David Wagner

Prior to doing my PhD at the University of Alberta, I taught grades 7-12 mathematics in Canada for six years and in Swaziland for two and a half years (as part of development work with Mennonite Central Committee). It was the experience of teaching mathematics in Canada, then Swaziland, then Canada that alerted me to the highly cultural nature of mathematics teaching, which I had thought was culture-free and values-free. This experience prompted me to leave teaching to investigate the cultural nature of mathematics and the impact of mathematics teaching practices on individuals and society.

All my research focuses on human interaction in mathematics and mathematics learning. Read more about my research projects here:


Leadership

Currently, I serve as:

I have served as:

Publications

The link in each item connects to the publication in whatever form I am allowed to share online (respecting publication agreements). Thus, the most recent publications are less likely to have full text available.

Journal articles

Mesa, V. & Wagner, D. (2019). Behind the door: A critical look at the process of publication in Educational Studies in Mathematics. Educational Studies in Mathematics, in press.

Andersson, A. & Wagner, D. (2019). Identities available in intertwined discourses: Mathematics student interaction. ZDM: The International Journal of Mathematics Education, 51(3), 529-540.

Wagner, D. (2019). Changing storylines in public perceptions of mathematics education. Canadian Journal of Science, Mathematics and Technology Education, 19(1), 61-72.

Culligan, K., & Wagner, D. (2018). This is not mathematics. For the Learning of Mathematics, 38(2), 14-18.

Tatsis, K., Wagner, D., & Maj-Tatsis, B. (2018). Authority and politeness: Conflict and alignment in mathematics group work. ZDM: The International Journal of Mathematics Education, 50 (8), 1029-39.

Andersson, A. & Wagner, D. (2018). Re-mythologizing mystery in mathematics: Teaching for open landscapes versus concealment. Education Sciences, 8(2), 41.

Andersson, A. & Wagner, D. (2017). Numbers for truth and reconciliation: Mathematical choices in ethically rich texts. Journal of Mathematics and Culture, 11(3), 18-35.

Abtahi, Y. & Wagner, D. (2016). Violence in un-rooted mathematics. For the Learning of Mathematics, 36(3), 39-40.

Herbel-Eisenmann, B., Wagner, D., Johnson, K., Suh, H. & Figueras, H. (2015). Positioning in mathematics education: Revelations on an imported theory. Educational Studies in Mathematics, 89(2), 185-204.

Wagner, D., Dicks, J. & Kristmanson, P. (2015). Students' language repertoires for prediction. The Mathematics Enthusiast, 12(1), 246-261.

Wagner, D. & Herbel-Eisenmann, B. (2014). Identifying authority structures in mathematics classroom discourse — a case of a teacher's early experience in a new context. ZDM: The International Journal of Mathematics Education, 46(6), 871-882.

Morgan, C., Craig, T., Schütte, M. & Wagner, D. (2014). Language and communication in mathematics education: An overview of research in the field. ZDM: The International Journal of Mathematics Education, 46(6), 843-853.

Wagner, D. & Herbel-Eisenmann, B. (2014). Mathematics teachers' representations of authority. Journal of Mathematics Teacher Education, 17(3), 201-225.

Jorgensen, R. & Wagner, D. (2013). Mathematics education with/for indigenous peoples. Mathematics Education Research Journal, 25: 1-3.

Wagner, D. (2012). Opening mathematics texts: Resisting the seduction. Educational Studies in Mathematics, 80(1-2), 153-169. [special issue on post-modern approaches to mathematics education research, edited by Tony Brown and Margaret Walshaw]

De Freitas, E., Esmonde, I., Wagner, D., Knipping, C., Lunney Borden, L. & Reid, D. (2012). Discursive authority and socio-cultural positioning in the mathematics classroom: New directions for teacher professional development. Canadian Journal for Science, Mathematics and Technology Education, 12(2), 137-159.

Wagner, D. (2011). Warm bodies using cold mathematics. Antistasis, 1(2), 7-9.

Wagner, D. (2011). Facing the mathematics: Students' critical awareness of the elusiveness of mathematical objects. Canadian Journal of Science, Mathematics and Technology Education, special issue on "Equitable access to participation in mathematical discussions: Looking at students' discourse, experiences, and perspectives" edited by Judit Moschkovich & Indigo Esmonde, 11 (3), 292-305.

Herbel-Eisenmann, B. & Wagner, D. (2010). Appraising lexical bundles in mathematics classroom discourse: Obligation and choice. Educational Studies in Mathematics, 75(1), 43-63. associated art (manipulated photo)

Herbel-Eisenmann, B., Wagner D. & Cortes, V. (2010). Lexical bundle analysis in mathematics classroom discourse: The significance of stance. Educational Studies in Mathematics, 75(1), 23-42.

Wagner D. & Davis, B. (2010). Feeling number: Grounding number sense in a sense of quantity. Educational Studies in Mathematics, 74(1), 39-51.

Wagner, D. (2010). Structuring cultural responsiveness. Mathematical Thinking and Learning, 12(3), 258-262. [a review of: Brian Greer, Swapna Mukhopadhyay, Arthur Powell & Sharon Nelson-Barber (eds.) (2009). Culturally Responsive Mathematics Education.]

Wagner D. & Herbel-Eisenmann, B. (2009). Re-mythologizing mathematics through attention to classroom positioning. Educational Studies in Mathematics, 72(1), 1-15.

Wagner, D. (2009). If mathematics is a language, how do you swear in it? The Montana Mathematics Enthusiast, 6(3), 449-458. [reprinted in Pitici, M. (2010). The best writing on mathematics 2010. Princeton, NJ: Princeton University Press.]

Wagner D. & Herbel-Eisenmann, B. (2008). 'Just don't': The suppression and invitation of dialogue in the mathematics classroom. Educational Studies in Mathematics, 67(2), 143-157.

Wagner D. (2008). 'Just go': Mathematics students' critical awareness of routine procedure. Canadian Journal of Science, Mathematics and Technology Education, 8(1), 35-48.

Stocker, D. & Wagner, D. (2007). Talking about teaching mathematics for social justice. For the Learning of Mathematics, 27(3), 17-21. [reprinted in Our Schools / Our Selves, 17(2), 69-8.]

