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Anne Watson's publications
Unclassified presentations
Finding Meno, MA conference 2016
Presentation to Altius conference, Oxford 2018
Connecting concepts: clarity, caring and staying human. Keynote address for Maths Mastery conference, Feb 2019.
Books
Rowe, D., & Watson, A. (2018). Faith and Experience in Education: Essays from Quaker Perspectives. Trentham Books: London
Watson, A. and Ohtani, M. (2015) (Eds.) Task Design in Mathematics Education: An ICMI study. Heidelberg: Springer. (click here for associated papers)
Watson, A., Jones, K. and Pratt, D. (2013) Key Ideas in Teaching Mathematics: Research-based guidance for ages 9-19 (Oxford University Press + Nuffield website)
Prestage, S., Watson, A., De Geest, E. (2007) Building Learning in Mathematics. London: Continuum.
Watson, A. and Winbourne, P. (eds.) (2007) New Directions for Situated Cognition in Learning Mathematics, pub. Springer
Watson, A. (2006) Raising Achievement in Secondary Mathematics Maidenhead, Open University Press
Watson, A. and Mason, J. (2005) Mathematics as a constructive activity: learners generating examples. Lawrence Erlbaum Publishers.
Watson, A., Houssart, J. and Roaf, R. (eds.) (2005): Supporting Mathematical Thinking pub. David Fulton.
Bills,C., Bills, L., Watson, A., and Mason, J. (2004) Thinkers. Derby, UK: Association of Teachers of Mathematics
Morgan, C., Watson, A. and Tikly, C. (2004)Teaching School Subjects, 11-19: Mathematics. London:RoutledgeFalmer
Watson, A., De Geest, E., & Prestage, S. (2003) Deep Progress in Mathematics: Report of the Improving Attainment in Mathematics Project. published by University of Oxford Department of Educational Studies.
Ollerton, M. and Watson, M. (2001) Inclusive Mathematics 11-18, Continuum, London.
A. Watson (ed.) (1998) Situated Cognition and the Learning of Mathematics, CMER/QED Books
A. Watson and J. Mason: (1998) Questions and Prompts for Mathematical Thinking, Association of Teachers of Mathematics, Derby
Jaworski, B. and Watson, A. (1994) (eds.) Mentoring in Mathematics Teaching Falmer, London
London:RoutledgeFalmer
Professional articles in Mathematics Teaching
MT Archive
1987 Mathematics and Dance
1995 Differentiation
ICME and teachers
2000 Student-generated examples
2007 Exploration
GCSE coursework
Habits of mind
Instilling thinking
Powers of three
Surprise
My mistakes
Thenwhats
Variation
2008 Notation
Fragments and coherence
2009 Seeing, convincing, proving
2010 How I learn
Immersion in multiplicity
Key understandings 1,2 & 3
Rich tasks
Self in professional judgement
2012 Division
2013 Tasks part 1
2014 Consolidation
2015 Incoherent role of sequences
Tasks in classrooms
2017 Values in the mathematics classroom
2017 Variation analysing and designing tasks (with others)
2017 Problem solving, mastery, variation. Anne Watson, Nick Andrews, Helen Drury, Jenni Ingram, Sue Lowndes, Jude Stratton, Gabriel Stylianides, pp. 32-35 Mathematics Teaching 259 Dec 2017
Adolescence and mathematics
Presentations and workshops
Adolescents and mathematics 2011
Adolescence and secondary mathematics 2008
Learning mathematics in adolescence 2008
Adolescence and shifts 2007
Adventure and adolescence 2007 (ppt)
Adventure and adolescence 2007 (paper)
Mathematical thinking in adolescence 2007
Adolescent learning and secondary mathematics, presentation at Canadian Mathematics Education Study Group, Quebec, Universite Laval 2007
Published papers
2007 Watson, A.: Adolescence and Secondary Mathematics. Proceedings of the British Society for Research into Learning Mathematics 27(3) pp. 108-113 Northampton: University of Northampton.
2010 Watson, A. Shifts of mathematical thinking in adolescence. Research in Mathematics Education. 12(2) 133-148. (draft)
2008 ‘Mathematics and adolescence: not so much a battleground, more a merging of the ways’ Ontario Mathematics Gazette. 47(1) 21-23.
Presentations and workshops
Adolescents and mathematics 2011
Adolescence and secondary mathematics 2008
Learning mathematics in adolescence 2008
Adolescence and shifts 2007
Adventure and adolescence 2007 (ppt)
Adventure and adolescence 2007 (paper)
Mathematical thinking in adolescence 2007
Adolescent learning and secondary mathematics, presentation at Canadian Mathematics Education Study Group, Quebec, Universite Laval 2007
Published papers
2007 Watson, A.: Adolescence and Secondary Mathematics. Proceedings of the British Society for Research into Learning Mathematics 27(3) pp. 108-113 Northampton: University of Northampton.
2010 Watson, A. Shifts of mathematical thinking in adolescence. Research in Mathematics Education. 12(2) 133-148. (draft)
2008 ‘Mathematics and adolescence: not so much a battleground, more a merging of the ways’ Ontario Mathematics Gazette. 47(1) 21-23.
