The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model

Mei-Shiu Chiu; Fou-Lai Lin; Kai-Lin Yang; Toshiyuki Hasumi; Tsung-Ju Wu; Pin-Syuan Lin

doi:10.29333/ejmste/12579

Full Text (PDF)

Mei-Shiu Chiu ¹ ^* , Fou-Lai Lin ² , Kai-Lin Yang ² , Toshiyuki Hasumi ¹ ³ , Tsung-Ju Wu ² , Pin-Syuan Lin ¹

More Detail

¹ National Chengchi University, Taipei City, TAIWAN² National Taiwan Normal University, Taipei City, TAIWAN³ Ming Chuan University, Taipei City, TAIWAN^* Corresponding Author

Abstract

This study aims to build a framework for affect-focused (or affective) mathematical teaching (AMT), while promoting higher-order mathematical learning (e.g., pattern finding and deep understanding). The data sources were the class mathematics grounding activity designed by Taiwan’s mathematics educators, aiming to enhance students’ affective performances in learning mathematics with a theoretical base on the enactivist perspective. Qualitative methodology identified features of affective mathematics teaching and formed a framework for AMT, which defines AMT as transforming natural languages to mathematical languages, highlighting student agenda of upward learning (interest, sense, utter, and present), met by teacher agenda of caring (cultivate, amuse, reflect, and explain). Finally, the enactivist embodiment activities are embedded in the pedagogical structure of 4E phases: entry, entertainment, enlightenment, and enrichment. Affect and cognition interplay in each phase.

Keywords

affect
cognition
mathematics education
qualitative methods

Supplementary Files

mgaStorySupp1mgaAnalysisChinese
mgaStorySupp2mga2-4story

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2022, Volume 18, Issue 12, Article No: em2187

