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Vignettes of Research on the Promise of Mathematical Making in Teacher Preparation

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Learning Mathematics in the Context of 3D Printing

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Abstract

In this chapter, we share research that explores the potential benefits of a novel Making experience within mathematics teacher preparation that we hypothesized would inform the pedagogical and curricular thinking of prospective teachers of elementary mathematics (PMTs). That experience tasks PMTs with digitally designing, 3D printing, and sharing an original manipulative with a child to support and promote their mathematical reasoning and understanding. With a focus on the design of new tools to support teaching and learning through the use of learner-centered design practices and digital fabrication technologies, this experience has prospective teachers exploring at the intersection of content, pedagogy, and design. We begin by sharing the findings of a pilot study that revealed a surprising breadth of teacher knowledge leveraged by PMTs through their Making activity. Those findings convinced us of the promise of a Making experience within mathematics teacher preparation. They also convinced us to pursue a research trajectory aimed at discerning what other benefits the experience might offer. We share several vignettes of research on that trajectory that take a variety of theoretical and methodological approaches to address research questions at the intersections of teacher identity, teacher knowledge, pedagogy, and design. We provide implications of our findings for teacher preparation and professional learning throughout the chapter and its conclusion.

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Notes

  1. 1.

    Greenstein et al. (2019); Greenstein and Olmanson (2018); Greenstein and Seventko (2017)

  2. 2.

    Greenstein et al. (2020)

  3. 3.

    Greenstein et al. (forthcoming).

  4. 4.

    Akuom and Greenstein (2021a)

  5. 5.

    Akuom and Greenstein (2021b)

  6. 6.

    Fernández et al. (2021)

  7. 7.

    Greenstein et al. (2021)

References

  • Akuom, D., & Greenstein, S. (2021a). Prospective Teachers’ Design Decisions, Rationales, and Resources: Re/claiming Teacher Agency Through Mathematical Making. Paper presented at the Virtual Annual Meeting of the American Educational Research Association (AERA). https://bit.ly/3tbXUPP.

  • Akuom, D., & Greenstein, S. (2021b). 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.

    Google Scholar 

  • Association of Mathematics Teacher Educators (AMTE). (2013). 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.

  • Autodesk Inc. (2020). Tinkercad [Computer software]. Retrieved from https://www.tinkercad.com/.

  • Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449–466. https://doi.org/10.2307/1001941

    Article  Google Scholar 

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • Bartell, T. G. (2011). Learning to Teach Mathematics for Social Justice: Negotiating Social Justice and Mathematical Goals. Journal for Research in Mathematics Education, 41(0).

    Google Scholar 

  • Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, & B. Davis (1995). Why Teach Mathematics? Mathematics Education and Enactivist Theory. For the Learning of Mathematics, 15(2), 2–9.

    Google Scholar 

  • Barton, A. C., Tan, E., & Greenberg, D. (2017). The makerspace movement: Sites of possibilities for equitable opportunities to engage underrepresented youth in STEM. Teachers College Record, 119(6), 11–44.

    Article  Google Scholar 

  • Brown, M. W. (2009). The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17–36). Routledge.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Chang, A. (2014). Identity Production in Figured Worlds: How Some Multiracial Students Become Racial Atravesados/as. The Urban Review, 46(1), 25–46.

    Article  Google Scholar 

  • Clapp, E. P., Ross, J., Ryan, J. O., & Tishman, S. (2016). Maker-Centered Learning: Empowering Young People to Shape Their Worlds. Wiley.

    Google Scholar 

  • Corbin, J., & Strauss, A. (2008). Basics of qualitative research: Techniques and procedures for developing grounded theory (3rd ed.). Sage Publications.

    Google Scholar 

  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Sage Publications, Inc.

    Google Scholar 

  • Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach. Orienta-Konsultit.

    Google Scholar 

  • Fernández, E., Pomponio, E., & Davidson, J. (2021). Dare to care: The impacts of a caring pedagogy on mathematical making, teaching, and learning. Paper presented at the Virtual Annual Meeting of the American Educational Research Association (AERA). https://bit.ly/3vtOBit.

