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Beliefs and engagement structures: behind the affective dimension of mathematical learning

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Abstract

Beliefs influencing students’ mathematical learning and problem solving are structured and intertwined with larger affective and cognitive structures. This theoretical article explores a psychological concept we term an engagement structure, with which beliefs are intertwined. Engagement structures are idealized, hypothetical constructs, analogous in many ways to cognitive structures. They describe complex “in the moment” affective and social interactions as students work on conceptually challenging mathematics. We present engagement structures in a self-contained way, paying special attention to their theoretical justification and relation to other constructs. We suggest how beliefs are characteristically woven into their fabric and influence their activation. The research is based on continuing studies of middle school students in inner-city classrooms in the USA.

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References

  • Abelson, R. P. (1981). Psychological status of the script concept. American Psychologist, 36(7), 715–729.

    Article  Google Scholar 

  • Alston, A., Goldin, G. A., Jones, J., McCulloch, A., Rossman, C., & Schmeelk, S. (2007). The complexity of affect in an urban mathematics classroom. In T. Lamberg & L. R. Wiest (Eds.), Exploring mathematics education in context: Proceedings of the 29th annual meeting of PME-NA, Lake Tahoe, NV (pp. 326–333). Reno: University of Nevada.

    Google Scholar 

  • Anderman, E. M., & Wolters, C. A. (2006). Goals, values, and affect: Influences on student motivation. In P. Alexander & P. Winne (Eds.), Handbook of educational psychology (pp. 369–389). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Anderson, E. (1999). Code of the street. NY: W. W. Norton.

    Google Scholar 

  • Beck, A. T. (1976). Cognitive therapy and the emotional disorders. NY: New American Library.

    Google Scholar 

  • Capraro, M. M., Capraro, R. M., & Henson, R. K. (2001). Measurement error of scores on the mathematics anxiety rating scale across studies. Educational and Psychological Measurement, 61, 373–386.

    Article  Google Scholar 

  • Cattell, R. B., & Scheier, I. H. (1961). The meaning and measurement of neuroticism and anxiety. NY: Ronald Press.

    Google Scholar 

  • Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. NY: Harper & Row.

    Google Scholar 

  • Dai, D. Y., & Sternberg, R. J. (Eds.). (2004). Motivation, emotion, and cognition: Integrative perspectives on intellectual functioning and development. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Dance, L. J. (2002). Tough fronts: The impact of street culture on schooling. NY: Routledge-Falmer.

    Google Scholar 

  • Davis, R. B. (1984). Learning mathematics: The cognitive science approach to mathematics education. Norwood, NJ: Ablex.

    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 

  • Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia, PA: Taylor & Francis.

    Google Scholar 

  • Epstein, Y. M., Goldin, G. A., Schorr, R. Y., Capraro, R., Capraro, M. M., & Warner, L. B. (2010). Measuring engagement structures in middle-grades urban mathematics classrooms. Paper presented at the 2010 annual meeting of AERA, Denver, CO.

  • Epstein, Y., Schorr, R. Y., Goldin, G. A., Warner, L., Arias, C., Sanchez, L., et al. (2007). Studying the affective/social dimension of an inner-city mathematics class. In T. Lamberg & L. R. Wiest (Eds.), Exploring mathematics education in context: Proceedings of the 29th annual meeting of PME-NA, Lake Tahoe, NV (pp. 649–656). Reno: University of Nevada.

    Google Scholar 

  • Evans, J., Morgan, C., & Tsatsaroni, A. (2006). Discursive positioning and emotion in school mathematics practices. Educational Studies in Mathematics, 63(2), 209–226.

    Article  Google Scholar 

  • Fennema, E., & Sherman, J. A. (1976). Fennema-Sherman Mathematics Attitudes Scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. Journal for Research in Mathematics Education, 7, 324–326.