Herbel-Eisenmann, B. & Wagner, D. (2007). A framework for uncovering the way a textbook may position the mathematics learner. For the Learning of Mathematics, 27(2), 8-14.

Wagner, D.(2007). Students' critical awareness of voice and agency in mathematics classroom discourse. Mathematical Thinking and Learning, 9(1), 31-50.

Wagner, D. (2003). We have a problem here: 5 + 20 = 45? Mathematics Teacher, 96(9), 612-616.

Pimm, D. & Wagner, D. (2003). Investigation, mathematics education and genre: An essay review of Candia Morgan's Writing Mathematically: The Discourse of Investigation. Educational Studies in Mathematics, 53(2), 159-178.

Wagner, D. (2003). Pointing at the flow of language (book review). Canadian Journal of Science, Mathematics and Technology Education, 3(3), 393-398.

Wagner, D. (2002). Teaching mathematics for peace. Connections, 26(2), 9-12. [reprinted in Delta-K, 40(1), 17-19]

Wagner, D. (2002). Who needs mathematics teachers? Delta-K, 39(1), 12-14.

Books

Moschkovich, J., Wagner, D., Bose, A., Rodrigues, J. & Schütte, M. (Eds.) (2018). Language and communication in mathematics education: International perspectives. Dordrecht: Springer.

Musafir, S., Wagner, D., Christodoulou, E., Schreiber, J., Down, L., Ainley-Taylor, M., Lausselet, N., Johnston, R., Vania, R. & Mochizuki, Y. (Eds). (2017) Textbooks for sustainable development: A guide to embedding. New Delhi: United Nations Educational, Scientific and Cultural Organization Mahatma Gandhi Institute of Education for Peace and Sustainable Development. video from book release

Hunter, R., Civil, M., Herbel-Eisenmann, B., Planas, N. & Wagner, D. (Eds.) (2017). Mathematical discourse that breaks barriers and creates space for marginalized learners. Rotterdam: Sense.

Herbel-Eisenmann, B., Choppin, J., Wagner, D. & Pimm, D. (eds.) (2012). Equity in discourse for mathematics education: Theories, practices, and policies. Mathematics Education Library. New York: Springer.

Small, M., Connelly, R., Hamilton, D., Grant McLoughlin, J., Sterenberg, G., and Wagner, D. (2008). Understanding mathematics: Textbook for Class VIII. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (258 pages)

Small, M., Connelly, R., Grant McLoughlin, J., Sterenberg, G., and Wagner, D. (2008). Teacher's guide to understanding mathematics: Textbook for Class VIII. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (344 pages)

Small, M., Connelly, R., Hamilton, D., Sterenberg, G., and Wagner, D. (2008). Understanding mathematics: Textbook for Class VII. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (320 pages)

Small, M., Connelly, R., Sterenberg, G., and Wagner, D. (2008). Teacher's guide to understanding mathematics: Textbook for Class VII. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (338 pages)

Small, M., Grant McLoughlin, J., Kirkpatrick, C., Wagner, D., and Zimmer, D. (2007). Understanding mathematics: Textbook for Class X. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (380 pages)

Small, M., Kirkpatrick, C., Wagner, D., and Long, J. (2007). Teacher's guide to understanding mathematics: Textbook for Class X. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (326 pages)

Small, M., Grant McLoughlin, J., Kirkpatrick, C., Wagner, D., and Zimmer, D. (2007). Understanding mathematics: Textbook for Class IX. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (360 pages)

Small, M., Grant McLoughlin, J., Kirkpatrick, C., Long, J., and Wagner, D. (2007). Teacher's guide to understanding mathematics: Textbook for Class IX. Curriculum and Professional Support Division, Department of School Education: Thimpu, Bhutan. (302 pages)

Jackson, R. & Wagner, D. (2004). Try this: investigative projects for senior high mathematics, Edmonton: IONCMASTE, University of Alberta. (85 pages)

Wagner, D. (1996). Math factor - Polynomial functions student workbook: The remainder and factor theorems. Alberta Education & ACCESS Television Network.

Wagner, D. (1996). Math factor - Polynomial functions student workbook: Factoring and graphing polynomial functions. Alberta Education & ACCESS Television Network.

Wagner, D. (1996). Math factor - Polynomial functions student workbook: Applications and problem solving. Alberta Education & ACCESS Television Network.

Wagner, D. (1996). Math factor - Polynomial functions student workbook: Review. Alberta Education & ACCESS Television Network.

Book chapters

Wagner, D. (2019). Situated mathematics: Positioning mathematics ideas as human ideas. Toh, T. & Yeo, J. (Eds.). Big ideas in mathematics: Yearbook 2019, Association of Mathematics Educators (pp. 47-70). Singapore: World Scientific.

Wagner, D. & Herbel-Eisenmann, B. (2018). A discourse-based framework for identifying authority structures in mathematics classrooms. In C. Knipping, H. Strähler-Pohl, U. Gellert (Eds.). Inside the mathematics class: Sociological perspectives on participation, inclusion, and enhancement (pp. 291-313). New York: Springer.

Andersson, A. & Wagner, D. (2018). The micro-politics of counting. In T. Bartell (Ed.). Toward equity and social justice in mathematics education (pp. 191-209). Dordrecht: Springer.

Lunney Borden, L., Wagner, D. & Johnson, N. (2018). Show me your math: Mi'kmaw community members explore mathematics. In C. Nicol, S. Dawson, J. Archibald, & F. Glanfield (eds.) Living culturally responsive mathematics curriculum and pedagogy: Making a difference with/in indigenous communities (in press). Rotterdam: Sense.

Wagner, D. & Andersson, A. (2018). Intersecting language repertoires when 4-year-olds count. In J. Moschkovich, D. Wagner, A. Bose, J. Rodrigues, & M. Schütte (Eds.). Language and communication in mathematics education: International perspectives (pp. 105-118). Dordrecht: Springer.

Tatsis, K. & Wagner, D. (2018). Authority and politeness: Complementary analyses of mathematics teaching episodes. In J. Moschkovich, D. Wagner, A. Bose, J. Rodrigues, & M. Schütte (Eds.). Language and communication in mathematics education: International perspectives (pp. 171-185). Dordrecht: Springer.

Wagner, D. & Moschkovich, J. (2018). International perspectives on language and communication in mathematics education. In J. Moschkovich, D. Wagner, A. Bose, J. Rodrigues, & M. Schütte (Eds.). Language and communication in mathematics education: International perspectives (pp. 3-9). Dordrecht: Springer.