  • 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).

    Google Scholar 

  • Glaser, B. G., & Strauss, A. L. (1967). The Discovery of Grounded Theory: Strategies for Qualitative Research: Aldine.

    Google Scholar 

  • 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.

    Google Scholar 

  • Greenstein, S., Jeannotte, D., & Pomponio, E. (forthcoming) Making as a Window into the Process of Becoming a Teacher: The Case of Moira. In Benken, B. (Ed.) AMTE Professional Book Series, Volume 5.

    Google Scholar 

  • 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 (pp. 810–816). Cinvestav/AMIUTEM/PME-NA.

    Google Scholar 

  • 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.

    Google Scholar 

  • Greenstein, S., & Olmanson, J. (2018). Reconceptualizing pedagogical and curricular knowledge development through making. Emerging Learning Design Journal, 4(1), 1–6.

    Google Scholar 

  • 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). Hoosier Association of Mathematics Teacher Educators.

    Google Scholar 

  • Gutiérrez, R. (2017). Political conocimiento for teaching mathematics. In A. Lischka, A. Tyminski, S. Kastberg, & W. Sanchez (Eds.), Building support for scholarly practices in mathematics methods (pp. 11–37). Information Age Publishing.

    Google Scholar 

  • Hackenberg, A. (2005). A model of mathematical learning and caring relations. For the Learning of Mathematics, 25(1), 45–51.

    Google Scholar 

  • Hackenberg, A. (2010). Mathematical caring relations in action. Journal for Research in Mathematics Education, 41(3), 236–273.

    Article  Google Scholar 

  • Halverson, E. R., & Sheridan, K. M. (2014). The maker movement in education. Harvard Educational Review, 84(4), 495–504, 563, 565.

    Google Scholar 

  • Harel, I., & Papert, S. (1991). Constructionism. Ablex.

    Google Scholar 

  • Heyd-Metzuyanim, E., & Sfard, A. (2012). Identity struggles in the mathematics classroom: On learning mathematics as an interplay of mathematizing and identifying. International Journal of Educational Research, 51, 128–145.

    Article  Google Scholar 

  • Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Maffia, A., & Maracci, M. (2019). Multiple artifacts in the mathematics class: Tentative definition of semiotic interference. Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Holland, D., Lachicotte, W., Jr., Skinner, D., & Cain, C. (1998). Identity and Agency in Cultural Worlds. Harvard University Press.

    Google Scholar 

  • Koehler, M., & Mishra, P. (2005). Teachers learning technology by design. Journal of Computing in Teacher Education, 21(3), 94–102.

    Google Scholar 

  • Koehler, M., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 9(1), 60–70.

    Google Scholar 

  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(Spring), 29–63.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates.

    Book  MATH  Google Scholar 

  • Maffia, A., & Maracci, M. (2019). Multiple artifacts in the mathematics class: Tentative definition of semiotic interference. Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education.

    Google Scholar 

  • Maher, C. (1987). The teacher as designer, implementer, and evaluator of children’s mathematical learning environments. Journal of Mathematical Behavior, 6(3), 295–303.

    Google Scholar 

  • Malafouris, L. (2013). How things shape the mind. MIT press.

    Google Scholar 

  • Maturana, H. R., & Varela, F. J. (1987). The tree of knowledge: The biological roots of human understanding. New Science Library/Shambhala Publications.

    Google Scholar 

  • Noddings, N. (2012). The caring relation in teaching. Oxford Review of Education, 38(6), 771–781.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. http://www.nctm.org/standards/content.aspx?id=322.

  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. Basic Books, Inc

    Google Scholar 

  • Patton, M. Q. (2002). Qualitative research and evaluation methods (3rd ed.). Sage Publications.

    Google Scholar 

  • Piaget, J. (1970). Genetic epistemology. Columbia University Press.