Algebra
Presentations and professional publications
Non-computational arithmetic 2014
What's X got to do with it? (NRich) 2014
Algebra keynote 2013
Algebra workshops 2013
Working algebraically 2012
Presentations and professional publications
Non-computational arithmetic 2014
What's X got to do with it? (NRich) 2014
Algebra keynote 2013
Algebra workshops 2013
Working algebraically 2012
Calculation
Mental and written calculation workshop 2013
Watson, A. (2013) Reflecting on calculation: when drilling becomes fulfilling. In B.Kaur (ed.) Nurturing reflective learners in mathematics. pp.151-166. Singapore: World Scientific. (draft)
Mental and written calculation workshop 2013
Watson, A. (2013) Reflecting on calculation: when drilling becomes fulfilling. In B.Kaur (ed.) Nurturing reflective learners in mathematics. pp.151-166. Singapore: World Scientific. (draft)
Deep Progress
(see also Adolescence)
Workshops and presentations
Deep progress 2007
Deep progress 2006
Papers
Watson, A. (2005) Deep progress in mathematics. Paper presented at Mathematics Teaching Conference, Moray House, Edinburgh, November 2005
Watson, A. (2006) Deep progress in mathematics: making a difference. Scottish Mathematical Council
Watson, A. & De Geest, E. (2005) Principled Teaching for Deep Progress: Improving Mathematical Learning Beyond Methods and Materials. Educational Studies in Mathematics 58, 209-234. ISSN 0013-1954. DRAFT
Watson, A., De Geest, E., & Prestage, S. (2003) Deep Progress in Mathematics: Report of the Improving Attainment in Mathematics Project. published by University of Oxford Department of Educational Studies. ISBN 0903535688
(see also Adolescence)
Workshops and presentations
Deep progress 2007
Deep progress 2006
Papers
Watson, A. (2005) Deep progress in mathematics. Paper presented at Mathematics Teaching Conference, Moray House, Edinburgh, November 2005
Watson, A. (2006) Deep progress in mathematics: making a difference. Scottish Mathematical Council
Watson, A. & De Geest, E. (2005) Principled Teaching for Deep Progress: Improving Mathematical Learning Beyond Methods and Materials. Educational Studies in Mathematics 58, 209-234. ISSN 0013-1954. DRAFT
Watson, A., De Geest, E., & Prestage, S. (2003) Deep Progress in Mathematics: Report of the Improving Attainment in Mathematics Project. published by University of Oxford Department of Educational Studies. ISBN 0903535688
Exemplification
Workshops and professional writing
Example spaces (Matematikbiennalen) 2008
Exploring example spaces 2006
The role of examples in mathematical reasoning 2013
Papers
Sandefur, J., Mason, J., Stylianides, G. J., & Watson, A. (2013). Generating and using examples in the proving process. Educational Studies in Mathematics, 83(3), 323-340.
Watson, A., Sandefur, J., Mason, J., & Stylianides, G. (2013) The use of examples to provide representations in proving. In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International 4 - 377 Group for the Psychology of Mathematics Education, Vol. 4, pp. 377-384. Kiel, Germany: PME
Watson, A. & Chick, H. (2011) Qualities of examples in learning and teaching. ZDM: The international journal in mathematics education 43(3) 283-294 (draft)
Sinclair, N., Watson, A., Zazkis, R. and Mason, J. (2011) The structure of personal example spaces. Journal of Mathematical Behavior. 30, 291-303. DRAFT.
Watson, A. and Shipman, S.(2008) Using learner-generated examples to introduce new concepts. Educational Studies in Mathematics. 69: 97-109. DRAFT
Bills, L. & Watson, A (2008) Editorial introduction. Special Issue: Role and use of exemplification in mathematics education Educational Studies in Mathematics. 69: 77-79
Watson, A. and Bills, L. (eds.) (2008) The Role of Examples in Mathematics Education. Special issue of Educational Studies in Mathematics. 69.
Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., Zaslavsky, O. (2006) Exemplification in mathematics education. in Novotna, J. Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education. (pp. 125-154) Charles University, Prague
Sinclair, N., Watson, A., Zazkis, R., (2005) Learner-generated examples In Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group. pp.45-53
Watson, A. & Mason, J. (2002) Extending example spaces as a learning/teaching strategy, in A.Cockburn and E.Nardi (eds.)Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education. Pp.4-377-4-384, University of Norwich.
Watson, A. and Mason, J.(2002). 'Student-generated Examples in the Learning of Mathematics' Canadian Journal of Science, Mathematics and Technology Education 2(2) pp.237-249
Mason, J. & Watson, A. (2001) 'Stimulating Students to Construct Boundary Examples' Questiones Mathematicae Suppl. 1 pp.123-132.
Watson, A. and Mason, J. (2000) 'Student generated examples' Mathematics Teaching 172, pp.59-62
Sinclair, N., Zazkis, R., Watson, A. (2004) ‘Learner generated examples’ Report of CMESG Working Group on Exemplification.
Mason, J. & Watson, A. (1999) 'Getting Students to Create Boundary Examples' Teaching and Learning Undergraduate Mathematics Newsletter 11, republished in Learning and Teaching Support Network Centre for Mathematics, Statistics and Operations Research Newsletter, 2001 pp.9-11
Workshops and professional writing
Example spaces (Matematikbiennalen) 2008
Exploring example spaces 2006
The role of examples in mathematical reasoning 2013
Papers
Sandefur, J., Mason, J., Stylianides, G. J., & Watson, A. (2013). Generating and using examples in the proving process. Educational Studies in Mathematics, 83(3), 323-340.
Watson, A., Sandefur, J., Mason, J., & Stylianides, G. (2013) The use of examples to provide representations in proving. In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International 4 - 377 Group for the Psychology of Mathematics Education, Vol. 4, pp. 377-384. Kiel, Germany: PME
Watson, A. & Chick, H. (2011) Qualities of examples in learning and teaching. ZDM: The international journal in mathematics education 43(3) 283-294 (draft)
Sinclair, N., Watson, A., Zazkis, R. and Mason, J. (2011) The structure of personal example spaces. Journal of Mathematical Behavior. 30, 291-303. DRAFT.
Watson, A. and Shipman, S.(2008) Using learner-generated examples to introduce new concepts. Educational Studies in Mathematics. 69: 97-109. DRAFT
Bills, L. & Watson, A (2008) Editorial introduction. Special Issue: Role and use of exemplification in mathematics education Educational Studies in Mathematics. 69: 77-79
Watson, A. and Bills, L. (eds.) (2008) The Role of Examples in Mathematics Education. Special issue of Educational Studies in Mathematics. 69.
Bills, L., Dreyfus, T., Mason, J., Tsamir, P., Watson, A., Zaslavsky, O. (2006) Exemplification in mathematics education. in Novotna, J. Proceedings of 30th Conference of the International Group for the Psychology of Mathematics Education. (pp. 125-154) Charles University, Prague
Sinclair, N., Watson, A., Zazkis, R., (2005) Learner-generated examples In Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group. pp.45-53
Watson, A. & Mason, J. (2002) Extending example spaces as a learning/teaching strategy, in A.Cockburn and E.Nardi (eds.)Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education. Pp.4-377-4-384, University of Norwich.
