Interactions and tensions between mathematical discourses and schoolwork discourses when solving dynamic geometry tasks: what is internally persuasive for students?

References

• Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. ZDM, 34(3), 66–72. https://doi.org/10.1007/BF02655708
   Google Scholar
• Baccaglini-Frank, A. (2019). Dragging, instrumented abduction and evidence, in processes of conjecture generation in a dynamic geometry environment. ZDM, 51(5), 779–791. https://doi.org/10.1007/s11858-019-01046-8
   Google Scholar
• Baccaglini-Frank, A. (2021). To tell a story, you need a protagonist: How dynamic interactive mediators can fulfill this role and foster explorative participation to mathematical discourse. Educational Studies in Mathematics, 106(2), 291–312. https://doi.org/10.1007/s10649-020-10009-w
   Web of Science ®Google Scholar
• Bakhtin, M. M. (1981). The dialogic imagination: Four essays. University of Texas Press.
   Google Scholar
• Bakhtin, M. M. (1986). Speech genres and other late essays. University of Texas Press.
   Google Scholar
• Bakker, A., Smit, J., & Wegerif, R. (2015). Scaffolding and dialogic teaching in mathematics education: Introduction and review. ZDM, 47(7), 1047–1065. https://doi.org/10.1007/s11858-015-0738-8
   Google Scholar
• Boulay, B., O’Shea, T., & Monk, J. (1981). The black box inside the glass box: Presenting computing concepts to novices. International Journal of Man-Machine Studies, 14(3), 237–249. https://doi.org/10.1016/S0020-7373(81)80056-9
   Google Scholar
• Bozkurt, G., & Ruthven, K. (2018). The activity structure of technology-based mathematics lessons: A case study of three teachers in English secondary schools. Research in Mathematics Education, 20(3), 254–272. https://doi.org/10.1080/14794802.2018.1474798
   Web of Science ®Google Scholar
• Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
   Google Scholar
• Bray, A., & Tangney, B. (2017). Technology usage in mathematics education research – A systematic review of recent trends. Computers & Education, 114, 255–273. https://doi.org/10.1016/j.compedu.2017.07.004
   Web of Science ®Google Scholar
• Bretscher, N. (2021). Challenging assumptions about relationships between mathematics pedagogy and ICT integration: Surveying teachers in English secondary schools. Research in Mathematics Education, 23(2), 142–158. https://doi.org/10.1080/14794802.2020.1830156
   Web of Science ®Google Scholar
• Cazden, C. B. (2001). Classroom discourse. The language of teaching and learning (2nd ed.). Heinemann.
   Google Scholar
• Civil, M. (2002). Everyday mathematics, mathematicians’ mathematics, and school mathematics: Can we bring them together? Journal for Research in Mathematics Education. Monograph, 11, 40–62. https://doi.org/10.2307/749964
   Google Scholar
• Common Core State Standards Initiative. (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices and the Council of Chief State School Officers.
   Google Scholar
• Dalton, S., & Hegedus, S. (2013). Learning and participation in high school classrooms. In S. J. Hegedus & J. Roschelle (Eds.), The SimCalc vision and contributions (pp. 145–166). Springer. http://link.springer.com/10.1007978-94-007-5696-0_9
   Google Scholar
• Detlefsen, M. (2008). Purity as an ideal of proof. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 179–197). Oxford University Press.
   Google Scholar
• Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23(2), 167–180. https://doi.org/10.1207/s15326985ep2302_6
   Web of Science ®Google Scholar
• Dutilh Novaes, C. (2020). The dialogical roots of deduction: Historical, cognitive, and philosophical perspectives on reasoning. Cambridge University Press. https://doi.org/10.1017/9781108800792
   Google Scholar
• Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103–131. https://doi.org/10.1007/s10649-006-0400-z
   Google Scholar
• Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111(23), 8410–8415. https://doi.org/10.1073/pnas.1319030111
   PubMed Web of Science ®Google Scholar
• Garfinkel, H. (1964). Studies of the routine grounds of everyday activities. Social Problems, 11(3), 225–250. https://doi.org/10.2307/798722
   Web of Science ®Google Scholar
• Gíslason, I. (2021). Discussing dependencies of variable points on the basis of a GeoGebra task: Meaning making in a teacher-class dialogue. Digital Experiences in Mathematics Education, 7(2), 301–322. https://doi.org/10.1007/s40751-021-00087-7
   Google Scholar
• Goodchild, S. (2001). Students’ goals: A case study of activity in a mathematics classroom. Caspar.
   Google Scholar
• Hansen, E. K. S. (2022). Students’ agency, creative reasoning, and collaboration in mathematical problem solving. Mathematics Education Research Journal, 34(4), 813–834. https://doi.org/10.1007/s13394-021-00365-y
   Google Scholar
• Hoyles, C. (2018). Transforming the mathematical practices of learners and teachers through digital technology. Research in Mathematics Education, 20(3), 209–228. https://doi.org/10.1080/14794802.2018.1484799
   Web of Science ®Google Scholar
• Inglis, M., & Mejía-Ramos, J. P. (2009). On the persuasiveness of visual arguments in mathematics. Foundations of Science, 14(1-2), 97–110. https://doi.org/10.1007/s10699-008-9149-4
   Google Scholar
• Ingram, J. (2021). Patterns in mathematics classroom interaction: A conversation analytic approach. Oxford University Press.
   Google Scholar
• Jones, K. (2000). Providing a foundation for deductive reasoning: Students’ interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1/2), 55–85. https://doi.org/10.1023/A:1012789201736
   Google Scholar
• Jónsdóttir, A. H., Briem, E., Hreinsdóttir, F., Þórarinsson, F., Magnússon, J. I., & Möller, R. G. (2014). Úttekt á stærðfræðikennslu í framhaldsskólum. [An evaluation of mathematics teaching in Icelandic upper secondary schools]. Mennta- og menningarmálaráðuneytið.
