Advertisement

“Opportunity to Aspire”: Promoting Mathematics Engagement and Aspiration for Challenging Mathematics

  • Clarence Ng
  • Brendan Bartlett
  • Stephen N. Elliott
Chapter

Abstract

In many OECD countries, including Australia, attention is required to examine and solve the problem of low levels of engagement in, and aspiration for, advanced mathematics among students coming from economically disadvantaged backgrounds. Not only are students from disadvantaged backgrounds in Australia overrepresented among those who fail to meet the benchmark in national and international tests of school mathematics; they are also underrepresented in mathematics-related degree programs at the university level. Few from disadvantaged groups have shown sustained aspirations for learning mathematics. It is, therefore, important to understand what motivates and sustains disadvantaged students’ aspirations and engagement in mathematics. In this chapter, classroom observations and interview data derived from a longitudinal study will be used to discuss the extent to which disadvantaged students’ aspiration is being promoted in their math classes. Based on the results, this chapter discusses classroom practices that are crucial for offering students the opportunity to aspire for deep learning in mathematics.

Keywords

Mathematics learning Mathematics aspiration Mathematics motivation Subject choice Learning intention Future goals Disadvantaged student 

References

  1. Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of educational psychology, 84(3), 261.CrossRefGoogle Scholar
  2. Assor, A., Kaplan, H., & Roth, G. (2002). Choice is good, but relevance is excellent: Autonomy-enhancing and suppressing teacher behaviours predicting students’ engagement in schoolwork. British Journal of Educational Psychology, 72(2), 261–278.CrossRefGoogle Scholar
  3. Aunola, K., Leskinen, E., & Nurmi, J. E. (2006). Developmental dynamics between mathematical performance, task motivation, and teachers’ goals during the transition to primary school. British Journal of Educational Psychology, 76(1), 21–40.CrossRefGoogle Scholar
  4. Balfanz, R., Herzog, L., & Mac Iver, D. J. (2007). Preventing student disengagement and keeping students on the graduation path in urban middle grades schools: Early identification and effective interventions. Educational Psychologist, 42(4), 223–235.CrossRefGoogle Scholar
  5. Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs: Prentice Hall.Google Scholar
  6. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Macmillan.Google Scholar
  7. Barrington, F. (2013). Update on the year 12 mathematics student numbers. Melbourne: AMSI.Google Scholar
  8. Bong, M. (2001). Between-and within-domain relations of academic motivation among middle and high school students: Self-efficacy, task value, and achievement goals. Journal of Educational Psychology, 93(1), 23–34.  https://doi.org/10.1037/0022-0663.93.1.23 CrossRefGoogle Scholar
  9. Borman, G. D., & Overman, L. T. (2004). Academic resilience in mathematics among poor and minority students. The Elementary School Journal, 104(3), 177–195.CrossRefGoogle Scholar
  10. Cerasoli, C. P., Nicklin, J. M., & Ford, M. T. (2014). Intrinsic motivation and extrinsic incentives jointly predict performance: A 40-year meta-analysis. Psychological Bulletin, 140(4), 980–1008.CrossRefGoogle Scholar
  11. Chouinard, R., Karsenti, T., & Roy, N. (2007). Relations among competence beliefs, utility value, achievement goals, and effort in mathematics. British Journal of Educational Psychology, 77(3), 501–517.CrossRefGoogle Scholar
  12. Chouinard, R., & Roy, N. (2008). Changes in high-school students’ competence beliefs, utility value and achievement goals in mathematics. British Journal of Educational Psychology, 78(1), 31–50.CrossRefGoogle Scholar
  13. Csikszentmihalyi, M. (1990). Flow: The psychology of optimal experience. New York: Harper Perennial.Google Scholar
