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Values in Mathematics Education: Its Conative Nature, and How It Can Be Developed

  • Seah, Wee Tiong (Melbourne Graduate School of Education, The University of Melbourne)
  • Received : 2019.05.21
  • Accepted : 2019.06.20
  • Published : 2019.06.30

Abstract

This article looks back and also looks forward at the values aspect of school mathematics teaching and learning. Looking back, it draws on existing academic knowledge to explain why the values construct has been regarded in recent writings as a conative variable, that is, associated with willingness and motivation. The discussion highlights the tripartite model of the human mind which was first conceptualised in the eighteenth century, emphasising the intertwined and mutually enabling processes of cognition, affect, and conation. The article also discusses what we already know about the nature of values, which suggests that values are both consistent and malleable. The trend in mathematics educational research into values over the last three decades or so is outlined. These allow for an updated definition of values in mathematics education to be offered in this article. Considering the categories of values that might be found in mathematics classrooms, an argument is also made for more attention to be paid to general educational values. After all, the potential of the values construct in mathematics education research extends beyond student understanding of and performance in mathematics, to realising an ethical mathematics education which is important for thriveability in the Fourth Industrial Revolution. Looking ahead, then, this article outlines a 4-step values development approach for implementation in the classroom, involving Justifying, Essaying, Declaring, and Identifying. With an acronym of JEDI, this novel approach has been informed by the theories of 'saying is believing', self-persuasion, insufficient justification, and abstract construals.