Wagner, D., Warmeling, A., Isoda, M. & Sinclair, P. (2017). Mathematics. In S. Musafir, D. Wagner, E. Christodoulou, J. Schreiber, L. Down, M. Ainley-Taylor, N. Lausselet, R. Johnston, R. Vania, & Y. Mochizuki (Eds). Textbooks for sustainable development: A guide to embedding (pp. 35-64). New Delhi: United Nations Educational, Scientific and Cultural Organization Mahatma Gandhi Institute of Education for Peace and Sustainable Development. video from book release

Wagner, D. (2017). Reflections on research positioning: Where the math is and where the people are. In H. Straehler-Pohl, N. Bohlmann & A. Pais (Eds.). The disorder of mathematics education: challenging the sociopolitical dimensions of research (pp. 291-306). New York: Springer.

Wagner, D. (2015). A speech act in mathematics education - the social turn. In P. Gates & R. Jorgensen (Eds.). Shifts in the field of mathematics education: Stephen Lerman and the turn to the social. (pp. 75-87). New York: Springer. purchase bookvideo from book release

Wagner, D. (2015). Questions and dilemmas associated with informal learning research: Introduction. In K. Sullenger & S. Turner (Eds). New ground: pushing the boundaries of studying informal learning in science, mathematics, and technology (pp. 107-112). Rotterdam: Sense Publishers.

Wagner, D. & Lunney Borden, L. (2015). Common sense and necessity in (ethno)mathematics. In K. Sullenger & S. Turner (Eds). New ground: pushing the boundaries of studying informal learning in science, mathematics, and technology (pp. 113-128). Rotterdam: Sense Publishers.

Lunney Borden, L. & Wagner, D. (2013). Naming method: "This is it, maybe, but you should talk to ...". In Jorgensen, R., Sullivan, P., & Grootenboer , P. (Ed.). Pedagogies to enhance learning for Indigenous students: Evidence based practice (pp. 105-122). New York: Springer. purchase book

Jablonka, E., Wagner, D. & Walshaw, M. (2012). Theories for studying social, political and cultural dimensions of mathematics education. In M. Clements, A. Bishop, C. Keitel, J. Kilpatrick & F. Leung (Eds.) Third International Handbook of Mathematics Education (pp. 41-66). Dordrecht: Springer.

Wagner, D. and Lunney Borden, L. (2012). Aiming for equity in (ethno)mathematics research. In Herbel-Eisenmann, B., Choppin, J., Pimm, D. & Wagner, D. (eds.) Equity in discourse for mathematics education: Theories, practices, and policies (pp. 69-88). Mathematics Education Library. New York: Springer. purchase book

Wagner, D., Choppin, J., & Herbel-Eisenmann, B. (2012). Inherent connections between discourse and equity in mathematics classroom. In Herbel-Eisenmann, B., Choppin, J., Pimm, D. & Wagner, D. (eds.) Equity in discourse for mathematics education: Theories, practices, and policies (pp. 1-16). Mathematics Education Library. New York: Springer. purchase book

Choppin, J., Herbel-Eisenmann, B. & Wagner, D. (2012). Conversations about policy and other implications of equitable discourse research. In Herbel-Eisenmann, B., Choppin, J., Pimm, D. & Wagner, D. (eds.) Equity in discourse for mathematics education: Theories, practices, and policies (pp. 205-222). Mathematics Education Library. New York: Springer. purchase book

Wagner, D. (2011). Mathematics and a non-killing worldview. In J. Pim (ed.). Engineering Nonkilling: Scientific Responsibility and the Advancement of Killing-Free Societies (pp. 109-120), Honolulu: Center for Global Nonkilling.

Lunney Borden, L. & Wagner, D. (2011). Qualities of respectful positioning and their connections to quality mathematics. In Atweh, B., Graven, M., Secada, W. & Valero, P. (eds.). Mapping equity and quality in mathematics education (pp. 379-391). New York: Springer. ISBN: 978-90-481-9802-3 purchase book

Wagner, D. (2010). If mathematics is a language, how do you swear in it? In Pitici, M. (ed.). The best writing on mathematics 2010. Princeton, NJ: Princeton University Press. [reprint of Wagner, D. (2009). If mathematics is a language, how do you swear in it? The Montana Mathematics Enthusiast, 6 (3), 449-458.] purchase book

Wagner, D. (2010). Intercultural positioning in mathematics. In B. Sriraman & V. Freiman (eds.) Interdisciplinarity for the 21st Century: Proceedings of the 3rd International Symposium on Mathematics and its Connections to Arts and Sciences, Moncton 2009. Monograph 11 in The Montana Mathematics Enthusiast Monographs in Mathematics Education, Information Age Publishing, Charlotte, NC.

Wagner, D. (2009). Critical language awareness: Listening to silence in the mathematics classroom. In Setati, K., Vithal, R., Malcolm, C., and Dhunpath, R. (eds.) Researching possibilities in mathematics, science and technology education (pp. 121-137). Hauppauge, NY: Nova. ISBN: 978-1-60692-292-7

Conference proceedings

Kim, M. & Wagner, D. (2019). Science and mathematics textbook authors' hopes for peace and sustainability in a changing world. American Educational Research Association Annual Meeting, Toronto, Canada.

Wagner, D., Amoah, E. & Yaro, K. (2019). Situated perspectives on creating mathematics tasks for peace and sustainability. In this symposium: Re-imagining the M in STEM: Mathematical actions for innovative, resilient, and culturally rich communities. American Educational Research Association Annual Meeting, Toronto, Canada.

Wagner, D., Andersson, A. & Herbel-Eisenmann, B. (2019). Available positions, identities and discourses in mathematics classrooms. Proceedings of the Tenth International Mathematics Education and Society Conference, (in press), Hyderabad, India.

Wagner, D., Culligan, K., Dicks, J., & Kristmanson, P. (2018). Language choice and meaning in prediction. Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (vol. 5, p. 186), Umeå, Sweden.

Wagner, D. (2017). Doing 43 times 12 with love. Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (vol. 1, p. 283), Singapore.

Moschkovich, J., Wagner, D., Bose, A., Rodrigues, J. & Schütte, M. (2017). Topic Study Group No. 31: Language and communication in mathematics education. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education (pp. 521-524), Dordrecht: Springer.

