education as a Scientific Discipline. KHDM-Report 05-2016. p224-231.
  • 2016 Mason, J. (2016). Overcoming the Algebra Barrier: being particular about the general, and generally looking beyond the particular, in homage to Mary Boole. In S. Stewart (Ed.) And the Rest is Just Algebra. Springer p97-117.
  • 2016 Mason, J. (2016). Probing Beneath the Surface of Experience. In J. Wilhelm (Ed.) Teacher Noticing.
  • 2016 Mason, J. & Hanna, G. (2016). Values in Caring for Proof. In B. Larvor (Ed.) Mathematical Cultures: the London meetings 2012-2014. Trends in the History of Science. Switzerland: Birkhauser (Springer International) p239-258.
2015
  • 2015 Mason, J. (submitted). Rising Above a Cause-and-Effect Stance in Mathematics Education Research. JMTE
  • 2015 Mason, J. (submitted). Mathematics Education: down to earth, pie in the sky or suspended animation? JMTE 
  • 2015 Mason, J. (2015). Bringing Reflection to the Fore Using Narrative Construction. Open Paper Comment on Eirini Geraniou & Manolis Mavrikis “Building Bridges To Algebra Through A Constructionist Learning Environment” in C. Kynagos & G. Futschek (Eds.) Consructivist Foundations 10 (3) p334-335.
  • 2015 Mason, J. (2015). Being Mathematical With and In-Front-Of Learners. Mathematics Teaching. ???
  • 2015 Mason, J. (2015). On Being Stuck On A Mathematical Problem: what does it mean to have something come-to-mind? LUMAT: 3(1) p101-121.
  • 2015 Mason, J. (2015). “When is a Problem?” ‘when’ is actually the problem!. Proceedings of conference on problem Solving, Santiago Chile Dec. 2013; submitted as chapter for proceedings
  • 2015 Mason, J. (2015). Developing & Using an Applet to Enrich Students’ Concept Image of Rational Polynomials. Teaching Mathematics and its Applications. doi: 10.1093/teamat/hrv004
  • 2015 Skilling, K. & Mason, J. (2015). Spaces of Values: what is available to be adopted by students. In O. Helenius (Ed.). Proceedings of MADIF 9. p137-147.
  • Mason, J. (2015). When is a Problem? Contribution in Honour of Jeremy Kilpatrick. In E. Silver & C. Keitel-Kreidt, (Eds.) Pursuing Excellence in Mathematics Education: essays in honor of Jeremy Kilpatrick. Mathematics Education Library. London: Springer.
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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