Watson, A. and Mason, J.(2002). 'Student-generated Examples in the Learning of Mathematics' Canadian Journal of Science, Mathematics and Technology Education 2(2) pp.237-249
Mason, J. & Watson, A. (2001) 'Stimulating Students to Construct Boundary Examples' Questiones Mathematicae Suppl. 1 pp.123-132.
Watson, A. and Mason, J. (2000) 'Student generated examples' Mathematics Teaching 172, pp.59-62
Sinclair, N., Zazkis, R., Watson, A. (2004) ‘Learner generated examples’ Report of CMESG Working Group on Exemplification.
Mason, J. & Watson, A. (1999) 'Getting Students to Create Boundary Examples' Teaching and Learning Undergraduate Mathematics Newsletter 11, republished in Learning and Teaching Support Network Centre for Mathematics, Statistics and Operations Research Newsletter, 2001 pp.9-11
Functions
Workshops and professional writing
Functions discussion at BSRLM 2011
Comparison of Students’ Understanding of Functions Israel/England 2014
Functions workshop notes 2014
Dysfunctioning with functions (MEI 2017)
Papers
Watson, A., Ayalon, M., & Lerman, S. (2018). Comparison of students’ understanding of functions in classes following English and Israeli national curricula. Educational Studies in Mathematics, 97(3), 255-272.
Ayalon, M., Watson, A. & Lerman, S. (2016) Students' conceptualisations of function revealed through definitions and examples. Research in Mathematics Education. DRAFT do not quote
Ayalon, M., Watson, A. & Lerman, S. (2016) Reasoning about variables in 11 to 18 year olds: informal, schooled and formal expression in learning about functions. Mathematics Education Research Journal DRAFT do not quote.
Ayalon, M., Watson, A., & Lerman, S. (2015). Progression Towards Functions: Students’ Performance on Three Tasks About Variables from Grades 7 to 12. International Journal of Science and Mathematics Education, 1-21. Online DOI 10.1007/s10763-014-9611-4
Ayalon, Watson and Lerman (2015) Functions represented as linear sequential data: relationships between presentation and student responses Educational Studies in Mathematics.online DRAFT
Ayalon, M., Watson, A., and Lerman, S. (2014) Comparison of Students’ Understanding of Functions throughout School Years in Israel and England. In Adams. G. (Ed.) Proceedings of the British Society for Research into Learning Mathematics 34(2) June 2014
Ayalon, M., Lerman, S., & Watson, A. (2013). Development of Students’ Understanding of Functions throughout School Years . Proceedings of the British Society for Research into Learning Mathematics, 33(2), 7-12.
Ayalon, M., Lerman, S., & Watson, A. (2013) Progression towards understanding functions: What does spatial generalisation contribute?. BCME-8, 16.
Ayalon, M., Lerman, S., & Watson, A. (2013). Graph-matching situations: some insights from a cross year survey in the UK. Research in Mathematics Education, 16(1) 73-74.
Watson, Anne, and Guershon Harel. (2013) "The role of teachers’ knowledge of functions in their teaching: A conceptual approach with illustrations from two cases." Canadian Journal of Science, Mathematics and Technology Education 13.2, 154-168. DRAFT
Crisp, R., Inglis, M., Mason, J. and Watson, A. (2012) Individual differences in generalization strategies. Research in Mathematics Education 14(3) 291-292 DRAFT
Understanding in Mathematics
Workshops and keynotes
Key understandings BCME 2010
Key understandings AMET 2010
Nuffield study ACME 2010
Key understandings NAMA 2009
Writings
Siemon, D., Horne, M., Clements, D., Confrey, J., Maloney, A., Samara, J., Tzur, R., Watson, A. (2017) Researching and using learning progressions (trajectories) in mathematics education. Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education. Pp. 109-136, Singapore.
Watson, A., Jones, K. and Pratt, D. (2010) Key Ideas in Teaching Mathematics: Research-based guidance for ages 9-19 (see books above)
Watson, A. (2010) Key understandings in learning mathematics. Scottish Mathematics Council Journal.40. 14-16.
Watson, A. (2010) Key understandings in school mathematics, 1, 2 & 3. Mathematics Teaching, 218,219,220. ATM
Nunes, T., Watson, A. and Bryant, P (2009): Key understandings in mathematics: a report to the Nuffield Foundation. (Nuffield foundation website)
Watson, A. (2002) What does it mean to understand something? In Haggarty, L. (ed.) Teaching Secondary School Mathematics: a Reader. London: Routledge
Watson, A. (2002) Teaching for understanding. In Haggarty, L. (2002) Aspects of teaching secondary mathematics. London: Routledge
Mathematics departments
Workshops and presentations
Changes in mathematics teaching 2009
Autonomous change 2008
Papers
Watson, A., De Geest, E. (2014) Department-initiated change. Educational Studies in Mathematics online first. DOI 10.1007/s10649-014-9549- DRAFT
Watson, A., and De Geest, E. (2011) Learning in mathematics through sequences of microtasks: making a difference for secondary learners International Journal of Science and Mathematics Education. 10(1), pp. 213–235. DRAFT
Beswick, K., Watson, A. & De Geest, E. (2010) Comparing theoretical perspectives for describing mathematics departments: Complexity and activity. Educational studies in mathematics. 75(2) 153-170. DOI: 10.1007/s10649-010-9248-3 DRAFT
Watson, A. and De Geest, E. (2010) Secondary Departments Making Autonomous Change. Proceedings of BCME 2010 p.130 ff.
