Research group: Mathematics Education

Mathematics is enacted and transformed through pedagogic practices, in schools and classrooms. We explore the teaching and learning of mathematics in:

• formal classrooms
• teacher development
• classroom interaction patterns
• the making of mathematical subjectivities

Projects address pedagogies specific to mathematical content, including the production of teachers’ and learners’ relationships with mathematics, and the particular semiotic and discursive practices associated with school mathematics.

• Ballantyne, M. & Brown, T. (2016) Close encounters of the curved kind. Mathematics Teaching 253:28-32
• Braathe, H.J. & Solomon, Y. (2015) Choosing Mathematics: the narrative of the self as a site of agency Educational Studies in Mathematics 89(2):151-166
• Brown, T., Hodson, E. & Smith, K. (2013) TIMSS mathematics has changed real mathematics forever. For the learning of Mathematics. 33(2):38-43
• Brown, T. & McNamara, O. (2011) Becoming a mathematics teacher: identity and identifications (Mathematics Education Library) Dordrecht: Springer
• Brown, T. & McNamara, O. (2011) A non-strategic future for mathematics in schools? Research Intelligence 116:24-25
• Calder, N. & Brown, T. (2010) ‘Learning through Digital Technologies’ in Walshaw, M (ed) Unpacking pedagogy: new perspectives for mathematics classrooms pp 223-244 Charlotte, North Carolina: Information Age Publishing
• de Freitas, E., Lerman, S., & Parks, A. N. (2017) ‘Qualitative methods’ in J. Cai (ed) Compendium for Research in Mathematics Education Reston, VA: National Council of Teachers of Mathematics
• de Freitas, E. (2016) Re-assembling the student body in classroom video data. International Journal of Qualitative Studies in Education 29(4):553-572
• de Freitas, E. & Zolkower, B. (2015) Tense and aspect in word problems about motion: Diagram, gesture and the felt experience of time.  Mathematics Education Research Journal 27(3):311-330
• de Freitas, E. (2013) ‘Mapping the materiality of mathematical discourse’ in D. Masny (ed) Cartographies of becoming in education: A Deleuzian perspective Continuum Publishing pp127-140
• de Freitas, E. & Zolkower, B. (2011) Developing teacher capacity to explore non-routine problems through a focus on the social semiotics of mathematics classroom discourse. Research in Mathematics Education 13 93 0:229-247
• Foyn, T., Solomon, Y. & Braathe, H.J. (2018) Clever girls’ stories: the girl they call a nerd Educational Studies in Mathematics, 98(1):77–93
• Smith, K., Hodson, E. & Brown, T. (2013) The discursive production of classroom mathematics. Mathematics Education Research Journal 25: 379-397
• Solomon, Y., Erikson, E., Smestad, B., Rodal, C. & Bjerke, A. (2017) Pre-Service Teachers Navigating intersecting Communities of Practice: early school placement Journal of Mathematics Teacher Education 20(2):141-158 
• Solomon, Y.  D. Radovic, L. Black (2016). ”I can actually be very feminine here”: contradiction and hybridity in becoming a female mathematician Educational Studies in Mathematics. 91(1)55-71
• Solomon, Y. & Croft, T. (2016) Understanding undergraduate disengagement from mathematics: addressing alienationInternational Journal of Educational Research  79:267-276
• Solomon, Y., Croft, T., Duah, F. & Lawson, D. (2014) Reshaping understandings of teaching learning relationships in undergraduate mathematics: an activity theory analysis. Learning, Culture and Social Interaction 3(4):323-333
• Zolkower, B. & de Freitas, E. (2012) Mathematical meaning-making in whole-class conversation: Functional-grammatical study of a paradigmatic text. Language and Dialogue 2(1):60-79

Mathematics curriculum reflects particular historical and cultural interests and changes over time. The curriculum serves the distinctive needs and values of different groups.

Designing curricular materials for learners demands a creative approach, plugging into the potential rich vibrancy of mathematical concepts and relations. Curriculum design explores key mathematical processes – problematising, modelling, attending to precision and structural relationships, and proving processes.

Projects focus on the design and study of mathematically rich learning tasks, piloted in both formal and informal contexts, and the impact of design at micro and macro levels across scales of mattering.

• de Freitas, E., Ferrara, F. & Ferrari, G. (2017) ‘The coordinated movements of a learning assemblage: Secondary school students exploring Wii graphing technology’ in Ferrara, F. & Ferrari, G. (eds) Innovation and technology in mathematics education Springer Verlag  

• de Freitas, E. & McCarthy, M.J. (2014) (Dis)orientation and spatial sense: Topological thinking in the middle grades. Pensamiento Numerica, PNA 9(1):41-51

• de Freitas, E. (2012) The diagram as story: Unfolding the event-structure of the mathematical diagram. For the Learning of Mathematics. 32 (2):27-33

• Dickinson, P., Eade, F., Gough, S., Hough, S. & Solomon, Y. (2016) ‘Implementing RME in England and the Cayman Islands – dealing with clashing educational ideologies’ in M. Van den Heuvel-Panhuizen (ed) Reflections from abroad on the Netherlands Didactic Tradition in Mathematics Education, Springer

