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Discrete Mathematics and the Affective Dimension of Mathematical Learning and Engagement

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Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

This paper describes certain characteristics of discrete mathematics that can enable teachers to evoke student interest and engagement , and develop students’ powerful affect in relation to math—emotion s, attitudes, beliefs, and values. Special affordances of discrete mathematics include interesting topics arising in familiar settings , special cases that are easy to set up and explore, a variety of natural representation s embodying mathematical structures, and few prerequisites needed for in-depth inquiry. We also list several possible domain-specific sources of commonly-occurring math anxiety (long-term negative affect ) which can be ameliorated through effective teaching making use of these features of discrete mathematics . An example from game theory illustrates our suggested approach. Pitfalls are also identified, including the too-early introduction of formal definitions, theorems, and problem-solving algorithms, or (alternatively) the relegation of discrete mathematics to a “slow track ” in the curriculum .

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References

  • Baloğlu, M., & Koçak, R. (2006). A multivariate investigation of the differences in mathematics anxiety. Personality and Individual Differences, 40, 1325–1335.

    Article  Google Scholar 

  • Csikszentmihalyi, M. (1990). Flow: The psychology of optimal performance. New York: Cambridge University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • DeBellis, V. A., & Rosenstein, J. G. (2004). Discrete mathematics in primary and secondary schools in the United States. ZDM Mathematics Education, 36(2), 46–55.

    Article  Google Scholar 

  • DeBellis, V. A., Rosenstein, J. G., Hart, E., & Kenney, M. (2009). Navigating through discrete mathematics in grades pre-K to 5. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Devine, A., Fawcett, K., Szűcs, D., & Dowker, A. (2012). Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and Brain Functions, 8, 33. Retrieved from www.behavioralandbrainfunctions.com/content/8/1/33.

  • Dweck, C. S. (2006). Mindset: The new psychology of success. New York: Ballantine Books.

    Google Scholar 

  • Ferguson, T. S. (2014). Game theory (2nd ed.). University of California: on-line resource available at https://www.math.ucla.edu/~tom/Game_Theory/Contents.html.

  • Goldin, G. A. (2000). Affective pathways and representation in mathematical problem solving. Mathematical Thinking and Learning, 2(3), 209–219.

    Article  Google Scholar 

  • Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59–72). Dordrecht: Kluwer.

    Google Scholar 

  • Goldin, G. A. (2004). Problem solving heuristics, affect, and discrete mathematics. ZDM Mathematics Education, 36(2), 56–60.

    Article  Google Scholar 

  • Goldin, G. A. (2009). The affective domain and students’ mathematical inventiveness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 181–194). Rotterdam: Sense.

    Google Scholar 

  • Goldin, G. A. (2014). Perspectives on emotion in mathematical engagement, learning, and problem solving. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 391–414). New York: Routledge.

    Google Scholar 

  • Goldin, G. A., Epstein, Y. M., Schorr, R. Y., & Warner, L. B. (2011). Beliefs and engagement structures: Behind the affective dimension of mathematical learning. ZDM Mathematics Education, 43, 547–556.

    Article  Google Scholar 

  • Hannula, M. S. (2006). Motivation in mathematics: Goals reflected in emotions. Educational Studies in Mathematics, 63, 165–178.

    Article  Google Scholar 

  • Hannula, M., Di Martino, P., Pantziara, M., Zhang, Q., Morselli, F., Heyd-Metzuyanim, E., Lutovac, S., Kaasila, R., Middleton, J. A., Jansen, A., & Goldin, G. A. (2016). Attitudes, beliefs, motivation and identity in mathematics education: An overview of the field and future directions. Springer International.

    Google Scholar 

  • Hart, E. W., Kenney, M., DeBellis, V. A., & Rosenstein, J. G. (2008). Navigating through discrete mathematics in grades 6-12. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Heinze, A., Anderson, I., & Reiss, K. (2004). Analyses: Discrete mathematics and proof in the high school. ZDM 36(2), 44–45. Analyses: Discrete mathematics and proof in the high school, Pt. 2. ZDM 36(3).