   Google Scholar
• Kazak, S., Wegerif, R., & Fujita, T. (2015). The importance of dialogic processes to conceptual development in mathematics. Educational Studies in Mathematics, 90(2), 105–120. https://doi.org/10.1007/s10649-015-9618-y
   Web of Science ®Google Scholar
• Knuth, E. J. (2000). Student understanding of the Cartesian connection: An exploratory study. Journal for Research in Mathematics Education, 31(4), 500–507. https://doi.org/10.2307/749655
   Web of Science ®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(1), 29–63. https://doi.org/10.3102/00028312027001029
   Web of Science ®Google Scholar
• Lemke, J. L. (1990). Talking science: Language, learning, and values. Ablex Publishing.
   Google Scholar
• Liljedahl, P., & Allan, D. (2013). Studenting: The case of “now you try one”. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 257–264). PME.
   Google Scholar
• Linell, P. (2009). Rethinking language, mind, and world dialogically. Information Age Publishing.
   Google Scholar
• Lisarelli, G. (2019). A dynamic approach to functions and their graphs: A study of students’ discourse from a commognitive perspective [Doctoral thesis, University of Firenze]. https://flore.unifi.it/retrieve/e398c37e-2ff8-179a-e053-3705fe0a4cff/TesiDottorato_Lisarelli.pdf
   Google Scholar
• Magidson, S. (2005). Building bridges within mathematics education: Teaching, research, and instructional design. The Journal of Mathematical Behavior, 24(2), 135–169. https://doi.org/10.1016/j.jmathb.2005.03.004
   Google Scholar
• Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267. https://doi.org/10.1023/A:1009973717476
   Google Scholar
• Mason, J. (2009). From assenting to asserting. In O. Skovsmose, P. Valero, & O. R. Christensen (Eds.), University science and mathematics education in transition (pp. 17–40). Springer. https://doi.org/10.1007/978-0-387-09829-6_2
   Google Scholar
• Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Pearson.
   Google Scholar
• Mehan, H. (1979). Learning lessons: Social organization in the classroom. Harvard University Press.
   Google Scholar
• Mellin-Olsen, S. (1987). The politics of mathematics education. Springer.
   Google Scholar
• Moreno-Armella, L., Hegedus, S. J., & Kaput, J. J. (2008). From static to dynamic mathematics: Historical and representational perspectives. Educational Studies in Mathematics, 68(2), 99–111. https://doi.org/10.1007/s10649-008-9116-6
   Google Scholar
• Morgan, C. (2016). Studying the role of human agency in school mathematics. Research in Mathematics Education, 18(2), 120–141. https://doi.org/10.1080/14794802.2016.1176595
   Web of Science ®Google Scholar
• Moschkovich, J. (2007). Examining mathematical discourse practices. For the Learning of Mathematics, 27(1), 24–30. https://www.jstor.org/stable/40248556
   Google Scholar
• Olsson, J. (2019). Relations between task design and students’ utilization of GeoGebra. Digital Experiences in Mathematics Education, 5(3), 223–251. https://doi.org/10.1007/s40751-019-00051-6
   Google Scholar
• Oner, D. (2016). Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical. International Journal of Computer-Supported Collaborative Learning, 11(1), 59–88. https://doi.org/10.1007/s11412-016-9227-5
   Google Scholar
• Otten, S., Engledowl, C., & Spain, V. (2015). Univocal and dialogic discourse in secondary mathematics classrooms: The case of attending to precision. ZDM, 47(7), 1285–1298. https://doi.org/10.1007/s11858-015-0725-0
   Google Scholar
• Papert, S. (1980). Mindstorms. Basic Books.
   Google Scholar
• Pólya, G. (1990). How to solve it: A new aspect of mathematical method (2nd ed). Penguin Books.
   Google Scholar
• Schoenfeld, A. H. (2014). What makes for powerful classrooms, and how can we support teachers in creating them? A story of research and practice, productively intertwined. Educational Researcher, 43(8), 404–412. https://doi.org/10.3102/0013189X14554450
   Web of Science ®Google Scholar
• Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge University Press.
   Google Scholar
• Swan, M. (2005). Standards unit: Improving learning in mathematics: Challenges and strategies. Department for Education and Skills Standards Unit.
   Google Scholar
• Swan, M., Pitts, J., Fraser, R., & Burkhardt, H. (1985). The language of functions and graphs: An examination module for secondary schools. Joint Matriculation Board and Shell Centre for Mathematical Education.
   Google Scholar
• Wardhaugh, R. (2006). An introduction to sociolinguistics (5th ed.). Blackwell Publishing.
   Google Scholar
• Watson, A. (2008). School mathematics as a special kind of mathematics. For the Learning of Mathematics, 28(3), 3–7. https://www.jstor.org/stable/40248612
   Google Scholar
• Watson, A. (2021). Care in mathematics education: Alternative educational spaces and practices. Springer. https://doi.org/10.1007/978-3-030-64114-6
   Google Scholar
• Willis, P. E. (2006). Learning to labour: How working class kids get working class jobs. Ashgate. (Original work published 1977).
   Google Scholar
• Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 1169–1207). Information Age Publishing.
   Google Scholar
• Zhen, B., Weber, K., & Mejia-Ramos, J. P. (2016). Mathematics majors’ perceptions of the admissibility of graphical inferences in proofs. International Journal of Research in Undergraduate Mathematics Education, 2(1), 1–29. https://doi.org/10.1007/s40753-015-0010-1
   Google Scholar