Inquiry in University Mathematics Teaching and Learning. The Platinum Project

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Reference

Ainsworth, S. E. (2008). The educational value of multiple-representations when learning complex scientific concepts. In J. K. Gilbert, M. Reiner & M. Nakhleh (Eds.), Visualization: theory and practice in science education (pp. 191–208). Springer Verlag. doi.org/10.1007/978-1-4020-5267-5_9

Artigue, M., Batanero, C., & Kent, P. (2007). Mathematics thinking and learning at post-secondary level. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1011–1049). Information Age Publishing.

Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797—810. doi.org/10.1007/s11858-013-0506-6

Bereiter C. (1985). Toward a solution of the learning paradox. Review of Educational Research, 55 (2), 201–226. doi.org/10.3102/00346543055002201

Blum, W. & Leiß, D. (2007). How do students’ and teachers deal with modelling problems? In C. Haines, P. Galbraith & W. Blum (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222–231). Horwoord. doi.org/10.1533/9780857099419.5.221

Blume, G. W., & Heid, M. K., (Eds.), Research on technology and the teaching and learning of mathematics: Volume 1. research syntheses. Information Age Publishing.

Bosch, M., Chevallard, Y., García, F. J., & Monaghan, J. (Eds.). (2019). Working with the Anthropological Theory of the Didactic in mathematics education: A comprehensive casebook. Routledge. doi.org/10.4324/9780429198168

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school (Expanded edition). The National Academies Press. doi.org/10.17226/9853

Breen, S. & O’Shea, A. (2019). Designing mathematical thinking tasks. PRIMUS, 29(1), 9–20. doi.org/10.1080/10511970.2017.1396567

Brousseau, G. (2002). Theory of didactical situation in mathematics (N. Balacheff, M. Cooper, R. Sutherland & V. Warfield (Eds. & Transl.). Kluwer Academic Publishers. doi.org/10.1007/0-306-47211-2

Bybee, R. W., Taylor, J. A., Gardner, A., Van Scotter, P., Powell, J. C., Westbrook, A., & Landes, N. (2006). The BSCS 5E instructional model: Origins, effectiveness, and applications. Biological Sciences Curriculum Study (BSCS). https://media.bscs.org/bscsmw/5es/bscs_5e_full_report.pdf

Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23(1), 2–33. doi.org/10.2307/749161

Davis, R.B., Maher, C.A., & Noddings, N. (Eds.) (1990). Constructivist views on the teaching and learning of mathematics. National Council of Teachers of Mathematics.

Donovan, M. S., & Bransford, J. D. (Eds.). (2005) How students learn: History, mathematics, and science in the classroom. The National Academies Press. doi.org/10.17226/10126

Dor´ee, S. I. (2017). Turning routine exercises into activities that teach inquiry: A practical guide. PRIMUS, 27(2), 179–188. doi.org/10.1080/10511970.2016.1143900

Dorier, J.-L. & Maaß, K. (2020). Inquiry-based mathematics education. In S. Lerman (Ed.), Ency-clopedia of mathematics education (2nd ed., pp. 384–388). Springer Verlag. doi.org/10.1007/978-3-030-15789-0_176

Eisenkraft, A. (2003). Expanding the 5E model. The Science Teacher, 70(6), 56–59.

Escher, M. C. (1958) Regelmatige vlakverdeling [Regular divsion of the plane] Stichting De Roos.