Beswick, K., Watson, A. & DeGeest, E. (2007): Describing Mathematics Departments: The Strengths and Limitations of Complexity Theory and Activity Theory Proceedings of annual conference of Mathematics Education Research Group of Australasia. University of Tasmania, Hobart pp. 113-122
Lessons and teaching
Workshops and professional presentations
Teaching, textbooks, tutors and tensions 2017
Teaching children to reason mathematically 2014
Progress in Mathematical Thinking 2010
Teaching mathematics mathematically 2009
Matching and patching BEAM 2009
How successful teachers structure subject matter 2008
The nature of participation accorded by tasks 2007
Trigonometry card sort
Teaching trigonometry DRAFT
Papers
Pedagogic advice given in the development of the new mathematics curriculum for Wales, 2018.
Ingram, J. and Watson, A. (2018) But are students communicating mathematically? For the Learning of Mathematics. 38(2), 19.
Watson, A. (2008) How successful teachers structure the subject matter.
Watson, A. (2007) Framework for analysing and comparing the mathematical engagement afforded in lessons. Paper presented at Agder College Kristiansand, 17th April 2007.
Watson, A. (2006) Some difficulties in informal assessment in mathematics. Assessment in Education 13(1) 289-303
Watson, A. (2004) Red herrings: post-14 ‘best’ mathematics teaching and curricula . British Journal of Educational Studies ISSN 0007-1005 pp.359-376
Watson, A. (2004) Affordances, constraints and attunements in mathematical activity. In O. McNamara and R. Barwell (eds.) Research in mathematics Education, volume 6: papers of the British Society for Research into Learning Mathematics pp. 23-34 ISSN 1479-4802 ISBN 0953849856
Watson, A. (2003) Use of Unison Responses in Mathematics Classrooms. In J. Winter and S. Pope (Eds.) Research in Mathematics Education Volume 4: Papers of the British Society for Research into Learning Mathematics. pp. 35 – 49.ISBN 0953849821
De Geest, E., Watson, A and Prestage, S (2003). Thinking in ordinary lessons: what happened when nine teachers believed their failing students could think mathematically In Proceedings of 27th Conference of the International Group for the Psychology in Mathematics Education (PME), 13-18 July 2003, Honolulu, Hawaii.
Watson, A. (2002) ‘Developing Mathematical Thinking with Low Attaining Students’ in C. Bergsten (ed.) Dokumentation av 1:e Matematikbiennalen Norrkoping, Sweden pp.191-193.
Prestage, S., Watson, A., & DeGeest, E. (2002) ’Developing Ways of Being Mathematical with Low Attaining Students’; paper presented at the Annual Conference of the British Educational Research Association, University of Exeter
Watson, A., Prestage S. & DeGeest, E. (2002) ‘Moving to the Edge of the Comfort Zone: Mathematical Thinking and Strategies Used to Promote It’. Paper presented at Annual Conference of the British Educational Research Association, University of Exeter.
De Geest, E., Watson, Anne and Prestage, Stephanie (2002). Building a holistic view of mathematical thinking - data evaluation of improving attainment in mathematics project._ In: Proceedings of the British Society into the Research and Learning of Mathematics, 22(3)> pp. 19–24
Watson, A. (2002) ‘Mathematical Thinking and Mathematical Achievement: Research Issues’ in Proceedings on MADIF3: Third Swedish Mathematics Education Research Seminar, Norrkoping, Sweden, January 2002 pp. 9-12.
Watson, A. (2000) Chorus Response in Cape Town Schools. Proceedings of the British Society for Research into Learning Mathematics 20(3), pp. 103-108
Workshops and professional presentations
Teaching, textbooks, tutors and tensions 2017
Teaching children to reason mathematically 2014
Progress in Mathematical Thinking 2010
Teaching mathematics mathematically 2009
Matching and patching BEAM 2009
How successful teachers structure subject matter 2008
The nature of participation accorded by tasks 2007
Trigonometry card sort
Teaching trigonometry DRAFT
Papers
Pedagogic advice given in the development of the new mathematics curriculum for Wales, 2018.
Ingram, J. and Watson, A. (2018) But are students communicating mathematically? For the Learning of Mathematics. 38(2), 19.
Watson, A. (2008) How successful teachers structure the subject matter.
Watson, A. (2007) Framework for analysing and comparing the mathematical engagement afforded in lessons. Paper presented at Agder College Kristiansand, 17th April 2007.
Watson, A. (2006) Some difficulties in informal assessment in mathematics. Assessment in Education 13(1) 289-303
Watson, A. (2004) Red herrings: post-14 ‘best’ mathematics teaching and curricula . British Journal of Educational Studies ISSN 0007-1005 pp.359-376
Watson, A. (2004) Affordances, constraints and attunements in mathematical activity. In O. McNamara and R. Barwell (eds.) Research in mathematics Education, volume 6: papers of the British Society for Research into Learning Mathematics pp. 23-34 ISSN 1479-4802 ISBN 0953849856
Watson, A. (2003) Use of Unison Responses in Mathematics Classrooms. In J. Winter and S. Pope (Eds.) Research in Mathematics Education Volume 4: Papers of the British Society for Research into Learning Mathematics. pp. 35 – 49.ISBN 0953849821
De Geest, E., Watson, A and Prestage, S (2003). Thinking in ordinary lessons: what happened when nine teachers believed their failing students could think mathematically In Proceedings of 27th Conference of the International Group for the Psychology in Mathematics Education (PME), 13-18 July 2003, Honolulu, Hawaii.
Watson, A. (2002) ‘Developing Mathematical Thinking with Low Attaining Students’ in C. Bergsten (ed.) Dokumentation av 1:e Matematikbiennalen Norrkoping, Sweden pp.191-193.
Prestage, S., Watson, A., & DeGeest, E. (2002) ’Developing Ways of Being Mathematical with Low Attaining Students’; paper presented at the Annual Conference of the British Educational Research Association, University of Exeter
Watson, A., Prestage S. & DeGeest, E. (2002) ‘Moving to the Edge of the Comfort Zone: Mathematical Thinking and Strategies Used to Promote It’. Paper presented at Annual Conference of the British Educational Research Association, University of Exeter.