Herbel-Eisenmann, B. & Wagner, D. (2017). Tracing teacher researchers' talk about and use of positioning. Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 523-526), Indianapolis, USA.

Andersson, A. & Wagner, D. (2017). Balancing Acts: Numbers for truth and reconciliation. Indigenous Mathematics Education Conference, Tromsø, Norway.

Lunney Borden, L. & Wagner, D. (2017). Ethnomathematics and reconciliation. Proceedings of the Ninth International Mathematics Education and Society Conference, (vol. 1, pp. 164-168), Volos, Greece.

Andersson, A. & Wagner, D. (2017). Love and bullying in mathematical conversations. Proceedings of the Ninth International Mathematics Education and Society Conference, (vol. 2, pp. 370-381), Volos, Greece.

Andersson, A. & Wagner, D. (2016). Language repertoires for mathematical and other discourses. Proceedings of the 38th Conference of the Psychology of Mathematics Education - North American Group, (pp. 1166-1172), Tucson, USA.

Culligan, K. & Wagner, D. (2016). This is not mathematics. Proceedings of the 38th Conference of the Psychology of Mathematics Education - North American Group, (p. 1404), Tucson, USA. the poster

Tatsis, K., & Wagner, D. (2016). Authority and politeness: A combined analysis of a teaching episode. 13th International Congress on Mathematical Education, Hamburg, Germany.

Wagner, D. & Andersson, A. (2016). 4-year-old language repertoire in a counting situation. 13th International Congress on Mathematical Education, Hamburg, Germany.

Andersson, A. & Wagner, D. (2015). Questions from ethnomathematics trajectories. Proceedings of the Eighth International Mathematics Education and Society Conference (p. 270-283), Portland, Oregon.

Culligan, K., & Wagner, D. (2015). Mathematics, language, and degrees of certainty: Bilingual students' mathematical communication and probability. Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, USA.

Wagner, D., & Andersson, A. (2015). The micro-politics of students' language repertoires in counting contexts. Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, USA.

Wagner, D., & Herbel-Eisenmann, B. (2015). Positioning positioning theory in its application to mathematics education research. Positioning Theory Symposium, Bruges, Belgium.

Wagner, D. (2015). Where the math is and where the people are: reflections on research positioning. The Disorder of Mathematics Education, Berlin, Germany.

Wagner, D., Dicks, J., & Kristmanson, P. (2015). Students' language repertoires for prediction. Proceedings of the 9th Congress of European Research in Mathematics Education, Prague, Czech Republic.

Wagner, D. (2014). Privileging local cultures and demographics in the mathematics classroom. Proceedings of the Joint Meeting of PME 38 and PME-NA 36. Vol. 1, pp. 61-66. Vancouver, Canada: PME. my response to Paola Valero's plenary panel paper

Civil, M. Herbel-Eisenmann, B., Hunter, R. & Wagner, D. (2014). Mathematical discourse that breaks barriers and creates spaces for marginalised students. Proceedings of the Joint Meeting of PME 38 and PME-NA 36. Vol. 1, p.244. Vancouver, Canada: PME.

Wagner, D. & Herbel-Eisenmann, B. (2013). Disbursing authority among mathematics students. Proceedings of the Seventh International Mathematics Education and Society Conference(pp. 483-491), Cape Town, South Africa.

Herbel-Eisenmann, B. & Wagner, D. (2013). Mathematics teachers' representations of authority. Proceedings of the Seventh International Mathematics Education and Society Conference(pp. 291-300), Cape Town, South Africa.

Wagner, D., Dicks, J., & Kristmanson, P. (2013). Students' language repertoires for investigating mathematics. Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Chicago, USA.

Caswell, B. & Wagner, D. (2012). Diversities in mathematics and their relation to equity. Proceedings of the Canadian Mathematics Education Study Group Conference (pp. 81-93), Quebec City, Canada.

Wagner, D. & Herbel-Eisenmann, B. (2012). Mathematics students trying to be democractic. American Educational Research Association, Vancouver, Canada.

Herbel-Eisenmann, B., Kristmanson, P., & Wagner, D. (2011). Modality in French immersion mathematics. ICMI Study 21 Conference: Mathematics Education and Language Diversity. Sao Paulo, Brazil.

Wagner, D., Kristmanson, P. & Herbel-Eisenmann, B. (2011). The use of modality in French immersion mathematics interaction. Canadian Association of Applied Linguistics Conference, Fredericton, Canada.

Wagner, D. (2010). The seductive queen - mathematics textbook protagonist. In U. Gellert, E. Jablonka, C. Morgan (Eds.) (2010). Proceedings of the Sixth International Mathematics Education and Society Conference (pp. 438-448), Berlin, Germany.

Wagner, David (2010). Intercultural positioning in mathematics. In B. Sriraman & V. Freiman (eds.) Interdisciplinarity for the 21st Century: Proceedings of the 3rd International Symposium on Mathematics and its Connections to Arts and Sciences, Moncton 2009. Monograph 11 in The Montana Mathematics Enthusiast Monographs in Mathematics Education, Information Age Publishing, Charlotte, NC.

Saint-Pierre, Y. & Wagner, D. (2009). Mathematics as social (in)justice / Mathématiques citoyennes face à l' (in)justice sociale. Proceedings of the Canadian Mathematics EducationStudy Group Conference, Toronto, Canada.

Herbel-Eisenmann, B., & Wagner, D. (2009). (Re)conceptualizing and sharing authority. In Tzekaki, M., Kaldrimidou, M. & Sakonidis, H. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 153-160. Thessaloniki, Greece: PME.

Wagner, D. & Herbel-Eisenmann, B. (2009). Re-mythologizing mathematics by positioning. In Tzekaki, M., Kaldrimidou, M. & Sakonidis, H. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 5, pp. 297-304. Thessaloniki, Greece: PME.

Esmonde, I., Moschkovich, J. & Wagner, D. (2009). Equity and discourse in mathematics classrooms: A focus on students. Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics, Thessaloniki, Greece.

Wagner, D. (2008). Positioning theory and intercultural conversations about mathematics. Symposium on the Occasion of the 100th Anniversary of International Commission on Mathematical Instruction, Rome, Italy.