    Book  Google Scholar 

  • Pratt, D., & Noss, R. (2010). Designing for mathematical abstraction. International Journal of Computers for Mathematical Learning, 15(2), 81–97.

    Article  Google Scholar 

  • Presmeg, N. (2006). Semiotics and the “Connections” Standard: Significance of Semiotics for Teachers of Mathematics. Educational Studies in Mathematics, V61(1), 163–182.

    Article  Google Scholar 

  • Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics, 84(3), 309–328.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Roth, W.-M. (2012). Cultural-historical activity theory: Vygotsky’s forgotten and suppressed legacy and its implication for mathematics education. Mathematics Education Research Journal, 24, 87–104.

    Article  Google Scholar 

  • Schad, M., & Jones, W. M. (2020). The Maker movement and education: A systematic review of the literature. Journal of Research on Technology in Education, 52(1), 65–78.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Schön, D. A. (1992). Designing as reflective conversation with the materials of a design situation. Knowledge-Based Systems, 5(1), 3–14.

    Article  Google Scholar 

  • Sfard, A. (2007). When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565–613.

    Article  Google Scholar 

  • Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.

    Book  Google Scholar 

  • Sfard, A., & Prusak, A. (2005). Telling identities: In search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34(4), 14–22.

    Article  Google Scholar 

  • Sherin, M., Jacobs, V., & Philipp, R. (Eds.). (2011). Mathematics teacher noticing: Seeing through teachers’ eyes (1st ed.). Routledge. https://doi.org/10.4324/9780203832714

  • Shulman, L. S. (1986, February). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Google Scholar 

  • Simmt, E. (2000). Mathematics knowing in action: A fully embodied interpretation. Paper presented at the Proceedings of the 2000 Annual Meeting of the Canadian Mathematics Education Study Group.

    Google Scholar 

  • Stinson, D. W. (2004). Mathematics as “gate-keeper” (?): Three theoretical perspectives that aim toward empowering all children with a key to the gate. The Mathematics Educator, 14(1), 8–18.

    Google Scholar 

  • Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169.

    Article  Google Scholar 

  • Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–127.

    Article  Google Scholar 

  • Thorp, L. (2005). The pull of the Earth: Participatory ethnography in the school garden. AltaMira Press.

    Google Scholar 

  • Vågan, A. (2011). Towards a sociocultural perspective on identity formation in education. Mind, Culture, and Activity, 18(1), 43–57.

    Article  Google Scholar 

  • Varela, F. J. (1987). Laying down a path in walking. In W. I. Thompson (Ed.), Gaia: A Way of Knowing (pp. 48–64). Lindisfarne Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.

    Google Scholar 

  • Yin, R. K. (2009). Case study research: Design and methods (4 ed.). Sage.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Montclair State University, New Jersey, USA

    Greenstein Steven, Akuom Denish, Pomponio Erin, Fernández Eileen, Davidson Jessica & York Toni

  2. Université du Québec À Montréal, Québec, Canada

    Jeannotte Doris

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  1. Greenstein Steven
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  2. Akuom Denish
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  3. Pomponio Erin
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  4. Fernández Eileen
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  5. Davidson Jessica
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  6. Jeannotte Doris
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  7. York Toni
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Correspondence to Greenstein Steven .

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Editors and Affiliations

  1. Mathematics Education, University of Siegen, Siegen, Germany

    Frederik Dilling

  2. Mathematics Education, University of Siegen, Siegen, Germany

    Felicitas Pielsticker

  3. Mathematics Education, University of Siegen, Siegen, Germany

    Ingo Witzke

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Steven, G. et al. (2022). Vignettes of Research on the Promise of Mathematical Making in Teacher Preparation. In: Dilling, F., Pielsticker, F., Witzke, I. (eds) Learning Mathematics in the Context of 3D Printing. MINTUS – Beiträge zur mathematisch-naturwissenschaftlichen Bildung. Springer Spektrum, Wiesbaden. https://doi.org/10.1007/978-3-658-38867-6_4

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