Journal of Research in Science, Mathematics and Technology Education

The Nature of Prospective Mathematics Teachers’ Designed Manipulatives and their Potential as Anchors for Conceptual and Pedagogical Knowledge

Denish O Akuom 1 * ,
Steven Greenstein 1 *
1 Montclair State University* Corresponding Author
Download PDF
Journal of Research in Science, Mathematics and Technology Education, Volume 5, Issue SI, June 2022, pp. 109-125
OPEN ACCESS VIEWS: 2070 DOWNLOADS: 562 Publication date: 15 Jun 2022
ABSTRACT
While traditionally teachers have been positioned as implementers of curricular materials designed by others, this work positions them as designers of their own curricular resources, thereby inviting opportunities for their exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic forms of mathematics teaching and learning by supporting these explorations. Toward that end, this paper reports on research that examines connections between the pedagogical/conceptual knowledge that prospective teachers embed in the designs of original manipulatives and how those designs mediate the pedagogical moves they make in teaching situations. The promise of this work is in connections that may offer a viable means to support bolder connections between teacher preparation and practice. We share findings from the analysis of prospective teachers’ design activity that conveys (1) the diversity of design decisions, rationales, and mediating resources that it entailed, and (2) how the designed manipulative act as anchors for their conceptual/pedagogical moves. The implications of these findings for teacher preparation and professional learning are considered.
KEYWORDS
Teacher Knowledge, Technology, Preservice Teacher Education, Making, 3D Designing
CITATION (APA)
Akuom, D. O., & Greenstein, S. (2022). The Nature of Prospective Mathematics Teachers’ Designed Manipulatives and their Potential as Anchors for Conceptual and Pedagogical Knowledge. Journal of Research in Science, Mathematics and Technology Education, 5(SI), 109-125. https://doi.org/10.31756/jrsmte.115SI
REFERENCES
  1. Akuom, D. & Greenstein, S. (2021). Prospective Mathematics Teachers' Designed Manipulatives As Anchors for Their Pedagogical and Conceptual Knowledge. Proceedings of the 43rd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Philadelphia.
  2. Akuom, D., Greenstein, S., & Fernández, E. (to appear) Mathematical Making in Teacher Preparation: Research at the Intersections of Knowledge, Identity, Pedagogy, and Design. Paper to be presented at the 44th Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Nashville.
  3. Association of Mathematics Teacher Educators. (2009). Standards for elementary mathematics specialists: A reference for teacher credentialing and degree programs. Retrieved from San Diego, CA: http://amte.net/sites/all/themes/amte/resources/EMS_Standards_AMTE2013.pdf
  4. Autodesk Inc. (2020). Tinkercad [Computer software]. Retrieved from https://www.tinkercad.com/
  5. Bower, M., Stevenson, M., Forbes, A., Falloon, G., & Hatzigianni, M. (2020). Makerspaces pedagogy: Supports and constraints during 3D design and 3D printing activities in primary schools. Educational Media International, 57(1), 1-28.
  6. Cai, J., & Cirillo, M. (2014). What do we know about reasoning and proving? Opportunities and missing opportunities from curriculum analyses. International Journal of Educational Research, 64, 132-140.
  7. Carvalho, L., Martinez-Maldonado, R., & Goodyear, P. (2019). Instrumental genesis in the design studio. International Journal of Computer-Supported Collaborative Learning, 14(1), 77-107.
  8. Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Sage Publications.
  9. Dewey, J. (1990). The school and society and the child and the curriculum. University Of Chicago Press.
  10. Gibson, J. J. (1977). The Theory of Affordances. In R. Shaw & J. Bransford (Eds.), Perceiving, Acting, and Knowing: Toward an Ecological Psychology. (pp. 67-82).
  11. Greenstein, S., Fernández, E. & Davidson, J. (2019). Revealing Teacher Knowledge Through Making: A Case Study of Two Prospective Mathematics Teachers. Proceedings of the 41st Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. St. Louis, MO.
  12. Greenstein, S., Jeannotte, D., Fernández, E., Davidson, J., Pomponio, E., & Akuom, D. (2020). Exploring the Interwoven Discourses Associated with Learning to Teach Mathematics in a Making Context. In A.I. Sacristán, J.C. Cortés-Zavala & P.M. Ruiz-Arias, (Eds.). Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico (pp. 810-816). Cinvestav/AMIUTEM/PME-NA.
  13. Greenstein, S., Jeannotte, D., & Pomponio, E. (to appear) Making as a Window into the Process of Becoming a Teacher: The Case of Moira. AMTE Professional Book Series, Volume 5.
  14. Greenstein, S. & Olmanson, J. (2018). Reconceptualizing Pedagogical and Curricular Knowledge Development Through Making. Emerging Learning Design Journal, 4(1), 1-6.
  15. Greenstein, S., Pomponio, E., & Akuom, D. (2021). Harmony and Dissonance: An Enactivist Analysis of the Struggle for Sense Making in Problem Solving. Proceedings of the 43rd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Philadelphia.