Gómez-Chacón, I. M., & Kuzniak, A. (2015). Spaces for geometric work: Figural, instrumental, and discursive geneses of reasoning in a technology environment. International Journal of Science and Mathematics Education, 13(1), 201–226. doi.org/10.1007/s10763-013-9462-4

Gómez-Chacón, I. M., Romero Albaladejo, I. M., & del Mar García López, M. M. (2016). Zig-zagging in geometrical reasoning in technological collaborative environments: A mathematical working space-framed study concerning cognition and affect. ZDM Mathematics Education, 48(6), 904– 924. doi.org/10.1007/s11858-016-0755-2

Goodchild, S., Apkarian, N., Rasmussen, C., & Katz, B. (2021). Critical stance within a community of inquiry in an advanced mathematics course for pre-service teachers. Journal of Mathematics Teacher Education, 24(3), 231–252. doi.org/10.1007/s10857-020-09456-2

Heck, A. (2012). Perspectives on an integrated computer learning environment [Doctoral dissertation, University of Amsterdam]. https://dare.uva.nl/record/409820

Heck, A. (2017). Using SOWISO to realize interactive mathematical documents for learning, practis ing, and assessing mathematics. MSOR Connections, 15(2), 6–16. doi.org/10.21100/msor.v15i2.412

Heid, M.K, & Blume G.W. (Eds.), Research on technology and the teaching and learning of mathematics: Volume 2. cases and perspectives. Information Age Publishing.

Holzkamp, K. (1995). Lernen: Subjektwissenschaftliche Grundlegung. Campus-Verlag.

Holzkamp, K. (2013). Basic concepts of critical psychology. In E. Schraube & U. Osterkamp (Eds.), Psychology from the standpoint of the subject: Selected writings of Klaus Holzkamp (pp. 19–27). Palgrave Macmillan. https://doi.org/10.1057/9781137296436_2

Hoyles, C., & Lagrange, J.-B. (Eds.). (2010). Mathematics education and technology: Rethinking the terrain. Springer Verlag. doi.org/10.1007/978-1-4419-0146-0

Hughes-Hallett, D., Gleason, A M., Mccallum, W. G., Flath, D. E., Frazer Lock, P., Gordo, S. P., . . . , Tecsosky-Feldman, J. (2005). Conceptests t/a calculus (4th ed.). John Wiley & Sons Canada.

Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. Falmer Press. ERIC. https://files.eric.ed.gov/fulltext/ED381350.pdf

Jaworski, B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9(2), 187–211. doi.org/10.1007/s10857-005-1223-z

Jaworski, B. (2015). Teaching for mathematical thinking: Inquiry in mathematics learning and teaching. Mathematics Teaching, 248, 28–34.

Jaworski, B. (2019). Inquiry-based practice in university mathematics teaching development. In D. Potari (Volume Ed.) & O. Chapman (Series Ed.), International handbook of mathematics teacher education: Vol. 1. Knowledge, beliefs, and identity in mathematics teaching and teaching development (pp. 275–302). Koninklijke Brill/Sense Publishers.

Kaput, J. J. (1992). Technology and mathematics education. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). Macmillan Publishing Company.

Kuster, G., Johnson, E., Keene, K., & Andrews-Larson, C. (2018). Inquiry-oriented instruction: A conceptualization of the instructional principle. PRIMUS 28(1), 13–30. doi.org/10.1080/10511970.2017.1338807

Kuster, G., Johnson, E., Rupnow, R., & Wilhelm, A. (2019). The inquiry-oriented instructional measure. International Journal of Research in Undergraduate Mathematics Education, 5(2), 183–204. doi.org/10.1007/s40753-019-00089-2

Kwon, O. (2003). Guided reinvention of Euler algorithm: An analysis of progressive mathematization in RME-based differential equations course. Journal of the Korean Society of Mathematical Education Series A: The Mathematical Education, 42(3), 387–402.

Laursen, S., & Rasmussen, C. (2019). I on the prize: Inquiry approaches in undergraduate mathematics. International Journal of Research in Undergraduate Mathematics Education, 5(1), 129–146. doi.org/10.1007/s40753-019-00085-6

Leung, A., & Baccaglini-Frank, A. (Eds.). (2017). Digital technologies in designing mathematics education tasks. Potential and pitfalls. doi.org/10.1007/978-3-319-43423-0

Levy, P., & Petrulis, R. (2012). How do first-year university students experience inquiry and research, and what are the implications for the practice of inquiry-based learning? Studies in Higher Education, 37(1), 85–101. doi.org/10.1080/03075079.2010.499166

Mason, J. (2002). Mathematics teaching practice: A guide for university and college lecturers. Horwood Publishing.