De Geest, E., Watson, Anne and Prestage, Stephanie (2002). Building a holistic view of mathematical thinking - data evaluation of improving attainment in mathematics project._ In: Proceedings of the British Society into the Research and Learning of Mathematics, 22(3)> pp. 19–24
Watson, A. (2002) ‘Mathematical Thinking and Mathematical Achievement: Research Issues’ in Proceedings on MADIF3: Third Swedish Mathematics Education Research Seminar, Norrkoping, Sweden, January 2002 pp. 9-12.
Watson, A. (2000) Chorus Response in Cape Town Schools. Proceedings of the British Society for Research into Learning Mathematics 20(3), pp. 103-108
Multiplicative reasoning
Workshops and presentations
Division workshop ATM
Division - the sleeping dragon DRAFT
Division
Division as problem solving
Multiplicative reasoning card sort
Papers
Venkat, H., Askew, M., Watson, A. & Mason, J. (2019) Architecture of Mathematical Structure. FLM 39(1), 19-23.
New Curriculum 2013
Workshops and professional presentations
Making mathematics count Bristol Heads 2015
Lurking algebra 2014
Making sense of primary NC 2014
New curriculum for mathematics a personal view 2014
Opportunities in the new curriculum: Edge Hill MAST newsletter 2014
Key Ideas in NC algebra 2013
New NC role for teacher educator 2013
Reasoning in the curriculum 2013
Maths in England's schools 2012
Algebra, ratios and function summary BSRLM 2011
Workshops and professional presentations
Making mathematics count Bristol Heads 2015
Lurking algebra 2014
Making sense of primary NC 2014
New curriculum for mathematics a personal view 2014
Opportunities in the new curriculum: Edge Hill MAST newsletter 2014
Key Ideas in NC algebra 2013
New NC role for teacher educator 2013
Reasoning in the curriculum 2013
Maths in England's schools 2012
Algebra, ratios and function summary BSRLM 2011
Nature of learning school mathematics
Workshops and presentations
Culture and complexity 2015
What makes a difference in secondary mathematics BBO Hub 2015
Structure 2015
Pedagogy and abstract concepts 2013
Deep connections 2012
Reflecting on calculation Singapore 2012
Motivating formal geometry 2012
Alignment 2012
Drilling, filling, skilling, fulfilling Hong Kong 2011
Shifts of understanding Hong Kong 2011
PME plenary Brazil 2010
What we do when we do mathematics ATM 2010
School mathematics education in England 2010
Modes of enquiry 2009
What do we have to learn Stirling 2009
What do we have to learn (paper) 2009
Developing mathematical thinking in the curriculum 2008
Fragments and coherence 2008
Choirs and orchestras 2008
Papers
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. pp. 73-88. Springer Publishers.
Watson, A. & Barton, B. (2011) Teaching mathematics as the contextual application of modes of mathematical enquiry. In T. Rowland & K. Ruthven (eds.) Mathematical knowledge in teaching. NY: Springer.pp.65-82. DRAFT
Watson, A. (2010) Shifts of mathematical thinking in adolescence. Research in Mathematics Education. 12(2) 133-148 DRAFT
Watson, A. (2008)Locating the spine of mathematics teaching. Invited plenary lecture. In M. Pinto & T. Kawasaki (eds.) Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education. (pp. 23-40) Brazil: University of Minho Gerais.
Mason, Stephens and Watson (2009) Appreciating mathematical structure for all, Mathematics Education Research Journal 21(2) 10-33 DRAFT
Mason, J. & Watson, A. (2009) The Menousa. For the Learning of Mathematics 29(2) 32-37
Watson, A. (2008) School mathematics as a special kind of mathematics. Paper presented at ICMI meeting in Rome
Watson, A. (2008) School mathematics as a special kind of mathematics, DRAFT. For the Learning of Mathematics. 28(3) 3-8
Watson, A. (2008) ‘Developing and deepening mathematical knowledge for teaching: being and knowing’ paper presented at ESRC funded seminar series Mathematical Knowledge in Teaching. Cambridge University.
Watson, A. (2005) Maths 14-19: Its nature, significance, concepts and modes of engagement. Invited paper presented to the Nuffield Review of 14-19 Education and Training.
Nature of learning school mathematics
Workshops and presentations
Culture and complexity 2015
What makes a difference in secondary mathematics BBO Hub 2015
Structure 2015
Pedagogy and abstract concepts 2013
Deep connections 2012
Reflecting on calculation Singapore 2012
Motivating formal geometry 2012
Alignment 2012
Drilling, filling, skilling, fulfilling Hong Kong 2011
Shifts of understanding Hong Kong 2011
PME plenary Brazil 2010
What we do when we do mathematics ATM 2010
School mathematics education in England 2010
Modes of enquiry 2009
What do we have to learn Stirling 2009
What do we have to learn (paper) 2009
Developing mathematical thinking in the curriculum 2008
Fragments and coherence 2008
Choirs and orchestras 2008
Papers
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. pp. 73-88. Springer Publishers.
Watson, A. & Barton, B. (2011) Teaching mathematics as the contextual application of modes of mathematical enquiry. In T. Rowland & K. Ruthven (eds.) Mathematical knowledge in teaching. NY: Springer.pp.65-82. DRAFT
Watson, A. (2010) Shifts of mathematical thinking in adolescence. Research in Mathematics Education. 12(2) 133-148 DRAFT
Watson, A. (2008)Locating the spine of mathematics teaching. Invited plenary lecture. In M. Pinto & T. Kawasaki (eds.) Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education. (pp. 23-40) Brazil: University of Minho Gerais.
Mason, Stephens and Watson (2009) Appreciating mathematical structure for all, Mathematics Education Research Journal 21(2) 10-33 DRAFT
Mason, J. & Watson, A. (2009) The Menousa. For the Learning of Mathematics 29(2) 32-37
Watson, A. (2008) School mathematics as a special kind of mathematics. Paper presented at ICMI meeting in Rome
Watson, A. (2008) School mathematics as a special kind of mathematics, DRAFT. For the Learning of Mathematics. 28(3) 3-8
Watson, A. (2008) ‘Developing and deepening mathematical knowledge for teaching: being and knowing’ paper presented at ESRC funded seminar series Mathematical Knowledge in Teaching. Cambridge University.