Keywords

SHGHEN_2019_v22n2_99_f0001.png 이미지

Figure 1. Conation as a bridge between cognition and affect, and behaviour

References

  1. ACARA (2016). NAPLAN results: Time series. Retrieved from https://reports.acara.edu.au/Home/TimeSeries.
  2. Aksoy, N. C., & Yazlik, D. O. (2017). Student errors in fractions and possible causes of these errors. Journal of Education and Training Studies, 5(11), 219-233. https://doi.org/10.11114/jets.v5i11.2679
  3. Atkinson, J. W. (1957). Motivational determinants of risk taking behavior. Psychological Review, 64, 359-372. https://doi.org/10.1037/h0043445
  4. Bar-Tal, D. (1990). Group beliefs: A conception for analyzing group structure, processes, and behavior. NY: Springer-Verlag.
  5. Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
  6. Bishop, A. J. (1996). How should mathematics teaching in modern societies relate to cultural values --- Some preliminary questions. Paper presented at the Seventh Southeast Asian Conference on Mathematics Education, Hanoi, Vietnam.
  7. Bishop, A. J., FitzSimons, G. E., Seah, W. T., & Clarkson, P. C. (2001). Do teachers implement their intended values in mathematics classrooms? In M. v. d. Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 169-176). Utrecht, The Netherlands: Freudenthal Institute.
  8. Bishop, A. J., Seah, W. T., & Chin, C. (2003). Values in mathematics teaching: The hidden persuaders? In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & F. Leong (Eds.), International handbook of mathematics education (2nd ed., pp. 715-763). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  9. Blankenship, K. L., Wegener, D. T., & Murray, R. A. (2012). Circumventing resistance: Using values to indirectly change attitudes. Journal of Personality and Social Psychology, 103(4), 606-621. https://doi.org/10.1037/a0029226
  10. Bronfenbrenner, U. (1992). Ecological systems theory. In R. Vasta (Ed.), Six theories of child development: Revised formulations and current issues (pp. 187-249). London: Jessica Kingsley.
  11. Cao, Z., Seah, W. T., & Bishop, A. J. (2006). A comparison of mathematical values conveyed in mathematics textbooks in China and Australia. In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West (pp. 483-493). New York, NY: Springer.
  12. Chan, Y. C., & Wong, N. Y. (2014). Worldviews, religions, and beliefs about teaching and learning: Perception of mathematics teachers with different religious backgrounds. Educational Studies in Mathematics, 87(3), 251-277 https://doi.org/10.1007/s10649-014-9555-1
  13. Chin, C., Leu, Y.-C., & Lin, F.-L. (2001). Pedagogical values, mathematics teaching, and teacher education: Case studies of two experienced teachers. In F.-L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 247-269). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  14. Clarkson, P., & Seah, W. T. (2011). Mathematical well-being (MWB): Developing a new construct. Paper presented at the 2011 Annual Meeting of the American Educational Research Association, New Orleans, LA.
  15. Clarkson, P., Seah, W. T., & Bishop, A. (2010). Mathematics wellbeing and teacher education. In R. Toomey, T. Lovat, N. Clement, & K. Dally (Eds.), Teacher education and values pedagogy: A student wellbeing approach (pp. 179-194). New South Wales, Australia: David Barlow Publishing.
  16. Clarkson, P., Seah, W. T., & Pang, J. S. (Eds.), (2019). Values and valuing in mathematics education: Scanning and scoping the territory. Cham, Switzerland: Springer.
  17. Clement, P. (2013). Values in science and in science education. Science & Technology Education for Development, Citizenship and Social Justice (IOSTE14) Journal, 1(1), 1-26.
  18. Cohen, G. L., Garcia, J., Purdie-Vaughns, V., Apfel, N., & Brzustoski, P. (2009). Recursive processes in self-affirmation: Intervening to close the minority achievement gap. Science, 324, 400-403. https://doi.org/10.1126/science.1170769
  19. 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
  20. Dede, Y. (2006). Values in Turkish middle school mathematics textbooks. Quality and Quantity, 40, 331-359. https://doi.org/10.1007/s11135-005-6133-8
  21. Duckworth, A. (2016). Grit: The power of passion and perseverance. NY: Scribner/Simon & Schuster.
  22. Dweck, C. S. (2006). Mindset: The new psychology of success. NY: Random House.
  23. Eccles, J., Adler, T. F., Futterman, R., Goff, S. B., Kaczala, C. M., Meece, J. L., et al. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motivation (pp. 75-146). San Francisco, CA: W.H. Freeman.
  24. Ernest, P. (2019). The ethical obligations of the mathematics teacher. Journal of Pedagogical Research, 3(1), 80-91. doi:10.33902/JPR.2019.6
  25. Feather, N. T. (1995). Values, valences, and choice: The influences of values on the perceived attractiveness and choice of alternatives. Journal of Personality and Social Psychology, 68, 1135-1151 https://doi.org/10.1037/0022-3514.68.6.1135