    Article  Google Scholar 

  • Finn, J. D. (1993). School engagement and students at risk. Washington, DC: U. S. Department of Education, National Center for Educational Statistics (ERIC Document Reproduction Service No. ED 362 322).

  • Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive-developmental inquiry. American Psychologist, 34(10), 906–911.

    Article  Google Scholar 

  • Fredricks, J. A., Blumenfeld, P. C., & Paris, A. H. (2004). School engagement: Potential of the concept, state of the evidence. Review of Educational Research, 74(1), 59–109.

    Article  Google Scholar 

  • Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39–57). Dordrecht: Kluwer.

    Google Scholar 

  • Goffman, E. (1974). Frame analysis. NY: Harper Colophon.

    Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • Goldin, G. A., Epstein, Y. M., & Schorr, R. Y. (2007). Affective pathways and structures in urban students’ mathematics learning. In D. K. Pugalee, A. Rogerson, & A. Schinck (Eds.), Mathematics education in a global community: Proceedings of the 9th international conference of the mathematics education into the 21st century project (pp. 260–265). Charlotte, NC: University of North Carolina.

    Google Scholar 

  • Goldin, G. A., Rösken, B., & Törner, G. (2009). Beliefs: No longer a hidden variable in mathematics teaching and learning processes. In J. Maass & W. Schlöglmann (Eds.), Beliefs and attitudes in mathematics education: new research results (pp. 1–18). Rotterdam: Sense.

    Google Scholar 

  • Gomez-Chacon, I. M. (2000). Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43, 149–168.

    Article  Google Scholar 

  • Green, T. F. (1971). The activities of teaching. Tokyo: McGraw-Hill.

    Google Scholar 

  • Greeno, J. G., & Goldman, S. V. (1988). Thinking practices in mathematics and science learning. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Greenwood, C. R. (1991). Longitudinal analysis of time, engagement, and achievement in at-risk versus non at-risk students. Exceptional Children, 57, 521–535.

    Google Scholar 

  • Grouws, D. A., & Lembke, L. O. (1996). Influential factors in student motivation to learn mathematics: The teacher and classroom culture. In M. Carr (Ed.), Motivation in mathematics (pp. 39–62). Cresskill, NJ: Hampton Press.

    Google Scholar 

  • Hannula, M. S. (2002). Attitude towards mathematics: Emotions, expectations and values. Educational Studies in Mathematics, 49, 25–46.

    Article  Google Scholar 

  • Jost, J. T., & Kay, A. C. (2010). Social justice: History, theory, and research. In S. T. Fiske, D. T. Gilbert, & G. Lindzey (Eds.), Handbook of social psychology (5th ed., Vol. 2, pp. 1122–1165). Hoboken, NJ: Wiley.

    Google Scholar 

  • Kloosterman, P. (1996). Students’ beliefs about knowing and learning mathematics: Implications for motivation. In M. Carr (Ed.), Motivation in mathematics (pp. 131–156). Cresskill, NJ: Hampton Press.

    Google Scholar 

  • Laurent, J., Catanzaro, S. J., Joiner, T. E., Jr., Rudolph, K. D., Potter, K. I., Lambert, S., et al. (1999). A measure of positive and negative affect for children: Scale development and preliminary validation. Psychological Assessment, 11(3), 326–338.

    Article  Google Scholar 

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

  • Lesh, R., Hamilton, E., & Kaput, J. J. (Eds.). (2007). Foundations for the future in mathematics education. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Linnenbrink, E. A. (2007). The role of affect in student learning: A multi-dimensional approach to considering the interaction of affect, motivation, and engagement. In P. A. Schutz & R. Pekrun (Eds.), Emotion in education (pp. 107–124). London: Elsevier.

    Google Scholar 

  • Linnenbrink, E. A., & Pintrich, P. R. (2000). Multiple pathways to learning and achievement: The role of goal orientation in fostering adaptive motivation, affect, and cognition. In C. Sansone & J. M. Harackiewicz (Eds.), Intrinsic and extrinsic motivation: The search for optimal motivation and performance (pp. 195–227). San Diego, CA: Academic Press; cited in Anderman & Wolters (2006).