Watson, A. (2005) Maths 14-19: Its nature, significance, concepts and modes of engagement. Invited paper presented to the Nuffield Review of 14-19 Education and Training.
Practice and research
Workshops and professional presentations
Why what works does not work IMA 'Barriers and Enablers' conference Glasgow 2015
Why what works does not work (paper) IMA 'Barriers and Enablers' conference Glasgow 2015
Practice and subject-specific educational research (paper) 2013
Practice and subject-specific educational research 2013
Issues in research and practice in mathematics education 2012
Classroom research: teacher-student interaction 2008
Putting research into practice 2008
Directions of research-informed PD 2007
Research impact in mathematics education
Workshops and professional presentations
Why what works does not work IMA 'Barriers and Enablers' conference Glasgow 2015
Why what works does not work (paper) IMA 'Barriers and Enablers' conference Glasgow 2015
Practice and subject-specific educational research (paper) 2013
Practice and subject-specific educational research 2013
Issues in research and practice in mathematics education 2012
Classroom research: teacher-student interaction 2008
Putting research into practice 2008
Directions of research-informed PD 2007
Research impact in mathematics education
Problem-solving
Workshops and professional presentations
Teaching mathematics using problem solving NC 2014
Problem-solving approach to mathematics 2013
Problem-solving presentation Kerala 2013
Division and other problem solving 2011
Workshops and professional presentations
Teaching mathematics using problem solving NC 2014
Problem-solving approach to mathematics 2013
Problem-solving presentation Kerala 2013
Division and other problem solving 2011
Teacher education
Workshops and presentations
What is the teacher educator's role in improving learning ratio ... NAMA 2012
Papers
Watson, A. (2015) Paper presented at National Education Conference Papua New Guinea, University of Goroka
Stylianides, G. J. and Watson, A. (2015) The interplay between mathematics and pedagogy: Designing tasks for mathematics teacher education in I.Thompson (Ed.) (2014) Designing Tasks in Secondary Education: Enhancing subject understanding and student engagement. London & New York: Routledge.
Watson, A. & Bills, L. (2010) Working mathematically on teaching mathematics: Preparing graduates to teach secondary mathematics. In O. Zaslavsky & P.Sullivan (eds.) Constructing knowledge for teaching secondary mathematics: tasks to enhance prospective and practicing teacher learning. NY: Springer.pp.89-102
Watson, A. and Mason, J. (2007) Taken-as-Shared: a review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education 10, 4-6, 205-215.
Workshops and presentations
What is the teacher educator's role in improving learning ratio ... NAMA 2012
Papers
Watson, A. (2015) Paper presented at National Education Conference Papua New Guinea, University of Goroka
Stylianides, G. J. and Watson, A. (2015) The interplay between mathematics and pedagogy: Designing tasks for mathematics teacher education in I.Thompson (Ed.) (2014) Designing Tasks in Secondary Education: Enhancing subject understanding and student engagement. London & New York: Routledge.
Watson, A. & Bills, L. (2010) Working mathematically on teaching mathematics: Preparing graduates to teach secondary mathematics. In O. Zaslavsky & P.Sullivan (eds.) Constructing knowledge for teaching secondary mathematics: tasks to enhance prospective and practicing teacher learning. NY: Springer.pp.89-102
Watson, A. and Mason, J. (2007) Taken-as-Shared: a review of common assumptions about mathematical tasks in teacher education. Journal of Mathematics Teacher Education 10, 4-6, 205-215.
Social justice and mathematics
(with special reference to previously low attaining young adolescents - see also Deep Progress above)
Workshops and professional presentations
The myth of ability PGCE session 2015
Learner differences Hong Kong 2011
Teachers' informal assessment practices - inequity 2008
Transforming learning capacity (paper)
Papers
Tresidder, G. and Watson, A. (2013) The Possibilities and Difficulties of Teaching Secondary Mathematics in All-Attainment Groups in Special Issue of FORUM for promoting 3-19 comprehensive education. DRAFT
Watson, A. (2010). Mathematics and comprehensive ideals. Invited paper FORUM: for promoting 3-19 comprehensive education special issue
Watson, A. (2002) 'Instances of Mathematical Thinking among Low Attaining Students in an Ordinary Secondary Classroom', Journal of Mathematical Behavior 20 pp.461-475
Morgan, C. and Watson, A. (2002) ‘The Interpretative Nature of Teachers’ Assessment of Students’ Mathematics: Issues for Equity’ Journal for Research in Mathematics Education. March 2002 pp.78-107
Watson, A. (2001) 'Changes in Mathematical Performance of Year 7 Pupils Who Were 'Boosted' for KS2 SATs. Paper presented at the annual conference of the British Educational Research Association, University of Lancaster
Watson, A.(2001) 'Low Attainers Exhibiting Higher-Order Mathematical Thinking' Support for Learning 16(4) Nov pp.179-183. ISSN 0268-2141.
Watson, A. (2000) 'Going Across the Grain: Mathematical Generalisations in a Group of Low Attainers' Nordic Studies in Mathematics Education 8,1: pp. 7-20.