https://doi.org/10.29333/ejmste/12579

Publication date: 26 Oct 2022

Article Views: 1533

Article Downloads: 930

Open Access References How to cite this article

References

Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy: Final report. King’s College, School of Education.
Burton, L. (1994). Children learning mathematics: Patterns and relationships. Simon & Schuster Education.
Chang, Y.-P., Lin, F.-L., & Yang, K.-L. (2021). The development of a workshop for cultivating leaders of mathematics-grounding activities in class. Educational Designer, 4(14).
Charmaz, K. (2000). Grounded theory: Objectivist and constructivist methods. In N. K. Denzin, & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 509-535). SAGE.
Chiu, M.-S. (2009). Approaches to the teaching of creative and non-creative mathematical problems. International Journal of Science and Mathematics Education, 7, 55-79. https://doi.org/10.1007/s10763-007-9112-9
Chiu, M.-S. (2020). Exploring models for increasing the effects of school information and communication technology use on learning outcomes through outside-school use and socioeconomic status mediation: The ecological techno-process. Educational Technology Research and Development, 68, 413-436. https://doi.org/10.1007/s11423-019-09707-x
Chu, Z.-C. (2020). Some people say manipulation is too time-consuming in mathematics class. Up To Date. Post Dated September 1, 2020. https://www.facebook.com/goechu/posts/3602472479765782
DeBellis, V. A., & Goldin, G. A. (2006). Affect and meta-affect in mathematical problem solving: A representational perspective. Educational Studies in Mathematics, 63(2), 131-147. https://doi.org/10.1007/s10649-006-9026-4
Derry, S. J., Pea, R. D., Barron, B., Engle, R. A., Erickson, F., Goldman, R., Hall, R., Koschmann, T., Lemke, J. L., Sherin, M. G., & Sherin, B. L. (2010). Conducting video research in the learning sciences: Guidance on selection, analysis, technology, and ethics. The Journal of the Learning Sciences, 19(1), 3-53. https://doi.org/10.1080/10508400903452884
Driver, R., & Oldham, V. (1986). A constructivist approach to curriculum development in science. Studies in Science Education, 13, 105-122. https://doi.org/10.1080/03057268608559933
Duval, R. (2000). Basic issues for research in mathematics education. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24^th Conference of the International Group for the Psychology of Mathematics Education (pp. 55-69). Nishiki Print.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131. https://doi.org/10.1007/s10649-006-0400-z
Empson, S. B. (2003). Low-performing students and teaching fractions for understanding: An interactional analysis. Journal for Research in Mathematics Education, 34, 305-343. https://doi.org/10.2307/30034786
Francisco, J. M. (2013). Learning in collaborative settings: Students building on each other’s ideas to promote their mathematical understanding. Educational Studies in Mathematics, 82(3), 417-438. https://doi.org/10.1007/s10649-012-9437-3
Fusch, P. I., & Ness, L. R. (2015). Are we there yet? Data saturation in qualitative research. The Qualitative Report, 20, 1408-1416. https://doi.org/10.46743/2160-3715/2015.2281
Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2, 209-219. https://doi.org/10.1207/S15327833MTL0203_3
Goldin, G. A. (2004). Problem solving heuristics, affect, and discrete mathematics. ZDM, 36, 56-60. https://doi.org/10.1007/BF02655759
Gomez-Chacon, I. M. (2000). Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43, 149-168. https://doi.org/10.1023/A:1017518812079
Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: Embodied and social theories. Research in Mathematics Education, 14, 137-161. https://doi.org/10.1080/14794802.2012.694281
Hannula, M. S. (2019). Young learners’ mathematics-related affect: A commentary on concepts, methods, and developmental trends. Educational Studies in Mathematics, 100, 309-316. https://doi.org/10.1007/s10649-018-9865-9
Hidi, S., & Renninger, K. A. (2006). The four-phase model of interest development. Educational psychologist, 41(2), 111-127. https://doi.org/10.1207/s15326985ep4102_4
Kopcha, T. J., Ocak, C., & Qian, Y. (2020). Analyzing children’s computational thinking through embodied interaction with technology: A multimodal perspective. Educational Technology Research and Development, 69, 1987-2012. https://doi.org/10.1007/s11423-020-09832-y
Maher, C. A., Palius, M. F., Maher, J. A., Hmelo-Silver, C. E., & Sigley, R. (2014). Teachers can learn to attend to students’ reasoning using videos as a tool. Issues in Teacher Education, 23(1), 31-47.
Marmur, O., & Koichu, B. (2021). Between expert and student perspectives: On the intersection of affect and heuristic-didactic discourse in the undergraduate classroom. Mathematical Thinking and Learning. https://doi.org/10.1080/10986065.2021.1940432
Marton, F. (1981). Phenomenography: Describing conceptions of the world around us. Instructional Science, 10, 177-200. https://doi.org/10.1007/BF00132516
Mason, J., Burton, L., & Stacey, K. (1996). Thinking mathematically. Addison-Wesley.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 575-596). Macmillan.
Menon, V., & Chang, H. (2021). Emerging neurodevelopmental perspectives on mathematical learning. Developmental Review, 60, 100964. https://doi.org/10.1016/j.dr.2021.100964
Middleton, J. A. (1995). A study of intrinsic motivation in the mathematics classroom: A personal constructs approach. Journal for Research in Mathematics Education, 26, 254-279. https://doi.org/10.2307/749130
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. SAGE.
Ministry of Education in Taiwan (2014). Curriculum guidelines of 12-year basic education. https://cirn.moe.edu.tw/Upload/file/32077/83646.pdf
Ministry of Education in Taiwan (2018). Curriculum guidelines of 12-year basic education: Mathematics. https://cirn.moe.edu.tw/Upload/file/27338/72246.pdf
Nunes, T. (1997). Systems of signs and mathematical reasoning. In T. Nunes, & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 29-44). Psychology Press.
OECD. (2014). PISA 2012 results (volumes I and III). OECD Publishing. https://www.oecd.org/pisa/aboutpisa/pisa-2012-results.htm
OECD. (2021). Beyond academic learning: First results from the survey of social and emotional skills. OECD Publishing. https://doi.org/10.1787/92a11084-en
Polya, G. (1945). How to solve it. Princeton University Press. https://doi.org/10.1515/9781400828678
Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405-435. https://doi.org/10.1016/j.jmathb.2003.09.002
Rodríguez‐Aflecht, G., Jaakkola, T., Pongsakdi, N., Hannula‐Sormunen, M., Brezovszky, B., & Lehtinen, E. (2018). The development of situational interest during a digital mathematics game. Journal of Computer Assisted Learning, 34(3), 259-268. https://doi.org/10.1111/jcal.12239
Schulman, S. M. (2013). According to Davis: Connecting principles and practices. The Journal of Mathematical Behavior, 32(2), 230-242. https://doi.org/10.1016/j.jmathb.2013.02.002
SDiME. (2022). Just do math. Department of Mathematics, National Taiwan Normal University. https://www.ime.ntnu.edu.tw/index.php/en/en-project-jdm/
Stigler, J. W., & Perry, M. (1990). Mathematics learning in Japanese, Chinese and American classrooms. In J. W. Stigler, R. A. Shweder, & G. Herdt (Eds.), Cultural psychology: Essays on comparative human development (pp. 328-353). Cambridge University Press. https://doi.org/10.1017/CBO9781139173728.011
Stipek, D., Salmon, J. M., Givvin, K. B., Kazemi, E., Saxe, G., & MacGyvers, V. L. (1998). The value (and convergence) of practices suggested by motivation research and promoted by mathematics education reformers. Journal for Research in Mathematics Education, 29, 465-488. https://doi.org/10.2307/749862
Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. SAGE.
Strauss, A., & Corbin, J. (1998). Grounded theory methodology: An overview. In N. K. Denzin, & Y. S. Lincoln (Eds.), Strategies of qualitative inquiry (pp. 158-183). SAGE.
Sun, Z., Xie, K., & Anderman, L. H. (2018). The role of self-regulated learning in students’ success in flipped undergraduate math courses. The Internet and Higher Education, 36, 41-53. https://doi.org/10.1016/j.iheduc.2017.09.003
Voskoglou, M. G. (2011). Problem solving from Polya to nowadays: A review and future perspectives. Progress in Education, 22(4), 65-82.
Wang, T. Y., Lin, F. L., & Yang, K. L. (2021). Success factors for a national problem-driven program aimed at enhancing affective performance in mathematics learning. ZDM-Mathematics Education, 53, 1121-1136. https://doi.org/10.1007/s11858-021-01285-8
Wilkinson, L. C., Bailey, A. L., & Maher, C. A. (2018). Students’ mathematical reasoning, communication, and language representations: A video-narrative analysis. ECNU Review of Education, 1(3), 1-22. https://doi.org/10.30926/ecnuroe2018010301
Wilmes, S. E., & Siry, C. (2021). Multimodal interaction analysis: A powerful tool for examining plurilingual students’ engagement in science practices. Research in Science Education, 51, 71-91. https://doi.org/10.1007/s11165-020-09977-z
Yang, K. L., Lin, F. L., & Tso, T. Y. (2021). An approach to enactivist perspective on learning: Mathematics-grounding activities. Asia-Pacific Education Researcher, 31, 657-666. https://doi.org/10.1007/s40299-021-00616-3
Yeager, D. S., Hanselman, P., Walton, G. M., Murray, J. S., Crosnoe, R., Muller, C., Tipton, E., Schneider, B., Hulleman, C. S., Hinojosa, C. P., Paunesku, D., Romero, C., Flint, K., Roberts, A., Trott, J., Iachan, R., Buontempo, J., Yang, S. M., Carvalho, C. M., ..., & Dweck, C. S. (2019). A national experiment reveals where a growth mindset improves achievement. Nature, 573(7774), 364-369. https://doi.org/10.1038/s41586-019-1466
Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63, 113-121. https://doi.org/10.1007/s10649-006-9028-2