  • Linnenbrink, E. A. & Pintrich, P. R (2002). Achievement goal theory and affect: An asymmetrical bidirectional model. Educational Psychologist, 37, 69–78; cited in Anderman & Wolters (2006).

    Google Scholar 

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

    Google Scholar 

  • Malmivuori, M.-L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63, 149–164.

    Article  Google Scholar 

  • Marks, H. M. (2000). Student engagement in instructional activity: Patterns in the elementary, middle, and high school years. American Educational Research Journal, 37, 153–184.

    Google Scholar 

  • McLeod, D. B. (1994). Research on affect and mathematics learning. Journal for Research in Mathematics Education, 25, 637–647.

    Article  Google Scholar 

  • McLeod, D. B., & McLeod, S. H. (2002). Synthesis—beliefs and mathematics education: Implications for learning, teaching, and research. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 115–123). Dordrecht: Kluwer.

    Google Scholar 

  • Middleton, J. A., & Spanias, P. A. (1999). Motivation for achievement in mathematics: Findings, generalizations, and criticisms of the research. Journal for Research in Mathematics Education, 30(1), 65–88.

    Article  Google Scholar 

  • Murray, H. A. (2008). 70th Anniversary edition, explorations in personality. NY: Oxford University Press.

    Google Scholar 

  • Op ‘t Eynde, P., De Corte, E., & Verschaffel, L. (2002). Framing students’ mathematics-related beliefs. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 13–37). Kluwer: Dordrecht.

    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 

  • Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62, 307–332.

    Google Scholar 

  • Pajares, M. F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24, 124–139.

    Article  Google Scholar 

  • Park, S. (2005). Student engagement and classroom variables in improving mathematics achievement. Asia Pacific Education Review, 6(1), 87–97. doi:10.1007/BF03024970.

    Article  Google Scholar 

  • Pekrun, R., Frenzel, A. C., Goetz, T., & Perry, R. P. (2007). The control-value theory of achievement emotions: An integrative approach to emotions in education. In P. Schutz & R. Pekrun (Eds.), Emotion in education (pp. 13–36). Burlington, MA: Academic Press.

    Google Scholar 

  • Pintrich, P. R. (2000). Multiple goals, multiple pathways: The role of goal orientation in learning and achievement. Journal of Educational Psychology, 92, 544–555.

    Article  Google Scholar 

  • Richardson, F., & Suinn, R. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19, 551–554.

    Article  Google Scholar 

  • Rogers, T. B. (1983). Emotion, imagery, and verbal codes: A closer look at an increasingly complex interaction. In J. Yuille (Ed.), Imagery, memory, and cognition: Essays in honor of Allan Paivio (pp. 295–305). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Rokeach, M. (1968). Beliefs, attitudes, and values: A theory of organization and change. San Francisco: Jossey-Bass.

    Google Scholar 

  • Rokeach, M. (1973). The nature of human values. NY: The Free Press.

    Google Scholar 

  • Ross, L., & Nisbett, R. E. (1991). The person and the situation: Perspectives of social psychology. NY: McGraw-Hill.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. NY: Academic Press.

    Google Scholar 

  • Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. NY: Routledge.

    Google Scholar 

  • Schorr, R. Y., Epstein, Y. M., Warner, L. B., & Arias, C. C. (2010a). Don’t disrespect me: Affect in an urban math class. In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 313–325). NY: Springer.

    Chapter  Google Scholar 

  • Schorr, R. Y., Epstein, Y. M., Warner, L. B., & Arias, C. C. (2010b). Mathematical truth and social consequences: The intersection of affect and cognition in a middle school classroom. Mediterranean Journal for Research in Mathematics Education, 9, 107–134.

    Google Scholar 

  • Schorr, R. Y., & Goldin, G. A. (2008). Students’ expression of affect in an inner-city SimCalc classroom. Educational Studies in Mathematics, 68, 131–148.