  26. Festinger, L., & Carlsmith, J. M. (1959). Cognitive consequences of forced compliance. Journal of Abnormal and Social Psychology, 58(2), 203-210. https://doi.org/10.1037/h0041593
  27. Fetler, M. (1999). High school staff characteristics and mathematics test results. Education Policy Analysis Archives, 7(9). Retrieved from https://epaa.asu.edu/ojs/article/view/544/667
  28. Fishbein, M., & Ajzen, I. (1975). Belief, attitude, intention and behavior. Reading, MA: Addison-Wesley.
  29. Frade, C., & Machado, M. C. (2008). Culture and affect: Influences of the teachers' values on students' affect. In O. Figueras (Ed.), Proceedings of the joint meeting of PME 32 & PME-NA XXX (Vol. 3, pp. 33-40). Mexico: Cinvestav-UMSNH.
  30. Freitas, A. L., Gollwitzer, P., & Trope, a. Y. (2004). The influence of abstract and concrete mindsets on anticipating and guiding others' self-regulatory efforts. Journal of Experimental Social Psychology, 40, 740-752.
  31. Friedrich, J. (1990). Learning to view psychology as a Science: Self-Persuasion through Writing. Teaching of Psychology, 17(1), 23-27. https://doi.org/10.1207/s15328023top1701_5
  32. Fuadiah, N. F., Suryadi, D., & Turmudi (2017). Some difficulties in understanding negative numbers faced by students: A qualitative study applied at secondary schools in Indonesia. International Education Studies, 10(1), 24-38. https://doi.org/10.5539/ies.v10n1p24
  33. Fujita, K., Trope, Y., Liberman, N., & Levin-Sagi, M. (2006). Construal levels and selfcontrol. Journal of Personality and Social Psychology, 90(3), 351-367. https://doi.org/10.1037/0022-3514.90.3.351
  34. Han, C. D., & Seah, W. T. (in press). What Australian students say they value most in their mathematics learning. In Mathematics education research: Impacting practice (Proceedings of the 42nd annual conference of the Mathematics Education Research Group of Australasia). Perth, Australia: MERGA.
  35. Hausmann, L. R. M., Levine, J. M., & Higgins, E. T. (2008). Communication and group perception: Extending the 'saying is believing' effect. Group Processes & Intergroup Relations, 11(4), 539-554. doi:https://doi.org/10.1177/1368430208095405
  36. Higgins, E. T. (2007). Value. In A. W. Kruglanski & E. T. Higgins (Eds.), Social psychology: Handbook of basic principles (pp. 454-472). New York: Guilford Press.
  37. Higgins, E. T., & Rholes, W. S. (1978). "Saying is believing": Effects of message modification on memory and liking for the person described. Journal of Experimental Social Psychology, 14(4), 363-378. doi:https://doi.org/10.1016/0022-1031(78)90032-X
  38. Hilgard, E. R. (1980). The trilogy of mind: Cognition, affection, and conation. Journal of the History of the Behavioral Sciences, 16, 107-117. https://doi.org/10.1002/1520-6696(198004)16:2<107::AID-JHBS2300160202>3.0.CO;2-Y
  39. Hulleman, C. S., & Harackiewicz, J. M. (2009). Promoting interest and performance in high school science classes. Science, 326, 1410-1412 https://doi.org/10.1126/science.1177067
  40. Jerrim, J. (2014). Why do East Asian children perform so well in PISA? An investigation of Western-born children of East Asian descent. London: Institute of Education, University of London.
  41. Kalogeropoulos, P., & Bishop, A. J. (2017). What is the role of value alignment in engaging mathematics learners? Paper presented at the 9th Meeting of the Mathematics Education and Society, Volos, Greece.
  42. Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 3-38). NY: Macmillan Publishing.
  43. Krathwohl, D. R., Bloom, B. S., & Masia, B. B. (1964). Taxonomy of educational objectives: The classification of educational goals (Handbook II: Affective domain). New York: David McKay.
  44. Leder, G. C. (2015). Gender and mathematics education revisited. In S. J. Cho (Ed.), The proceedings of the 12th International Congress on Mathematical Education (pp. 145-151). Cham: Springer.
  45. Leder, G. C., Pehkonen, E., & Torner, G. n. (2003). Setting the scene. In G. C. Leder, E. Pehkonen, & G. n. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 1-10). NY: Kluwer.
  46. Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning. (pp. 19-44). London: Ablex Publishing.
  47. Leu, Y.-C., & Wu, C.-J. (2002). The origins of pupils' awareness of teachers' mathematics pedagogical values: Confucianism and Buddhism-driven. In Pre-conference proceedings of the ICMI Comparative Study Conference 2002 Hong Kong (pp. 49-55). Hong Kong: The University of Hong Kong.
  48. Lewin, K. (1938). The conceptual representation and the measurement of psychological forces. Durham, NC: Duke University Press.
  49. Lim, C. S. (2010). Using NVivo 8 to explore photo-voice. In J. Lim (Ed.), Proceedings of the International Workshop on Computer-Aided Qualitative Research Asia (pp. 48-59). The Netherlands: Merlien Institute.
  50. Masters, G. (2016, November 30). Australian students slipping in maths and science studies. The Australian, p. A5.
