Educational Design of Mathematics Content: Report From a Pioneering Workshop
Keywords:contemplation, contemplative-somatic practices, contemplative mathematics, somatic learning, phenomenology, contemplative arts research, embodiment theory, enactivism, Feldenkrais Method, meditation, Qigong, somatic
Researchers in the field of mathematics education are beginning to appreciate the potential of contemplative practices such as mindfulness to alleviate students’ stress and increase their focus. What researchers do not yet know is whether, and if so how, bringing focused attention to somatic experience through a wide variety of contemplative–somatic practices (i.e., yoga, Feldenkrais, body–mind centering, and attending to bodily sensations in meditation) may support student learning of specific mathematical content. As a first step toward conceptualizing and ideating the pedagogical design and facilitation of content-oriented contemplative exercises, we convened a workshop to explore these ideas. Here we report on findings from this pioneering workshop, which brought together international scholars and practitioners interested in the relations between contemplative–somatic practice and mathematical reasoning and learning. This report elaborates on participants’ experiences and derived pedagogical insights to offer the field new horizons in the development of the theory and practice of contemplative mathematics.
Abrahamson, D., Sánchez-García, R., & Smyth, C. (2016). Metaphors are projected constraints on action: An ecological dynamics view on learning across the disciplines. In C.-K. Looi, J. L. Polman, U. Cress, & P. Reimann (Eds.), “Transforming learning, empowering learners,” Proceedings of the International Conference of the Learning Sciences (ICLS 2016) (Vol. 1, “Full Papers,” pp. 314–321). Singapore: International Society of the Learning Sciences.
Abrahamson, D., Shayan, S., Bakker, A., & Van der Schaaf, M. F. (2016). Eye-tracking Piaget: Capturing the emergence of attentional anchors in the coordination of proportional motor action. Human Development, 58(4–5), 218–244.
Brady, R. (2007). Learning to stop, stopping to learn: Discovering the contemplative dimension in Education. Journal of Transformative Education, 5(4), 372–394.
Brunyé, T., Mahoney, C., Giles, G., Rapp, D., Taylor, H., & Kanarek, R. (2013). Learning to relax: Evaluating four brief interventions for overcoming the negative emotions accompanying math anxiety. Learning and Individual Differences, 27, 1–7.
Cole, A. (2004). Mathematics and the Feldenkrais method. The Feldenkrais Journal, 17, 17–26.
Desbordes, G., Gard, T., Hodge, E. A., Hölzel, B. K., Kerr, K., Lazar, S. W., ...Vago, D. R. (2015). Moving beyond mindfulness: Defining equanimity as an outcome measure in meditation and contemplative research. Mindfulness, 6(2), 356–372.
Gendlin, E. (2010). Focusing: How to gain direct access to your body's knowledge (25th ed.). London, England: Random House.
Gendlin, E. (1997). Experiencing and the creation of meaning: A philosophical and psychological approach to the subjective. Evanston, IL: Northwestern University Press.
Giorgi, A. (2012). The descriptive phenomenological psychological method. Journal of Phenomenological Psychology, 42, 3–12.
Glasser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory. Chicago: Aldine.
Hutto, D. D., Kirchhoff, M. D., & Abrahamson, D. (2015). The enactive roots of STEM: Rethinking educational design in mathematics. Educational Psychology Review, 27(3), 371–389.
Jordan, B., & Henderson, A. (1995). Interaction analysis: Foundations and practice. Journal of the Learning Sciences, 4(1), 39–103.
Mason, J. (2003). On the structure of attention in the learning of mathematics. Australian Mathematics Teacher, 59(4), 17–25.
Morgan, P. (2012). Following contemplative education students’ transformation through their “ground-of-being” experiences. Journal of Transformative Education, 1(1), 23–42.
Morgan, P. (2013). Learning feelings: Foundations of contemplative education (Doctoral thesis). University of New South Wales, Sydney, Australia. Retrieved from http://www.unsworks.unsw.edu.au/primo_library/libweb/action/dlDisplay.do?docId=unsworks_11740&vid=UNSWORKS
Morgan, P. (2017). Per-(Me-Thou)-ability: Foundations of intersubjective experience in contemplative education. In O. Gunnlaugson, E. W. Sarath, H. Bai, & C. Scott (Eds.), The intersubjective turn in contemplative education: Shared approaches to contemplative learning & inquiry across disciplines. Albany, NY: SUNY Press.
Morgan, P., & Abrahamson, D. (2016). Cultivating the ineffable: The role of contemplative practice in enactivist learning. For the Learning of Mathematics, 36(3), 31–37.
Petitmengin, C. (2007). Towards the source of thoughts: The gestural and transmodal dimension of lived experience. Journal of Consciousness Studies, 14(3), 54–82.
Rodd, M. (2006). Commentary: Mathematics, emotion and special needs. Educational Studies in Mathematics, 63(2), 227–234.
Rothfield, P. (2009). Feeling feelings, the work of Russell Dumas through Whitehead's Process and reality. Inflexions: A Journal of Research-Creation, 2, 1–20.
Roth, W. (2012). First–person methods: Toward an empirical phenomenology of experience (Vol. 3). Rotterdam, The Netherlands: Sense Publishers.
Stelter, R. (2000). The transformation of body experience into language. Journal of Phenomenological Psychology, 31(1), 63–77.
Strauss, A. L., & Corbin., J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, CA.: SAGE Publications.
Varela, F. J., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT Press.
Wolcott, F. (2013). On contemplation in mathematics. Journal of Humanistic Mathematics, 3(1), 74–95.
Authors who publish with this journal sign a publishing agreement after their paper has been accepted. Through the agreement, authors transfer copyright to CMind, the Center for Contemplative Mind in Society, the publisher of JOCI. Authors may enter into additional contractual arrangements for the non-exclusive distribution of the journal's published version of their work (e.g., to publish it in a book), with an acknowledgement of its initial publication in this journal. Authors are also permitted and encouraged to post their work online (e.g., in institutional repositories or on their website), with acknowledgement of its initial publication in this journal and retaining the formatting as published in JOCI.