  16. Greenstein, S. & Seventko, J. (2017). Mathematical Making in Teacher Preparation: What Knowledge is Brought to Bear? In E. Galindo & J. Newton, (Eds.). Proceedings of the 39th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 821-828). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
  17. Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273-289.
  18. Halverson, E. R., & Sheridan, K. M. (2014). The Maker movement in education. Harvard Educational Review, 84(4), 495-504, 563, 565.
  19. Harel, I., & Papert, S. (1991). Constructionism. Ablex.
  20. Kamii, C., & Housman, L. B. (2000). Young children reinvent arithmetic: Implications of Piaget’s theory. Teachers College Press, Teachers College, Columbia University
  21. Kalantzis, M., & Cope, B. (2010). The teacher as designer: Pedagogy in the new media age. E-learning
  22. and Digital Media, 7(3), 200-222
  23. Kazemi, E., Franke, M., & Lampert, M. (2009, July). Developing pedagogies in teacher education to support novice teachers’ ability to enact ambitious instruction. In Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 12-30).
  24. Koehler, M., & Mishra, P. (2005). Teachers learning technology by design. Journal of Computing in Teacher Education, 21(3), 94-102.
  25. Leander, K. M., & Osborne, M. D. (2008). Complex positioning: Teachers as agents of curricular and pedagogical reform. Journal of Curriculum Studies, 40(1), 23-46.
  26. Maher, C. (1987). The teacher as designer, implementer, and evaluator of children’s mathematical learning environments. Journal of Mathematical Behavior, 6(3), 295-303.
  27. Malafouris, L. (2013). How things shape the mind. MIT press.
  28. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.
  29. National Academy of Education. (2005). A good teacher in every classroom: Preparing the highly qualified teachers our children deserve. San Francisco: Jossey-Bass.
  30. Nathan, M. J. (2014). Grounded Mathematical Reasoning. In L. Shapiro (Ed.). The Routledge Handbook of Embodied Cognition (pp. 171-183). New York: Routledge.
  31. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. Basic Books, Inc
  32. Piaget, J. (1970). Genetic epistemology. New York City: Columbia University Press.
  33. Pinar, W. F., Reynolds, W. M., Slattery, P., & Taubman, P. M. (1995). Understanding Curriculum. Peter Lang.
  34. Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction. International Journal of Computers for Mathematical Learning, 15(2), 81-97.
  35. Priestley, M., Edwards, R., Priestley, A., & Miller, K. (2012). Teacher agency in curriculum making: Agents of change and spaces for manoeuvre. Curriculum Inquiry, 42(2), 191-214.
  36. Remillard, J. (2018). Mapping the Relationship Between Written and Enacted Curriculum: Examining Teachers’ Decision Making. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education (pp. 483-500). Springer International Publishing.
  37. Scheiner, T. (2015). Shifting the emphasis toward a structural description of (mathematics) teachers’ knowledge (Vol. 4). K. Beswick, T. Muir, J. Fielding-Wells. Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (pp. 129-136). Hobart, Australia: Uniprint, University of Tasmania.
  38. Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. R. (2019). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 17(1), 153-172.
  39. Schön, D. A. (1992). Designing as reflective conversation with the materials of a design situation. Knowledge-Based Systems, 5(1), 3-14.
  40. Sherin, M., Jacobs, V., & Philipp, R. (Eds.). (2011). Mathematics Teacher Noticing: Seeing Through Teachers’ Eyes (1st ed.). Routledge. https://doi.org/10.4324/9780203832714
  41. Smith, K., Gamlem, S. M., Sandal, A. K., & Engelsen, K. S. (2016). Educating for the future: A conceptual framework of responsive pedagogy. Cogent Education, 3(1), 1227021.
  42. Spillane, J. P., & Zeuli, J. S. (1999). Reform and teaching: Exploring patterns of practice in the context of national and state mathematics reforms. Educational Evaluation and Policy Analysis, 21(1), 1-27.
  43. Stroup, W. M., Ares, N. M., & Hurford, A. C. (2004). A taxonomy of generative activity design supported by next-generation classroom networks. Proceedings of the 28th Annual Conference of Psychology in Mathematics Education – North America, Ontario, CA.
  44. Svihla, V., Reeve, R., Sagy, O., & Kali, Y. (2015). A fingerprint pattern of supports for teachers’ designing of technology-enhanced learning. Instructional Science, 43(2), 283-307.
  45. Ünver, G. (2014). Connecting Theory and Practice in Teacher Education: A Case Study. Educational Sciences: Theory and Practice, 14(4), 1402-1407.
  46. Valente, J. A., & Blikstein, P. (2019). Maker Education: Where Is the Knowledge Construction?. Constructivist Foundations, 14(3).
  47. Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77-101.
  48. von Glasersfeld, E. (1995). Radical Constructivism: A Way of Knowing and Learning. The Falmer Press.
  49. Yin, R. K. (2009). Case study research: Design and methods (4 ed.). Sage.
LICENSE
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.