  51. Matthews, J. S. (2018). When am I ever going to use this in the real world? Cognitive flexibility and urban adolescents' negotiation of the value of mathematics. Journal of Educational Psychology, 110(5), 726-746. https://doi.org/10.1037/edu0000242
  52. Middleton, J.A. (1995). A study of intrinsic motivation in the mathematics classroom: A personal constructs approach. Journal for Research in Mathematics Education, 26(3), 254-279. https://doi.org/10.2307/749130
  53. Murphy, S. (2018). School location and socioeconomic status and patterns of participation and achievement in senior secondary mathematics. Mathematics Education Research Journal, 30. Retrieved from https://link-springer com.ezp.lib.unimelb.edu.au/content/pdf/10.1007%2Fs13394-018-0251-9.pdf
  54. Ozsoyi, N., Akkaya, Y., Tosun, T., Umurbek, M., Guclu, M., & Eray, F. (2018). Obtaining of helplessness value in the secondary education mathematics curriculum by creative drama activities. European Journal of Education Studies, 5(8), 165-184.
  55. Reitan, R. M., & Wolfson, D. (2000). Conation: A neglected aspect of neuropsychological functioning. Archives of Clinical Neuropsychology, 15(5), 443-453. https://doi.org/10.1093/arclin/15.5.443
  56. Rogers, C. (1951). Client-centered therapy: Its current practice, implications and theory. London: Constable.
  57. Schein, E. H. (1956). The Chinese Indoctrination Program for prisoners of war. Psychiatry, 19(2), 149-172. https://doi.org/10.1080/00332747.1956.11023044
  58. Schwartz, S. H. (1992). Universals in the content and structure of values: Theoretical advances and empirical tests in 20 countries. In M. P. Zanna (Ed.), Advances in experimental social psychology (Vol. 25, pp. 1-65). San Diego, CA: Academic Press.
  59. Schwartz, S. H. (2012). An overview of the Schwartz Theory of Basic Values. Online Readings in Psychology and Culture, 2(1). Retrieved from https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1116&context=orpc
  60. Seah, W. T. (2018). Improving mathematics pedagogy through student/teacher valuing: Lessons from five continents. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education (pp. 561-580). Cham, Switzerland: Springer International Publishing.
  61. Seah, W. T., & Bishop, A. J. (2000, April 24-28). Values in mathematics textbooks: A view through two Australasian regions. Paper presented at the 81st Annual Meeting of the American Educational Research Association, New Orleans, LA. (ERIC Document Reproduction Service No. ED 440 870).
  62. Seah, W. T., & Ho, S. Y. (2009). Values operating in effective mathematics lessons in Australia and Singapore: Reflections of pre-service teachers. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 57-64). Thessaloniki, Greece: International Group for the Psychology of Mathematics Education.
  63. Sheldon, K. M., Arndt, J., & Houser-Marko, L. (2003). In search of the Organismic Valuing Process: The human tendency to move towards beneficial goal choices. Journal of Personality, 71(5), 835-869. https://doi.org/10.1111/1467-6494.7105006
  64. Thomson, S., de Bortoli, L., & Underwood, C. (2017a). PISA 2015: Reporting Australia's results. Victoria, Australia: Australian Council for Educational Research.
  65. Thomson, S., Wernert, N., O'Grady, E., & Rodrigues, S. (2017). TIMSS 2015: Reporting Australia's results. Victoria, Australia: Australian Council for Educational Research.
  66. Thomson, S., Wernert, N., O'Grady, E., & Rodrigues, S. (2016). TIMSS 2015: A first look at Australia's results. Victoria, Australia: Australian Council for Educational Research.
  67. Torelli, C. J., & Kaikati, A. M. (2009). Values as predictors of judgments and behaviors: The role of abstract and concrete mindsets. Journal of Personality and Social Psychology, 96(1), 231-247. https://doi.org/10.1037/a0013836
  68. Vallerand, R. J., Deshaies, P., Cuerrier, J.-P., Pelletier, L. G., & Mongeau, C. (1992). Ajzen and Fishbein's Theory of Reasoned Action as applied to moral behavior: A confirmatory analysis. Journal of Personality and Social Psychology, 62(1), 98-109. https://doi.org/10.1037/0022-3514.62.1.98
  69. Verweij, M., Senior, T. J., D., J. F. D., & Turner, R. (2015). Emotion, rationality, and decisionmaking: How to link affective and social neuroscience with social theory. Frontiers in Neuroscience, 9, 332. https://doi.org/10.3389/fnins.2015.00332
  70. Walton, G. M. (2014). The new science of wise psychological interventions. Current Directions in Psychological Science, 23(1), 73-82. https://doi.org/10.1177/0963721413512856
  71. Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25, 68-81. https://doi.org/10.1006/ceps.1999.1015
  72. Zhang, Q., Barkatsas, T., Law, H. Y., Leu, Y.-C., Seah, W. T., & Wong, N.-Y. (2016). What primary students in the Chinese Mainland, Hong Kong and Taiwan value in mathematics learning: A comparative analysis. International Journal of Science and Mathematics Education, 14(5), 907-924. https://doi.org/10.1007/s10763-014-9615-0