How to cite this article

APA

Chiu, M.-S., Lin, F.-L., Yang, K.-L., Hasumi, T., Wu, T.-J., & Lin, P.-S. (2022). The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2187. https://doi.org/10.29333/ejmste/12579

Vancouver

Chiu MS, Lin FL, Yang KL, Hasumi T, Wu TJ, Lin PS. The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model. EURASIA J Math Sci Tech Ed. 2022;18(12):em2187. https://doi.org/10.29333/ejmste/12579

AMA

Chiu MS, Lin FL, Yang KL, Hasumi T, Wu TJ, Lin PS. The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model. EURASIA J Math Sci Tech Ed. 2022;18(12), em2187. https://doi.org/10.29333/ejmste/12579

Chicago

Chiu, Mei-Shiu, Fou-Lai Lin, Kai-Lin Yang, Toshiyuki Hasumi, Tsung-Ju Wu, and Pin-Syuan Lin. "The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 12 (2022): em2187. https://doi.org/10.29333/ejmste/12579

Harvard

Chiu, M.-S., Lin, F.-L., Yang, K.-L., Hasumi, T., Wu, T.-J., and Lin, P.-S. (2022). The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2187. https://doi.org/10.29333/ejmste/12579

MLA

Chiu, Mei-Shiu et al. "The interplay of affect and cognition in the mathematics grounding activity: Forming an affective teaching model". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 12, 2022, em2187. https://doi.org/10.29333/ejmste/12579