Watson, A. (2000) 'Mathematics Teachers as Informal Assessors: Practices, Problems and Recommendations' Educational Studies in Mathematics. 41: pp.69-91
Watson, A. (1999) ‘Paradigmatic Conflicts in Informal Mathematics Assessment as Sources of Social Inequity’ in Burton, L. (ed.) Educational Review, 50,2, pp. 105-115
Watson, A. (1998) 'Potential Sources of Inequity in Teachers' Informal Judgements about Pupils' Mathematics' in P. Gates (ed.) Proceedings of the First International Mathematics Education and Society Conference, Nottingham ISBN 095338120X,pp.337-344
Watson, A. (1995) ‘Evidence for Pupils' Achievements in Mathematics’, For the Learning of Mathematics, Vol 15/1, pp.16-20
(with special reference to previously low attaining young adolescents - see also Deep Progress above)
Workshops and professional presentations
The myth of ability PGCE session 2015
Learner differences Hong Kong 2011
Teachers' informal assessment practices - inequity 2008
Transforming learning capacity (paper)
Papers
Tresidder, G. and Watson, A. (2013) The Possibilities and Difficulties of Teaching Secondary Mathematics in All-Attainment Groups in Special Issue of FORUM for promoting 3-19 comprehensive education. DRAFT
Watson, A. (2010). Mathematics and comprehensive ideals. Invited paper FORUM: for promoting 3-19 comprehensive education special issue
Watson, A. (2002) 'Instances of Mathematical Thinking among Low Attaining Students in an Ordinary Secondary Classroom', Journal of Mathematical Behavior 20 pp.461-475
Morgan, C. and Watson, A. (2002) ‘The Interpretative Nature of Teachers’ Assessment of Students’ Mathematics: Issues for Equity’ Journal for Research in Mathematics Education. March 2002 pp.78-107
Watson, A. (2001) 'Changes in Mathematical Performance of Year 7 Pupils Who Were 'Boosted' for KS2 SATs. Paper presented at the annual conference of the British Educational Research Association, University of Lancaster
Watson, A.(2001) 'Low Attainers Exhibiting Higher-Order Mathematical Thinking' Support for Learning 16(4) Nov pp.179-183. ISSN 0268-2141.
Watson, A. (2000) 'Going Across the Grain: Mathematical Generalisations in a Group of Low Attainers' Nordic Studies in Mathematics Education 8,1: pp. 7-20.
Watson, A. (2000) 'Mathematics Teachers as Informal Assessors: Practices, Problems and Recommendations' Educational Studies in Mathematics. 41: pp.69-91
Watson, A. (1999) ‘Paradigmatic Conflicts in Informal Mathematics Assessment as Sources of Social Inequity’ in Burton, L. (ed.) Educational Review, 50,2, pp. 105-115
Watson, A. (1998) 'Potential Sources of Inequity in Teachers' Informal Judgements about Pupils' Mathematics' in P. Gates (ed.) Proceedings of the First International Mathematics Education and Society Conference, Nottingham ISBN 095338120X,pp.337-344
Watson, A. (1995) ‘Evidence for Pupils' Achievements in Mathematics’, For the Learning of Mathematics, Vol 15/1, pp.16-20
Task design
Workshops and professional presentations
Publications
Watson, A. (2016). Parameters for practice and research in task design in mathematics education. Paper presented at TSG 36: Task Design 13th International Congress in Mathematical Education, Hamburg July 25th.
Stylianides, G., Sandefur, J., & Watson, A. (2016) Mathematical induction and explanation. Journal of Mathematical Behavior DRAFT do not quote
Watson, A. and Ohtani, M. (2015) Themes and issues in mathematics education concerning task design: Editorial introduction. In Watson, A. and Ohtani, M. (eds.) Task Design in Mathematics Education: An ICMI study. (pp. 3-18 ) Heidelberg: Springer
Watson, A. and Ohtani, M. (2015) (Eds.) Task Design in Mathematics Education: An ICMI study. Heidelberg: Springer.
Watson, A. and Thompson, D. (2015) Design issues related to text-based tasks. In Watson, A. and Ohtani, M. (eds.)
Task Design in Mathematics Education: An ICMI study. (pp.143-190) Heidelberg: Springer.
Stylianides, G. J. and Watson, A. (2015) The interplay between mathematics and pedagogy: Designing tasks for mathematics teacher education in I.Thompson (Ed.) (2014) Designing Tasks in Secondary Education: Enhancing subject understanding and student engagement. London & New York: Routledge.
McDonald, S., and Watson, A. (2010) What's in a task: generating rich mathematical activity (NCSL booklet)
Watson, A. (2008) Different versions of the 'same' task: continuous being and discrete action. Paper presented at MADIF 2008.
Watson, A. (2008). Task transformation is the teacher’s responsibility. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (eds.) Proceedings of International Group for the Psychology of Mathematics Education, vol. 1 pp.147-154. Morelia, Mexico
Watson, A. and Sullivan, P. (2008) Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (ed.) International Handbook of Mathematics Teacher Education Volume 2. pp.109-134. Rotterdam: Sense Publishers.
Watson, A. (2007) The nature of participation afforded by tasks, questions and prompts in mathematics classrooms. Research in Mathematics Education 9(1).111-126.
Watson, A. (2004) Dance and Mathematics: Engaging Senses in Learning. Australian Senior Mathematics Journal 19(1) pp. 16
Watson, A. (2004) Dance and mathematics: power of novelty in the teaching of mathematics. paper presented at ICME 2004.
Workshops and professional presentations
- Presentation at ICME 13 2016
- Powerpoint for presentation at ICME 13 2016
- Questioning in mathematics 2013
- Embedding enrichment 2013
- Task design workshop Singapore 2012
- Mathematical thinking and task design 2012
- Toulouse design workshop 2010
- DfE tasks 2010
- Task design TSG 34 ICME 2008
- Mathematically powerful task design 2008
- Good tasks and good questions 2007
- Designing and using tasks effectively
Publications
Watson, A. (2016). Parameters for practice and research in task design in mathematics education. Paper presented at TSG 36: Task Design 13th International Congress in Mathematical Education, Hamburg July 25th.
Stylianides, G., Sandefur, J., & Watson, A. (2016) Mathematical induction and explanation. Journal of Mathematical Behavior DRAFT do not quote
Watson, A. and Ohtani, M. (2015) Themes and issues in mathematics education concerning task design: Editorial introduction. In Watson, A. and Ohtani, M. (eds.) Task Design in Mathematics Education: An ICMI study. (pp. 3-18 ) Heidelberg: Springer
Watson, A. and Ohtani, M. (2015) (Eds.) Task Design in Mathematics Education: An ICMI study. Heidelberg: Springer.
Watson, A. and Thompson, D. (2015) Design issues related to text-based tasks. In Watson, A. and Ohtani, M. (eds.)
Task Design in Mathematics Education: An ICMI study. (pp.143-190) Heidelberg: Springer.