  14. Deci, E. L., Vallerand, R. J., Pelletier, L. G., & Ryan, R. M. (1991). Motivation in education: The self-determination perspective. Educational Psychologist, 26(3-4), 325–346.CrossRefGoogle Scholar
  15. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132.CrossRefGoogle Scholar
  16. Eccles, J. S., Wigfield, A., & Schiefele, U. (1998). Motivation to succeed. In W. Damon & N. Eisenberg (Eds.), Handbook of child psychology (Vol. 3, 5th ed., pp. 1017–1095). Hoboken, NJ: Wiley.Google Scholar
  17. Frenzel, A. C., Goetz, T., Pekrun, R., & Watt, H. M. G. (2010). Development of mathematics interest in adolescence: Influences of gender, family, and school context. Journal of Research on Adolescence, 20(2), 507–537.CrossRefGoogle Scholar
  18. Garon-Carrier, G., Boivin, M., Guay, F., Kovas, Y., Dionne, G., Lemelin, J. P., et al. (2016). Intrinsic motivation and achievement in mathematics in elementary school: A longitudinal investigation of their association. Child Development, 87(1), 165–175.CrossRefGoogle Scholar
  19. Haberman, M. (1991). Pedagogy of poverty versus good teaching. Phi Delta Kappan, 73(4), 290–294.Google Scholar
  20. Hagger, M. S., Sultan, S., Hardcastle, S. J., & Chatzisarantis, N. L. (2015). Perceived autonomy support and autonomous motivation toward mathematics activities in educational and out-of-school contexts is related to mathematics homework behavior and attainment. Contemporary Educational Psychology, 41, 111–123.CrossRefGoogle Scholar
  21. Harackiewicz, J. M., Rozek, C. S., Hulleman, C. S., & Hyde, J. S. (2012). Helping parents to motivate adolescents in mathematics and science: An experimental test of a utility value intervention. Psychological Science, 23(8), 899–906.  https://doi.org/10.1177/0956797611435530 CrossRefPubMedGoogle Scholar
  22. Hulleman, C. S., Godes, O., Hendricks, B. L., & Harackiewicz, J. M. (2010). Enhancing interest and performance with a utility value intervention. Journal of Educational Psychology, 102(4), 880–895.CrossRefGoogle Scholar
  23. Kennedy, J., Lyons, T., & Quinn, F. (2014). The continuing decline of science and mathematics enrolments in Australian high schools. Teaching Science: The Journal of the Australian Science Teachers Association, 60(2), 34–46.Google Scholar
  24. Khattab, N. (2015). Students’ aspirations, expectations and school achievement: What really matters? British Educational Research Journal, 41(5), 731–748.CrossRefGoogle Scholar
  25. Kiemer, K., Gröschner, A., Pehmer, A. K., & Seidel, T. (2015). Effects of a classroom discourse intervention on teachers’ practice and students’ motivation to learn mathematics and science. Learning and Instruction, 35, 94–103.CrossRefGoogle Scholar
  26. Krapp, A. (2005). Basic needs and the development of interest and intrinsic motivational orientations. Learning and Instruction, 15, 381–395.CrossRefGoogle Scholar
  27. Lau, S., & Nie, Y. (2008). Interplay between personal goals and classroom goal structures in predicting student outcomes: A multilevel analysis of person-context interactions. Journal of Educational Psychology, 100, 15–29.CrossRefGoogle Scholar
  28. Lee, W., Lee, M. J., & Bong, M. (2014). Testing interest and self-efficacy as predictors of academic self-regulation and achievement. Contemporary Educational Psychology, 39(2), 86–99.CrossRefGoogle Scholar
  29. León, J., Núñez, J. L., & Liew, J. (2015). Self-determination and STEM education: Effects of autonomy, motivation, and self-regulated learning on high school math achievement. Learning and Individual Differences, 43, 156–163.CrossRefGoogle Scholar
  30. Lepper, M. R., Henderlong Corpus, J., & Iyengar, S. S. (2005). Intrinsic and extrinsic motivational orientations in the classroom: Age differences and academic correlates. Journal of Educational Psychology, 97, 184–196.CrossRefGoogle Scholar
  31. Linnenbrink, E. A. (2005). The dilemma of performance approach goals: The use of multiple goal contexts to promote students’ motivation and learning. Journal of Educational Psychology, 97(2), 197–213.CrossRefGoogle Scholar