Herbel-Eisenmann, B., Wagner, D. & Cortes, V. (2008). Encoding authority: Pervasive lexical bundles in mathematics classrooms. Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education held jointly with the 30th Conference of PME-NA, Morelia, Mexico, vol. 3, pp. 153-160.

Wagner, D. & Herbel-Eisenmann, B. (2007). Discursive tools for suppressing and inviting dialogue in the mathematics classroom. Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, USA.

Wagner, D. & Lunney, L. (2007). 'Show me your math': inviting children to do ethnomathematics. Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, USA.

Lunney, L. & Wagner, D. (2007). After this research: Questioning authority when non-Aboriginal people do research in Aboriginal communities. 24th Annual Qualitative Analysis Conference.

Herbel-Eisenmann, B., Choppin, J., Staples, M. & Wagner, D. (2007). Discussion group on mathematics classroom discourse. Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Lake Tahoe, USA.

Wagner, D. & Lunney, L. (2006). Common sense, necessity, and intention in ethnomathematics. In Alatorre, S., Cortina, J., Sáiz, M., & Méndez, A. (Eds), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Merida, Mexica, vol. II, 521-523.

Lunney, L. & Wagner, D. (2006). Ethnomathematics and audience. Proceedings of the Canadian Mathematics Education Study Group Conference, Calgary, Canada, pp. 147-148.

Lunney, L. & Wagner, D. (2006). Fostering mawkinutimatimk in research and classroom practice. In Alatorre, S., Cortina, J., Sáiz, M., & Méndez, A. (Eds), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Merida, Mexica, vol. II, 505-507.

Wagner, D., Choppin, J., Herbel-Eisenmann, B., Pimm, D., and Staples, M. (2006). Discussion group on mathematics classroom discourse. In Alatorre, S., Cortina, J., Sáiz, M., & Méndez, A. (Eds), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Merida, Mexica, vol. I, 79-82.

Herbel-Eisenmann, B., Choppin, J., Empson, S., Lehrer, R., Seymour, J., Staples, M. & Wagner, D. (2006). Connecting discourse, teaching, and curriculum. National Council of Teachers of Mathematics Research Pre-session, St. Louis, Missouri.

Wagner, D. (2005) Silence and voice in the mathematics classroom. Canadian Mathematics Education Study Group Conference, Ottawa, Canada, 119-126.

Herbel-Eisenmann, B. & Wagner, D. (2005). In the middle of nowhere: How a textbook can position the mathematics learner. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Melbourne, Australia, vol. III, 121-128.

Herbel-Eisenmann, B. & Wagner, D. (2005). A framework for examining the positioning of learners in a mathematics textbook. Proceedings of the 26th Conference of the North American Group for the Psychology of Mathematics Education, Roanoke, Virginia.

Wagner, D. (2004). "Just go": Mathematics students' critical awareness of the de-emphasis of routine procedures. Proceedings of the 26th Conference of the North American Group for the Psychology of Mathematics Education, Toronto, Canada, vol. II, pp. 737-744.

Wagner, D. (2004). Critical awareness of voice in mathematics classroom discourse: learning the steps in the "dance of agency". Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway, vol. IV, pp. 401-408.

Wagner, D. (2003). Teachers and students listening to themselves. In N. Pateman, B. Dougherty & J. Zilliox (Eds.). Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of PME-NA, Honolulu, USA, vol. 4, pp. 355-363.

Other publications

Newsletter Articles

Wagner, D. (2018). Supporting newcomers to the PME research community. PME Newsletter, June 2018, 14.

Wagner, D. (2016). The math fairy. CMESG Newsletter/Bulletin GCEDM, 33 (1), 6-7.

Wagner, D. (2014). False alarm raises suspicion. CMESG Newsletter/Bulletin GCEDM, 30 (2), 5-6.

Lunney Borden, L. & Wagner, D. (2011). Show me your math. CMS Notes, 43 (2), 10-11.

Wagner, D. (2011). Free trade. CMESG Newsletter/Bulletin GCEDM, 28 (1), 4-5.

Theses

Wagner, D. (2004). Silence and Voice in the Secondary Mathematics Classroom. (unpublished doctoral dissertation, University of Alberta, Edmonton, Canada)

Wagner, D. (2002). Being in a Mathematical Place: Brief Immersions in Pure Mathematics Investigation. (unpublished masters thesis, University of Alberta, Edmonton, Canada)

Teacher Resources (see more under books)

Wagner, D. (2005). Stacking squares: using geometric representation to investigate the addition of radicals. Illuminations, National Council of Teachers of Mathematics.

Wagner, D. (2000). Rocky road, in Alberta Assessment Consortium Public Domain Resources.

Media Links

Interviewed by Harry Forrestell for New Brunswick evening news, December 4, 2013 regarding the release of the 2012 PISA results

Essay and three radio interviews regarding education issues in the New Brunswick provincial election, September 2014

Unpublished Papers

to Globe and Mail (May 2007), "Counting Destruction", not published

to Globe and Mail (October 3, 2006), "The public construction of truth", not published

Kau'i Keliipio & David Wagner (2004). Exploring mathematics outside institutional walls. Western Canadian Association for Student Teaching Conference, Edmonton, Canada. [Note: excerpts from this session were aired nationally on CBC radio's "The Current" but no longer archived.]


Elaboration on research

math for sustainabilitymathematical languageclassroom interactionIndigenous contextsmath and authoritysmaller scale research

Mathematics for peace and sustainability

The goal of mathematics education should be to orient children to community goals of peace and environmental sustainability and to equip them with mathematical understanding and skills that support their engagement with these community issues. In this vein, I have been working with a team of like-minded scholars and teachers gathered by the Mahatma Gandhi Institute of Education for Peace and Sustainable Development (MGIEP), under the leadership of Shankar Musafir. We developed a guidebook for textbook authors who want to centre education on peace, sustainability and global citizenship (MGIEP-UNESCO, 2017). My co-authors for the mathematics chapter were Antonius Warmeling (Germany), Parvin Sinclair (India) and Masami Isoda (Japan). The interdisciplinary team that led the development of the guidebook (Lorna Down, Nadia Lausselet, Ronald Johnston, myself, and, from MGIEP, Shankar Musafir and Yoko Mochizuki) continues to work on these goals with authorities in countries/regions who wish to re-orient their curriculum to honour these community needs. If you are interested in considering concrete moves in this direction for your community, please contact me, and I will put you in touch with Shankar at MGIEP. Here is a link to the project website and a video of me introducing the mathematics chapter at the guidebook's release in Bangkok in 2017.