    Article  Google Scholar 

  • Schunk, D. H. (2001). Social-cognitive theory and self-regulated learning. In B. Zimmerman & D. Schunk (Eds.), Self-regulated learning and academic achievement: Theoretical perspectives (2nd ed., pp. 125–151). Mahwah, NJ: Erlbaum; cited in Anderman & Wolters (2006).

  • Schunk, D. H., & Zimmerman, B. J. (Eds.). (2008). Motivation and self-regulated learning: Theory, research, and applications. NY: Routledge.

    Google Scholar 

  • Schutz, P., & Pekrun, R. (Eds.). (2007). Emotion in education. Burlington, MA: Academic Press (Elsevier).

  • Skinner, E., Kindermann, T., & Furrer, C. (2009). A motivational perspective on engagement and disaffection: Conceptualization and assessment of children’s behavioral and emotional participation in academic activities in the classroom. Educational and Psychological Measurement, 69, 493–525.

    Article  Google Scholar 

  • Törner, G. (2002). Mathematical beliefs—a search for a common ground. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 73–94). Dordrecht: Kluwer.

    Google Scholar 

  • Turner, J. C., & Meyer, D. K. (2009). Understanding motivation in mathematics: What is happening in classrooms? In K. R. Wentzel & A. Wigfield (Eds.), Handbook of motivation at school (pp. 527–552). NY: Routledge.

    Google Scholar 

  • van de Sande, C., & Greeno, J. G. (2010). A framing of instructional explanations: Let us explain with you. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 69–82). NY: Springer.

    Chapter  Google Scholar 

  • Wellborn, J. G. (1991). Engaged and disaffected action: The conceptualization and measurement of motivation in the academic domain. Unpublished doctoral dissertation, University of Rochester, NY; cited in Skinner et al. (2009).

  • Wigfield, A., & Eccles, J. S. (1992). The development of achievement task values: A theoretical analysis. Developmental Review, 12, 265–310.

    Article  Google Scholar 

  • Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25, 68–81.

    Article  Google Scholar 

  • Wigfield, A., & Eccles, J. S. (2002). The development of competence beliefs, expectancies for success, and achievement values from childhood through adolescence. In A. Wigfield & J. S. Eccles (Eds.), Development of achievement motivation (pp. 91–120). San Diego, CA: Academic Press.

    Chapter  Google Scholar 

  • Zajonc, R. B. (1980). Feeling and thinking: Preferences need no inferences. American Psychologist, 35, 151–175.

    Article  Google Scholar 

  • Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational Studies in Mathematics, 63(2), 113–121.

    Article  Google Scholar 

  • Zimmerman, B. J., & Schunk, D. H. (2008). Motivation: An essential dimension of self-regulated learning. In D. H. Schunk & B. J. Zimmerman (Eds.), Motivation and self-regulated learning: Theory, research, and applications (pp. 1–30). NY: Routledge.

    Google Scholar 

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Acknowledgments

The authors thank Robert Capraro, Mary Margaret Capraro, and Nicole Shechtman for stimulating discussions. This research was partly supported by the US National Science Foundation (NSF), Grants 0138806, ESI-0333753, and REESE-1008770. Any opinions, findings, conclusions, or recommendations are the authors’ and do not necessarily reflect the views of the NSF.

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  1. Rutgers University, New Brunswick, NJ, USA

    Gerald A. Goldin & Yakov M. Epstein

  2. Rutgers University, Newark, NJ, USA

    Roberta Y. Schorr

  3. William Paterson University, Wayne, NJ, USA

    Lisa B. Warner

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

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Goldin, G.A., Epstein, Y.M., Schorr, R.Y. et al. Beliefs and engagement structures: behind the affective dimension of mathematical learning. ZDM Mathematics Education 43, 547–560 (2011). https://doi.org/10.1007/s11858-011-0348-z

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