• Hough, S., Solomon, Y., Dickinson, P. & Gough, S. (2017)  Investigating the impact of a Realistic Mathematics Education approach on achievement and attitudes in Post-16 GCSE resit classes Manchester: MMU/The Nuffield Foundation

• Sinclair, N., de Freitas, E. & Ferrara, F. (2013) Virtual encounters: The murky and furtive world of mathematical inventiveness ZDM – The International Journal of Mathematics Education 45(2):239-252

• Sinclair, N. & de Freitas, E. (2013) ‘The virtual curriculum: New ontologies for a mobile mathematics’ in Y. Li (ed) Mathematics curriculum in school education New York: Springer pp559-580

Aesthetics and art play a significant role in mathematical activity.

This area explores how mathematics comes to matter through material practices of various kinds, such as diagramming, gesturing and sculpting.

Our projects address the creative dimensions of mathematics in informal contexts such as museums, public parks, workplaces and community centres, and in the role of particular media (digital and other) in shaping mathematical experiences. Projects also address the role of technics in studying sensation and embodied experiences in diverse science, technology, engineering, and mathematics learning environments.  

• Brown, T., Heywood, D., Solomon, Y. & Zagorianakos, A. (2012) Experiencing the Space We share: rethinking objectivity and subjectivity. Zentralblatt fur Didaktik der Mathematik: The international journal on mathematics education45:561-572
• Brown, T. & Heywood, D. (2010) Geometry, subjectivity and the seduction of language: The regulation of spatial perception. Educational Studies in Mathematics 77(2-3):351-367
• de Freitas, E., Sinclair, N., Healey, L. (in press) Mathematical bodies: Material ecologies of teaching and learning ZDM: International Journal on Mathematics Education
• de Freitas, E. (2017) ‘The mathematical labour of artful mathematics’ in Stephanie Bunn (ed) Beauty in material practice. Routledge
• de Freitas, E. & Sinclair, N. (2014) Mathematics and the body: Material entanglements in the classroom. Cambridge University Press. Book awarded an AERA book award from Division of Curriculum Studies
• de Freitas, E. & Sinclair, N. (2014) The haptic nature of gesture: Rethinking gesture with new multi-touch digital technologies. Gesture Studies 14(3):351-374
• de Freitas, E. & Sinclair, N. (2013) New materialist ontologies in mathematics education: The body in/of mathematics. Educational Studies in Mathematics 83(3):453-470
• de Freitas, E. & Bentley, S. (2012) Material encounters with mathematics: The case for museum-based cross-curricular integration. International Journal of Educational Research 3:36-47
• de Freitas, E. & Sinclair, N. (2012) Diagram, gesture, agency: Theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics 80(1-2):133-152
• de Freitas, E. (2010). Making mathematics public: Aesthetics as the distribution of the sensible Educational Insights 13(1) Special Issue: Performing the sign: Mathematics, democracy and the arts. University of British Columbia Press

We study mathematics as both a pragmatic and speculative activity.

This area pursues philosophical and historical insights into mathematical activity and behavior of all kinds - be it expert, novice, embodied, sensuous, controlling, conceptual, algorithmic, revolutionary, human and nonhuman.

Our projects aim to increase our understanding of how mathematics – in all its diverse manifestation – operates in the world as both an expression of human cultures, but also as a kind of worldingin itself (making and mutating possible worlds). Philosophical tools are put to work in analysing ontological and epistemological questions pertaining to learning, teaching, doing and becoming mathematical. 

For example, a key question for mathematics education can be framed in this way: what kinds of new mathematical ontologies are possible in different environments?