Mason, J. (2008). From assenting to asserting. In O. Skovmose, P. Valero & O. R. Christensen (Eds.), University science and mathematics education in transition (pp. 17–40). Springer Verlag. doi.org/10.1007/978-0-387-09829-6

Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Pearson Education. Mason, J., & Johnston-Wilder, K. (2006). Designing and using mathematical tasks (2nd ed.). Tarquin.

Mayer, R. E. (2020). Multimedia learning (3rd ed.). Cambridge University Press. doi.org/10.1017/9781316941355

National Research Council (2000). Inquiry and the national science education standards: A guide for teaching and learning. The National Academies Press. doi.org/10.17226/9596

Pedaste, M., Mäeots, M., Siiman, L., de Jong, T., van Riesen, S., Kamp, E., Manoli, C., Zacharia, Z., & Tsourlidaki, E. (2015). Phases of inquiry-based learning: Definitions and the inquiry cycle. Educational Research Review, 14, 47–61. doi.org/10.1016/j.edurev.2015.02.003

Pointon, A., & Sangwin, C. J. (2003), An analysis of undergraduate core material in the light of hand- held computer algebra systems. International Journal for Mathematical Education in Science and Technology, 34(5), 671–686. doi.org/10.1080/0020739031000148930

Rasmussen, C., & Blumenfeld, H. (2007). Reinventing solutions to systems of linear differential equations: A case of emergent models involving analytic expressions. Journal of Mathematical Behavior, 26(3), 195–210. doi.org/10.1016/j.jmathb.2007.09.004

Rasmussen, C., Dunmyre, J., Fortune, N., & Keene, K. (2019). Modeling as a means to develop new ideas: The case of reinventing a bifurcation diagram, PRIMUS, 29 (6), 509–526. https://doi.org/10.1080/10511970.2018.1472160

Rasmussen, C., Keene, K., Dunmyre, J., & Fortune, N. (2018). Inquiry oriented differential equations: Course materials. https://iode.wordpress.ncsu.edu

Rasmussen, C., & Kwon, O. N. (2007). An inquiry oriented approach to undergraduate mathematics. Journal of Mathematical Behavior, 26(3), 189–194. doi.org/10.1016/j.jmathb.2007.10.001

Rasmussen, C., & Marrongelle, K. (2006). Pedagogical content tools: Integrating student reasoning and mathematics in instruction. Journal for Research in Mathematics Education, 37(5), 388– 420. doi.org/10.2307/30034860

Rogovchenko, Y., Rogovchenko, S., & Thomas, S. (2018). The use of nonstandard problems in an ODE couse for engineers. In E. Bergqvist, M. Österholm, C. Granberg & L. Schuster (Eds.), Proceedings of the 42nd conference for the Psychology of Mathematics Education (Vol. 4, pp. 283– 290). http://hdl.handle.net/11250/2596252

Ross, K. A. (2013). Elementary analysis: The theory of calculus (2nd ed.). Springer Verlag. doi.org/10.1007/978-1-4614-6271-2

Saíz, E. (2020). Geometría dinámica y teselaciones [Dynamic geometry and tesselations]. www.geogebra.org/m/zvhyf6xj

Sandoval, W. A., Bell, P., Coleman, E., Enyedy, N., & Suthers, D. (2000). Designing knowledge representations for epistemic practices in science learning. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.75.7691&rep=rep1&type=pdf

Scanlon, E., Taylor, Z. W., Raible, J., Bates, J., & Chini, J. J. (2021). Physics webpages create barriers to participation for people with disabilities: Five common web accessibility errors and possible solutions. International Journal of STEM Education, 8, article 25. doi.org/10.1186/s40594-021-00282-3

Schattschneider, D. (1986). In black and white: how to create perfectly colored symmetric patterns. Computer & Mathematics with Applications, 12(3), 673–695. doi.org/10.1016/0898-1221(86)90418-9

Schattschneider, D. (2010). The mathematical side of M. C. Escher. Notices of the American Mathematical Society, 57(6), 706–718.