The collaboration on this guidebook has inspired me to consider different ways of approaching the need for change in the way mathematics is taught. One approach is represented in a small scale project called "Doing mathematics with love", which I briefly described in this conference paper: Wagner (2017). I have had numerous lovely interactions with colleagues and others around the central question in this project: When have you done mathematics with a feeling of love/caring? One of these conversations was with Dr. Yasmine Abtahi (Abtahi & Wagner, 2017). Related to this, I have been working with Dr. Annica Andersson to think about how love and aggression are entangled with mathematics and expressed in classroom interaction. Annica and I are finding that developing a framework for this is very complex.

The collaboration on the guidebook also inspired a project with Dr. Mijung Kim, a Science Educator, in which we are exploring the hopes of science and mathematics textbook authors. We have only begun this work, which is supported by the Social Sciences and Humanities Research Council of Canada.

The focus on peace and social justice in mathematics education is not new for me. David Stocker and I published a conversation about teaching mathematics for social justice (Stocker & Wagner, 2007). Also, as part of my role on the Nonkilling Science and Technology Research Committee, I wrote a chapter in a book on science and nonviolence (Wagner, 2011, pp. 109-120). As far back as 2002, before I started my PhD, I published an article called "Teaching mathematics for peace" (Wagner, 2002).

How do students express their mathematical ideas?

Dr. Joseph Dicks, Dr. Paula Kristmanson (both of the Second Language Research Institute of Canada) and I are working on a SSHRC-funded project (Students' language repertoires for investigating mathematics, 2012-2017) to examine the role of language in the learning and doing of mathematics. Because everything we know and learn about mathematics is filtered through language, it is important for educators to understand the range of language resources students have for talking about mathematical concepts and processes. This longitudinal study will follow seven cohorts of mathematics students, each year recording them working in groups on mathematics problems and subsequently interviewing the groups. The research will be conducted in French Immersion programs, and with English first language and additional language students in English-medium classes. The research questions:

  • What linguistic resources do mathematics students use to express conjecture?
  • How do mathematics students think about the meaning of expressions of conjecture?

Here are some of the publications and presentations from this project:

Bourgoin, R., Kristmanson, P., Dicks, J. & Wagner, D. (2014). Talking about math: Linguistic repertoires of French immersion students. Association canadienne de linguistique appliquée. St. Catharine's, Ontario.

Culligan, K. (2015, April). Exploring students' first language use in second language mathematics. Paper presented at the Ireland International Conference on Education, Dublin, Ireland.

Culligan, K. (2014, July). The purpose and implications of first language use in second language mathematics tasks. Proceedings of the Joint Meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the North American Chapter of the Psychology of Mathematics Education (PME-NA 36), Vancouver, Canada.

Culligan, K., Dicks, J., Kristmanson, P. (2015). Les interactions orales pendant la résolution des problàmes mathématiques en immersion française : le rôle de l'échafaudage. Association francophone pour le savoir, Rimouski, Québec.

Culligan, K., Dicks, J., Kristmanson, P., & Roy, A. (2015, April). Collaborative problem solving in French immersion mathematics. Paper presented at the Ireland International Conference on Education, Dublin, Ireland.

Culligan, K., Dicks, J., Kristmanson, P., & Wagner, D. (2014, October). Student language strategies for mathematical exploration in French immersion. Paper presented at the 5th International Conference on Dual Language/Immersion Education, Salt Lake City, Utah, USA.

Culligan, K., Dicks, J., Kristmanson, P., & Wagner, D. (2014, May). Collaborative problem-solving in FI Mathematics. Paper presented at the Canadian Association of Applied Linguistics, St. Catharine's, Ontario.

Culligan, K., & Wagner, D. (2015). Mathematics, language, and degrees of certainty: Bilingual students' mathematical communication and probability. Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, USA.

Le Bouthillier, J. Bourgoin, R., Roy, A. (2015). Enseigner la langue seconde par le biais des mathématiques : Implications pédagogiques. Association francophone pour le savoir, Rimouski, Québec.

Wagner, D. (2015). Mathematics, language, and understanding. New Brunswick Teachers Association Council. Fredericton, Canada.

Wagner, D., & Andersson, A. (2015). The micro-politics of students' language repertoires in counting contexts. Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, USA.

Wagner, D., Dicks, J., & Kristmanson, P. (2015). Students' language repertoires for prediction. Proceedings of the 9th Congress of European Research in Mathematics Education, Prague, Czech Republic.

Wagner, D., Dicks, J., & Kristmanson, P. (2015). Students' language repertoires for prediction. The Mathematics Enthusiast, 12, 246-261.

Wagner, D., Dicks, J., & Kristmanson, P. (2013). Students' language repertoires for investigating mathematics. Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Chicago, USA.

Wagner, D., Kristmanson, P. & Herbel-Eisenmann, B. (2011). The use of modality in French immersion mathematics interaction. Canadian Association of Applied Linguistics Conference, Fredericton, Canada.

How do interactions in mathematics classroooms impact the development of understanding?

Dr. Beth Herbel-Eisenmann and I have investigated mathematics classroom discourse to understand better how students' understanding of mathematics develops. In our first collaboration, we used mathematics classroom transcripts from her research project to pursue a concern raised by participant students in my research. In my research, students had raised questions about their math teachers' frequent use of the word just because the word suggests simplicity when concepts may not be so simple (Wagner, 2008), so Dr. Herbel-Eisenmann and I used a large body of transcripts from her research to categorize, quantify, and develop understanding of the way just is used in mathematics classrooms (Wagner & Herbel-Eisenmann, 2008). This has led to our ongoing conversations about the way positioning works in mathematics learning (Wagner & Herbel-Eisenmann, 2009).

In our second collaboration, Dr. Herbel-Eisenmann and I built off of her investigation of mathematics textbooks to develop a framework for uncovering the way a textbook may position the mathematics learner (Herbel-Eisenmann & Wagner, 2007).