• Brown, T. (forthcoming) Theorising mathematics education. New York: Springer
• Brown, T. (2017) ‘Concepts and commodities in mathematical learning’ in E. de Freitas, N. Sinclair & A. Coles (eds) What is a mathematical concept? pp189-202 Cambridge: Cambridge University Press
• Brown, T., Solomon Y. & Williams, J. (eds) (2016) Special Issue on Mathematics education and contemporary theory Educational Studies in Mathematics  92(3)
• Brown, T., Solomon, Y. & Williams, J. (2016) Theory in and for mathematics education: in pursuit of a critical agenda. Educational Studies in Mathematics 92(3):287-297
• Brown, T. (2016) Rationality and belief in learning mathematics. Educational Studies in Mathematics. 92(1):75-90
• Brown, T. & Walshaw, M. (2012) Mathematics education and contemporary theory: Guest editorial. Educational Studies in Mathematics, 80(1-2):1-8
• Brown, T. (2011) Mathematics education and subjectivity: cultures and cultural renewal. (Mathematics Education Library) Dordrecht: Springer
• Brown, T. (2010) Truth and the renewal of knowledge: The case of mathematics education Educational Studies in Mathematics. 75(3):329-343
• Brown, T (2010) Cultural continuity and consensus in mathematics in education. International Journal of Philosophy of Mathematics Education 25
• de Freitas, E. (2018) The mathematical continuum: A haunting problematic The mathematical enthusiast 15(1):148-158
• de Freitas, E., Sinclair, N. & Coles, A. (2017) (eds) What is a mathematical concept? Cambridge University Press
• de Freitas, E. (2017) ‘The new materialism of Charles Hinton: Spatial reasoning in 4D digital mazes’ in Ferrara, F. & Ferrari, G. Innovation and technology in mathematics education. Springer Verlag
• de Freitas, E. (2017) ‘Pre-service teachers using core philosophical questions to analyze mathematical behavior’ in B. Gold (ed) Teaching the philosophy of mathematics. Mathematics Association of America pp313-330
• de Freitas, E. & Walshaw, M. (2016) Alternative theoretical frameworks for mathematics education research: Theory meets Data. Dordrecht: Springer-Verlag Publishing
• de Freitas, E., Dixon-Ramon, E. & Lather, P. (2016) Alternative ontologies of number: Rethinking the quantitative in computational culture. Special issue of Cultural Studies – Critical Methodologies 16(5)
• de Freitas, E. (2016) Number sense and calculating children: Multiplicity, measure and Mathematical monsters. Discourse: Studies in the Cultural Politics of Education 37(5):650-661
• de Freitas, E. (2016) Material encounters and media events: What (kind of mathematics) can a body do? Educational Studies in Mathematics 91(2):185-202
• de Freitas, E. & Ferrara, F. (2015) Movement, memory, and mathematics: Henri Bergson and the ontology of learning. Studies in Philosophy of Education 34(6):565-585
• de Freitas, E. (2013) The mathematical event: Mapping the axiomatic and the problematic in school mathematics. Studies in Philosophy and Education 32:581-599
• de Freitas, E. (2013) What were you thinking? A Deleuzian/Guattarian analysis of communication in the mathematics classroom. Educational Philosophy and Theory 45(3):287-300
• de Freitas, E. (2013) ‘Mapping the materiality of mathematical discourse’ in D. Masny (ed) Cartographies of becoming in education: A Deleuzian perspective. Continuum Publishing pp127-140

Political contexts and market conditions can often trump educational principles in setting the terms of educational practices.

Processes of learning and teaching mathematics are no exception, operating within prevalent ideologies and governance models. A major challenge then is to rethink the breadth of mathematics education in resistance to reductive conceptions of mathematics, and to critique mathematics education as participating in conditions of economic and other inequity.

Our research analyses the politics of mathematics education and its research, and its place in the social world. Projects and publications address the production of mathematical hierarchies and the role of mathematics in national and international economic structures.

• Brown, T. (2017) ‘The political shaping of teacher education in STEM areas’ in J. Clandinin & J. Husu. Sage international handbook of teacher education (pp665-680) New York: Sage
• Brown, T. & Clarke, D. (2013) ‘Institutional contexts for research in mathematics education’ in Clements, M. A., Bishop, A., Keitel, C., Kilpatrick, J. & Leung, F. (eds) Third International Handbook of Mathematics Education (pp459-484)New York: Springer
• Brown, T. (2012) Subjectivity and cultural adjustment in mathematics education: a response to Wolff-Michael Roth. Educational Studies in Mathematics 80(3):475-490
• de Freitas, E. (2017) The biosocial subject: Rethinking the biopolitics of mathematics education. Keynote presentation and conference proceeding publication, at 9th International Mathematics Education and Society Conference, Volos, Greece
• de Freitas, E (2016) The Cognitive Labour of Mathematics Dis/ability: neurocognitive approaches to number sense International Journal of Education Research 79:220-230
• de Freitas, E. & Sinclair, E. (2014) The politics of the mathematics aesthetic: Curricular consensus and acts of dissensus. Philosophy of Mathematics Education Journal 28 ISSN 1465-2978
• de Freitas, E., Wagner, D., Esmonde, E., Christine, & Reid, D. (2012) Exploring authority and positioning in mathematics classroom discourse: Professional development workshop activities for teachers. The Canadian Journal of Mathematics, Science and Technology Education. 12(2):137-159
• de Freitas, E. (2012)  ‘The emotional labor of imagining otherwise: Undoing the mastery model of mathematics teacher identity’ in J. Faulkner (ed)  Disrupting pedagogies and teaching the knowledge society: Countering conservative norms with creative practices IGI Global Publishing (pp174-185)
• de Freitas, E. (2010) ‘Regulating mathematics classroom discourse: Text, context and intertextuality’ in M. Walshaw (ed) Unpacking pedagogy: New perspectives for mathematics. Charlotte, NC: Information Age Publishing Inc. (pp131-161)
• Jurdak, M. Vithal, R., de Freitas, E., Gates, P., Kollosche, D. (2016) Social and political dimensions of mathematics education: Current thinking. ICME Topical Survey, Springer Verlag
• Walshaw, M. & Brown, T. (2012) Affective productions of mathematical experience. Educational Studies in Mathematics, 80(1-2):185-200