Schreffler, J., Vasquez III, E., Chini, J. J., & James, W. (2019). Universal Design for Learning in postsecondary STEM education for students with disabilities: A systematic literature review. International Journal of STEM Education, 6, article 8. doi.org/10.1186/s40594-019-0161-8

Sfard, A. (2008). Thinking as communicating. Cambridge University Press. doi.org/10.1017/CBO9780511499944

Sfard, A., & McClain, K. (2002). Analyzing tools: Perspective on the role of designed artifacts in mathematics learning. Journal of the Learning Sciences, 11(2&3), 153–388. doi.org/10.1080/10508406.2002.9672135

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructive perspective. Journal for Research in Mathematics Education, 26(2), 114–145. doi.org/10.2307/749205

Smith, G. H., Wood, L. N., Coupland, M., Stephenson, B., Crawford, K., & Ball, G. (1996). Con- structing mathematical examinations to assess a range of knowledge and skills. International Journal for Mathematical Education in Science and Technology, 27(1), 65–77. doi.org/10.1080/0020739960270109

Stein, M. K., Grover, B. W. & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488. doi.org/10.3102/00028312033002455

Swan, M. (2008). Designing a multiple representation learning experience in secondary algebra. Educational Designer, 1(1). www.educationaldesigner.org/ed/volume1/issue1/article3

Treffert-Thomas, S., Jaworski, B., Hewitt, D., Vlaseros, N., & Anastasakis, M. (2019). Students as partners in complex mumber task design. In U. T. Jankvist, M. van den Heuvel-Panhuizen & M. Veldhuis (Eds.), Proceedings of the eleventh Congress of the European Society for Research in Mathematics Education (pp. 4859–4866). https://hal.archives-ouvertes.fr/hal-02459928

Trouche, L. (2020a). Instrumentalization in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed., pp. 392–403). Springer Verlag. doi.org/10.1007/978-3-030-15789-0_80

van den Heuvel-Panhuizen, M., & van Zanten, M. (2020). Realistic Mathematics Education: A brief history of a longstanding reform movement. Mediterranean Journal for Research in Mathematics Education, 17(1), 65–73. doi.org/10.1016/j.cub.2014.12.009

van Joolingen, W. R. & Zacharia, Z. C. (2009). Developments in inquiry learning. In N. Balacheff, S. Ludvigsen, T. de Jong, A. Lazonder & S. Barnes (Eds.), Technology enhanced learning: Principles and products (pp. 21–37). Springer Verlag. doi.org/10.1007/978-1-4020-9827-7_2

von Glaserfeld, E. (1995). Radical constructivism: A way of knowing and learning. Falmer Press. ERIC. https://files.eric.ed.gov/fulltext/ED381352.pdf

Watson, A., & Ohtani, M. (Eds.). (2015). Task design in mathematics education. Springer Verlag. doi.org/10.1007/978-3-319-09629-2

Watson, A., Ohtani, M., Ainley, J., Bolite-Frant, J., Doorman, M., Kieran, C., . . . , & Yang, Y. (2013). Introduction. In C. Margolinas (Ed.), Task design in mathematics education (Proceedings of the ICMI Study 22). https://hal.archives-ouvertes.fr/hal-00834054

Wenning, C. J. (2005) Levels of inquiry: hierarchies of pedagogical practices and inquiry processes. Journal of Physics Teacher Education Online, 2(3), 3–11.

World Wide Web Consortium (2018). Web Content Accessibility Guidelines (WCAG) 2.2. www.w3.org/TR/WCAG/