In our third collaboration (the most exciting of our collaborations, in my view), Dr. Herbel-Eisenmann and I collaborated with her colleague Dr. Viviana Cortes to use a new method from linguistics to investigate mathematics classroom discourse. Most research on discourse in mathematics education investigates language or interaction episodes that researchers identify as being important. Some research investigates language that others identify as important - for example, our work on just, which was identified by students as important (described above). But now, in this third collaboration, we used lexical bundle analysis, in which a computer program objectively identifies language patterns that are common in the discourse. Our work, then, was to map these common language patterns and consider what their prevalence means for the development of mathematical understanding. We report on this in two articles. The second one carries the more interesting results (Herbel-Eisenmann & Wagner, 2010). The first one focuses on the methodology but has some interesting analysis too (Herbel-Eisenmann, Wagner & Cortes, 2010).

Dr. Herbel-Eisenmann and I have collaborated with others too, to facilitate collaboration among scholars who research discourse in mathematics learning. Most significantly, along with Dr. Jeffrey Choppin, we secured an NSF grant to host a conference (Investigating Equitable Discourse Practices in Mathematics Classrooms) bringing together discourse- and equity-focused mathematics educators from around the world. We had noted that equity work could be supported by discourse analysis techniques, and that discourse scholarship in mathematics tended to have underlying equity issues that were often unarticulated. Among other products of this conference, we developed a book that identifies the inherent connections between discourse and equity in mathematics education (Herbel-Eisenmann, Choppin, Wagner & Pimm, 2012).

To Indigenize school mathematics...

Mi'kmaq and Wolastoqiyik communities are confronted with many issues that require or may benefit from mathematical knowledge. For example, they need to balance sustainable economies with management of natural resources, they face on-going negotiations surrounding treaties and land claims, and they are confronting population increase with insufficient infrastructure. Mathematical and scientific knowledge is important in all these endeavours, but most Indigenous youth are not choosing to pursue studies in mathematics and the sciences.

While the reasons for these choices are varied, one cannot overlook the apparent disconnect between Indigenous knowledge and the Western world view of mathematics and science, which students are exposed to in our school systems. For centuries, Indigenous people have addressed problems that have similarities to the problems addressed by academic mathematics and science. This historical connection ought not to be ignored.

I have been working with Dr. Lisa Lunney Borden, to bring together community elders, adults, and youth in conversations about the role of mathematical processes within local cultures in Indigenous communities. In our conversations, we have considered ways to engage more the youth in the study of mathematics. The key questions have been: "What mathematics is already present in Indigenous culture?" (this kind of research is called ethnomathematics) and "How can this Indigenous knowledge be incorporated into the learning and teaching of mathematics so as to better meet the needs of Indigenous students?" An example of the insights gleaned in our conversation with elders can be found in this book chapter: Wagner & Lunney Borden, 2015.

Out of these conversations emerged the Show Me Your Math (SMYM) event. Since 2006, it has drawn the participation of over a thousand Mi'kmaw and Maliseet children who showed others the mathematics practised in their communities. These children, from kindergarten to grade 12 have participated from communities in Nova Scotia, New Brunswick, Quebec, Newfoundland and Labrador. See http://showmeyourmath.ca for more details. Here is the video prompt we developed with community leaders:


Dr. Lunney Borden and I have published a number of book chapters relating to the Show Me Your Math event, including:

The most straightforward overview of the Show Me Your Math program can be found in an article we wrote for the Canadian Math Society newsletter (Lunney Borden and Wagner, 2011). Here is an example of a prominant news agency reporting on SMYM: from CTV news in 2013.

How can teachers develop their students' mathematical authority?

Though mathematics is a powerful discipline with strong traditions and expectations, students in mathematics classrooms only experience the discipline through their teachers and other mostly textual media. In a quantitative investigation of middle school mathematics classes, Dr. Beth Herbel-Eisenmann and I had found that issues of authority are pervasive in the discourse (Herbel-Eisenmann & Wagner, 2010). These questions are especially important in mathematics because of its characteristic interest in truth and proof. However, our study of the discourse showed that authority structures are more dependent on social positioning than on logic and proof. Our questions about authority include:

  • How are truth and value established in mathematics?
  • Who should decide what mathematical questions are worth pursuing?
  • On what basis should these decisions be made?

We worked together with a group of mathematics teachers who wanted to pay attention to the way authority was working in their classrooms, and to develop better approaches to it. From this collaboration we have learned that research has barely scratched the surface of understanding the significance of authority in math classrooms. Math teachers have a wide range of conceptualizations of authority (Herbel-Eisenmann & Wagner, 2014, 2009), and the way authority relationships develop is complex (Wagner & Herbel-Eisenmann, 2014, 2009). The collaboration with teachers helped us understand the connections between mathematics, classrooms, and democratic participation (Wagner & Herbel-Eisenmann, 2012). This project was funded by a SSHRC grant (Positioning and Authority in Mathematics Classrooms, 2008-2012).

Smaller scale research

In addition to the larger research programs described in my bio, I have done some relatively small investigations, all of which still relate to my interest in human interaction in mathematics and mathematics learning.

I'd say that all my work relates to mathematics education in relation to society. For example, my article, "If mathematics is a language, how do you swear in it?" (Wagner, 2009) shows how mathematics has been and can be a force for breaking norms. And I reflected on some of my international work in mathematics education in another article (Wagner, 2012). Also, two collaborations have addressed the understanding of quantity: Dr. Brent Davis and I promoted activities that develop quantity sense, and we considered how the lack of quantity sense impacts society (Wagner & Davis, 2010), and Dr. Annica Andersson and I investigated the politics of counting (Andersson and Wagner, 2018).

Investigating the field of mathematics education research may also be described as research. I have done some of this. Currently, I am working with Dr. Vilma Mesa to reflect on 50 years of the journal Educational Studies in Mathematics. I have also reflected on the way authority and positioning operate within the field and how this relates to authority in mathematics learning, as my contribution in a Festschrift (a collection of celebratory writing) (Wagner, 2015). Here is my video that was played at the release of the book:



In an invited contribution to the Third International Handbook of Mathematics Education (Jablonka, Wagner & Walshaw, 2012), my colleagues and I investigated how our field uses theory from a variety of traditions ranging from sociology, linguistics, and others. This is a challenge for education research, because we draw on theory and tools that are not designed for the same research orientations and questions that many of us bring to education research. Thus, along with Dr. Beth Herbel-Eisenmann, I have worked at developing theory for our field. In particular, we have tried to bring clarity to the concept of positioning, which is used widely in the field, but too often haphazardly (Wagner & Herbel-Eisenmann, 2009). More recently, we have elaborated on this along with some of her graduate students (Herbel-Eisenmann, Wagner, Johnson, Suh, & Figueras, 2015).