Stylianides, G. J. and Watson, A. (2015) The interplay between mathematics and pedagogy: Designing tasks for mathematics teacher education in I.Thompson (Ed.) (2014) Designing Tasks in Secondary Education: Enhancing subject understanding and student engagement. London & New York: Routledge.
McDonald, S., and Watson, A. (2010) What's in a task: generating rich mathematical activity (NCSL booklet)
Watson, A. (2008) Different versions of the 'same' task: continuous being and discrete action. Paper presented at MADIF 2008.
Watson, A. (2008). Task transformation is the teacher’s responsibility. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (eds.) Proceedings of International Group for the Psychology of Mathematics Education, vol. 1 pp.147-154. Morelia, Mexico
Watson, A. and Sullivan, P. (2008) Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (ed.) International Handbook of Mathematics Teacher Education Volume 2. pp.109-134. Rotterdam: Sense Publishers.
Watson, A. (2007) The nature of participation afforded by tasks, questions and prompts in mathematics classrooms. Research in Mathematics Education 9(1).111-126.
Watson, A. (2004) Dance and Mathematics: Engaging Senses in Learning. Australian Senior Mathematics Journal 19(1) pp. 16
Watson, A. (2004) Dance and mathematics: power of novelty in the teaching of mathematics. paper presented at ICME 2004.
Variation
Workshops and professional presentations
Variation Work Group GlowHub booklet (2018) see GlowHub website
Variation/invariance: pupils’ experience: Edge Hill University March 2018 ppt
BCME variation slides
Variation cut loose (OUP) 2017 variation_cut_loose.pptx
Variation and mastery (NCETM) 2016
Variation: the acoustic version (GlowMaths Hub Gloucestershire June 2017)
Analysis of some primary lesson segments using variation 2017
Thoughts about variation and example spaces 2017
ATM workshop problems 2016
What varies and what stays the same Middlesex 2015
Enacting variation theory 2014
Papers
Al-Murani, T., Kilhamn, C., Morgan, D., & Watson, A. (2018). Opportunities for learning: the use of variation to analyse examples of a paradigm shift in teaching primary mathematics in England. Research in Mathematics Education, 1-19.
Watson, A. (ed.) (2018) Variation in mathematics: A collection of writings from ATM Mathematics Teaching. Association of Teachers of Mathematics, Derby, UK.
Al Murani, T. , Kilhamn, C. , Morgan, D. & Watson, A. (2017) Observations about some UK primary teaching tht has been influenced by the mastery agenda. Paper presented at BSRLM June 10th Oxford.
Watson, A. (2016) Pedagogy of variations: synthesis of various notions of variation pedagogy. in Huang, R. & Li, Y. (eds.) Teaching and learning mathematics through variation. p85-105. Rotterdam: SensePublishers
Watson, A. (2014) Mathematical instruction practices and classroom environment in China: a preface. In Li, Y. and Huang, R. (eds.) How Chinese teach mathematics and improve teaching. pp.101-104. London: Routledge.
Al-Murani, T. and Watson, A. (2009) Exchange systematicity: interactional dynamics of variation in mathematics lessons. Paper presented to Variation Theory SIG at EARLi conference, Amsterdam
Kullberg, A., Watson, A. & Mason, J. (2009) Variation within, and covariation between, representations. PME Thessaloniki
Watson, A. and Mason, J. (2007) Variation and mathematical structure. Mathematics Teaching 194.
Watson, A. & Mason, J. (2006) Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making. Mathematical Thinking and Learning. 8(2) pp.91-111
Mason, J. & Watson, A. (2005) Mathematical Exercises: what is exercised, what is attended to, and how does the structure of the exercises influence these? Invited symposium paper presented at EARLi, University of Cyprus, August 2005
Workshops and professional presentations
Variation Work Group GlowHub booklet (2018) see GlowHub website
Variation/invariance: pupils’ experience: Edge Hill University March 2018 ppt
BCME variation slides
Variation cut loose (OUP) 2017 variation_cut_loose.pptx
Variation and mastery (NCETM) 2016
Variation: the acoustic version (GlowMaths Hub Gloucestershire June 2017)
Analysis of some primary lesson segments using variation 2017
Thoughts about variation and example spaces 2017
ATM workshop problems 2016
What varies and what stays the same Middlesex 2015
Enacting variation theory 2014
Papers
Al-Murani, T., Kilhamn, C., Morgan, D., & Watson, A. (2018). Opportunities for learning: the use of variation to analyse examples of a paradigm shift in teaching primary mathematics in England. Research in Mathematics Education, 1-19.
Watson, A. (ed.) (2018) Variation in mathematics: A collection of writings from ATM Mathematics Teaching. Association of Teachers of Mathematics, Derby, UK.
Al Murani, T. , Kilhamn, C. , Morgan, D. & Watson, A. (2017) Observations about some UK primary teaching tht has been influenced by the mastery agenda. Paper presented at BSRLM June 10th Oxford.
Watson, A. (2016) Pedagogy of variations: synthesis of various notions of variation pedagogy. in Huang, R. & Li, Y. (eds.) Teaching and learning mathematics through variation. p85-105. Rotterdam: SensePublishers
Watson, A. (2014) Mathematical instruction practices and classroom environment in China: a preface. In Li, Y. and Huang, R. (eds.) How Chinese teach mathematics and improve teaching. pp.101-104. London: Routledge.
Al-Murani, T. and Watson, A. (2009) Exchange systematicity: interactional dynamics of variation in mathematics lessons. Paper presented to Variation Theory SIG at EARLi conference, Amsterdam
Kullberg, A., Watson, A. & Mason, J. (2009) Variation within, and covariation between, representations. PME Thessaloniki
Watson, A. and Mason, J. (2007) Variation and mathematical structure. Mathematics Teaching 194.
Watson, A. & Mason, J. (2006) Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making. Mathematical Thinking and Learning. 8(2) pp.91-111
Mason, J. & Watson, A. (2005) Mathematical Exercises: what is exercised, what is attended to, and how does the structure of the exercises influence these? Invited symposium paper presented at EARLi, University of Cyprus, August 2005