    Google Scholar 

  • Hidi, S., Renninger, K. A., & Krapp, A. (2004). Interest, a motivational variable that combines affective and cognitive functioning. In D. Y. Dai & R. J. Sternberg (Eds.), Motivation, emotion, & cognition: integrative perspectives on intellectual functioning and development (pp. 89–115). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Jansen, A., & Middleton, J. A. (2011). Motivation matters and interest counts: Fostering engagement in mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Leder, G., Pehkonen, E., & Törner, G. (Eds.). (2002). Beliefs: A hidden variable in mathematics education? Dordrecht: Kluwer.

    Google Scholar 

  • Maasz, J., & Schlöglmann, W. (Eds.). (2009). Beliefs and attitudes in mathematics education: New research results. Rotterdam, Netherlands: Sense.

    Google Scholar 

  • McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 575–596). New York, NY: Macmillan.

    Google Scholar 

  • MFO. (2002). Miniworkshop: Discrete mathematics and proof in the high school. In G. A. Goldin, K. Reiss (Eds.), Mathematisches Forschungsinstitut Oberwolfach, Report No. 50/2002.

    Google Scholar 

  • Middleton, J. A., Jansen, A., & Goldin, G. A. (2017, in press). The complexities of mathematical engagement: Motivation, affect, and social interactions. In J. Cai (Ed.), Compendium for research in mathematics education. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Op’t Eynde, P., De Corte, E., & Verschaffel, L. (2007). Students’ emotions: A key component of self-regulated learning? In P. Schutz & R. Pekrun (Eds.), Emotion in education (pp. 185–204). Burlington, MA: Academic Press.

    Google Scholar 

  • Paterson, J., & Sneddon, J. (2011). Conversations about curriculum change: Mathematical thinking and team-based learning in a discrete mathematics course. International Journal of Mathematical Education in Science and Technology, 42(7), 879–889.

    Google Scholar 

  • Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–318). Charlotte, NC: Information Age.

    Google Scholar 

  • Pieronkiewicz, B. (2015). Affective transgression as the core objective of mathematics education. Philosophy of Mathematics Education, 29.

    Google Scholar 

  • Rosen, K. H. (2012). Discrete mathematics and its applications (7th ed.). New York: McGraw-Hill.

    Google Scholar 

  • Rosenstein, J. G. (2014). Problem solving and reasoning with discrete mathematics (preliminary edition, with accompanying activity book). Highland Park, NJ: Shiviti Publications.

    Google Scholar 

  • Sheffield, L. J. (2017). Dangerous myths about “gifted” mathematics students. ZDM—The International Journal on Mathematics Education, doi:10.1007/s11858-016-0814-8.

  • Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.

    Google Scholar 

  • Snow, R. E. (1996). Self-regulation as meta-conation? Learning and Individual Differences, 8(3), 261–267.

    Article  Google Scholar 

  • Snow, R. E., Corno, L., & Jackson, D., III. (1996). Individual differences in affective and conative functions. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 243–310). New York, NY: Macmillan.

    Google Scholar 

  • Tobias, S. (1993). Overcoming math anxiety. New York, NY: W. W. Norton & Company.

    Google Scholar 

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Authors and Affiliations

  1. Rutgers University, New Brunswick, NJ, USA

    Gerald A. Goldin

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  1. Gerald A. Goldin
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Correspondence to Gerald A. Goldin .

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Editors and Affiliations

  1. Mathematics Department, Grand View University, Des Moines, Iowa, USA

    Eric W. Hart

  2. Department of Mathematics and Statistics, Georgetown University, Washington, District of Columbia, USA

    James Sandefur

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Goldin, G.A. (2018). Discrete Mathematics and the Affective Dimension of Mathematical Learning and Engagement. In: Hart, E., Sandefur, J. (eds) Teaching and Learning Discrete Mathematics Worldwide: Curriculum and Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70308-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-70308-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70307-7

  • Online ISBN: 978-3-319-70308-4

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