Some of my mathematics

Investigations

The word investigation is used in mathematics classes in various way. Sometimes it is a series of instructions that are designed to help students notice something. But the kind of investigation I refer to here is the investigation idea from the United Kingdom in the 1980s. A good investigation has relatively straightforward instructions that allow students to try out variations of a mathematical idea, and asks them to identify patterns, relationships and/or generalizations. I wrote extensively about this tradition of investigations in chapter 2 of my masters thesis.

Here are two that I designed and used in grade 10 classrooms to gather data for the masters thesis:

I also published an article in the NCTM's journal Mathematics Teacher (Wagner, 2003), based on student work on the Playing with Squares task. I have used that task very often working with novice and experienced mathematics teachers. I was also asked to submit a series of materials related to the task for the NCTM's exemplar lessons, called Illuminations:

High school mathematics content

It is important for high school mathematics teachers to be fluent in the mathematics they teach and to be able to explain it well. Therefore, when I teach courses preparing high school mathematics teachers, I have a content quiz. They have to pass the quiz to pass the course.

Initially this quiz was procedure focused. I gave them this bank of 40 questions to prepare. For the one-hour quiz, they'd be given 8 randomly-selected questions from the bank (but with the numbers in the question changed a little). They had to get 6 correct in order to pass. The problem with this quiz was that it did not model the kind of assessment that I wanted to promote. Nevertheless, procedural fluency is important for teachers and students.

More recently the quiz has been concept focused. For this I give them a bank of about 20 questions to prepare. The quiz is a 15 minute individual interview, in which I ask them randomly selected questions from the bank (chosen by drawing a playing card). They have to explain their answer to me. And then I ask them another question. Etcetera.

Dynamic system simulation

Dynamic systems are not taught in school mathematics, but they should be because the mathematics is acccessible (especially with new technologies) and because dynamic system understanding is increasingly important in our world. I would like to work more at dynamic systems for school mathematics, but for now I'll share one example.

In this game, three or more people play in a wide open space (e.g., a park). Each person chooses two others to be their reference points. When the leader says go, everyone moves to try to form an equilateral triangle with their two reference points. For example, if I choose Gcina and Karma as my reference people, I try to position myself to form the third vertex on an equilateral triangle that has Gcina and Karma as the other vertices. Of course, they are moving too, trying to position themselves to form equilateral triangles with their chosen reference people.

I modelled this dynamic system using Geometer's Sketchpad software. Here are a few highlights. But I encourage others to explore this game themselves before and after watching my videos below. This simulation has each person moving at the same speed (which is not realistic), and the people have a low tolerance for deviation from the perfect position (again, not very realistic).

Watch these videos in order: 1, 2, 3, 4, 5, 6

Mathematical games

Free Trade Game

Division Game

This game was invented by my daughter Sophia when she was 8 years old. (So it's not really my math; it's my daughter's math.) She wanted to invent an interesting game that would give her practice with division. When playing it she would often comment on how much division we need to do if we are to be competitive in the game. She called the game Demainder - substituting the R in remainder for a D from division.

I find it interesting that she invented this game because she often talked very negatively about the mathematics she did for school. No one suggested that she invent a game to practice division. It was her idea. She is very good at mathematics but didn't enjoy doing worksheets and repetitive procedures.

Players:

  • 2 players, who know how to divide small numbers

To Start:

  • Take the face cards out of a standard playing card deck. This game requires the cards from 1 to 10.
  • Deal ten cards to each player.
  • Place the remainder of the cards in a pile face down.

The Object:

  • The object of the game is to get rid of your cards.
  • The first person to run out of cards (to have less than three cards) wins.

To Play:

  • On your turn, you use three of your cards to make a division question for the other player. For example, you can make 10 divided by 3 by putting down a 9, an Ace and a 3, i.e. (9 + 1) ÷ 3.
  • You take 3 cards from the deck to replace these three cards you just played.
  • The other player can put down one or more cards to answer your division question (This is how she or he gets rid of her/his cards). She or he can play the quotient or the remainder. For example, if the question is 10 ÷ 3, as in above, the answer is 3 remainder 1.
    So the player could play an Ace to represent the remainder (1), a 3 to represent the quotient, or any combination of cards that add up to 3 to make the quotient (i.e., an Ace and a 2, or three Aces).
  • If the other player cannot play an 'answer', she or he must pick up a card from the deck as a penalty, and you have the opportunity to play the answer to your own question. If you cannot answer your own question, you do not pick up from the deck.
  • There is one limitation to the questions you can play: The question must have a solution that is greater than 1 remainder 1. The reason for this rule is to disallow questions that require an Ace for the answer. There aren't enough Aces.
  • When the deck is depleted, shuffle the played cards to replenish the deck.

Strategy/Mathematics:

  • The best questions to make give the other player limited choice for playing answers - for example, questions with low numbers for answers (high numbers make it possible for the other player to play out multiple cards), questions that have no remainder, or questions for which the quotient and the remainder are equal (e.g. for 10 ÷ 4, the answer is 2 remainder 2, so only 2 is a viable play).

Fractals

A colleague expressed interest in self-similarity in fractals, so I made these short videos to give a brief introduction:

You may be interested in the code I used for these. These are done using Logo software. The routines are very simple. And then for the demos I ran the routines multiple times with different levels of iteration.



Interests

In addition to work and spending time with my family, I enjoy...

  • Playing Soccer: I play soccer in the local league for people over 35 (unfortunately called the Fredericton City Old Boys).
  • Photography: Lately, I've paid attention to doors and empty chairs. I plan to develop a photo gallery soon to share here.
  • Making stuff: Often for my research and teaching, I get drawn into creating something just the way I envision it. These obsessions are much more than support for teaching and research. They are for the sheer pleasures of design and learning the new media. For example, this website design was my 2018 Winter holiday obsession. I plan to share some of my other designs here soon.

Contact

  • David Wagner
  • Faculty of Education
  • University of New Brunswick
  • P.O. Box 4400
  • Fredericton, New Brunswick
  • Canada E3B 5A3