  32. Luo, Y. L., Kovas, Y., Haworth, C., & Plomin, R. (2011a). The etiology of mathematical self-evaluation and mathematics achievement: Understanding the relationship using a cross-lagged twin study from ages 9 to 12. Learning and Individual Differences, 21, 710–718.CrossRefGoogle Scholar
  33. Ma, X. (1997). Reciprocal relationships between attitude toward mathematics and achievement in mathematics. Journal of Educational Research, 90, 221–229.CrossRefGoogle Scholar
  34. Marsh, H. W., Trautwein, U., Ludtke, O., Koller, O., & Baumert, J. (2005). Academic self-concept, interest, grades, and standardized test scores: Reciprocal effects models of causal ordering. Child Development, 76, 397–416.CrossRefGoogle Scholar
  35. Martin, A. J., Anderson, J., Bobis, J., Way, J., & Vellar, R. (2012). Switching on and switching off in mathematics: An ecological study of future intent and disengagement among middle school students. Journal of Educational Psychology, 104(1), 1–18.CrossRefGoogle Scholar
  36. Martin, D. P., & Rimm-Kaufman, S. E. (2015). Do student self-efficacy and teacher-student interaction quality contribute to emotional and social engagement in fifth grade math? Journal of School Psychology, 53(5), 359–373.CrossRefGoogle Scholar
  37. McPhan, G., Morony, W., Pegg, J., Cooksey, R., & Lynch, T. (2008). Maths? Why not? Canberra: Department of Education, Employment and Workplace Relations.Google Scholar
  38. Meece, J. L., Wigfield, A., & Eccles, J. S. (1990). Predictors of math anxiety and its consequences for young adolescents’ course enrollment intentions and performance in mathematics. Journal of Educational Psychology, 82, 60–70.CrossRefGoogle Scholar
  39. Meyer, D. K., Turner, J. C., & Spencer, C. A. (1997). Challenge in a mathematics classroom: Students’ motivation and strategies in project-based learning. The Elementary School Journal, 97(5), 501–521.CrossRefGoogle Scholar
  40. 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, 65–88.CrossRefGoogle Scholar
  41. Middleton, M. J., Kaplan, A., & Midgley, C. (2004). The change in middle school students’ achievement goals in mathematics over time. Social Psychology of Education, 7(3), 289–311.  https://doi.org/10.1037/0022-0663.80.4.514 CrossRefGoogle Scholar
  42. Murayama, K., Pekrun, R., Lichtenfeld, S., & vom Hofe, R. (2013). Predicting long-term growth in students’ mathematics achievement: The unique contributions of motivation and cognitive strategies. Child Development, 84, 1475–1490.CrossRefGoogle Scholar
  43. Nagy, G., Watt, H. M. G., Eccles, J. S., Trautwein, U., Ludtke, O., & Baumert, J. (2010). The development of students’ Mathematics self-concept in relation to gender: Different countries, different trajectories? Journal of Research on Adolescence, 20(2), 482–506.CrossRefGoogle Scholar
  44. Ng, C. (2005). Academic self-schemas and their self-congruent learning patterns: Findings verified with culturally different samples. Social Psychology of Education, 8(3), 303–328.CrossRefGoogle Scholar
  45. Ng, C. (2014). Examining the self-congruent engagement hypothesis: The link between academic self-schemas, motivation, learning and achievement within an academic year. Educational Psychology, 34(6), 730–762.CrossRefGoogle Scholar
  46. Ng, C. (2016). High school students’ motivation to learn mathematics: The role of multiple goals. International Journal of Science and Mathematics Education, 16, 357–375.  https://doi.org/10.1007/s10763-016-9780-4 CrossRefGoogle Scholar
  47. Noyes, A., Wake, G., & Drake, P. (2011). Widening and increasing post-16 mathematics participation: Pathways, pedagogies and politics. International Journal of Science and Mathematics Education, 9, 483–501.CrossRefGoogle Scholar
  48. Ntoumanis, N. (2005). A prospective study of participation in optional school physical education based on self-determination theory. Journal of Educational Psychology, 97, 444–453.CrossRefGoogle Scholar
  49. Pajares, F., & Graham, L. (1999). Self-efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24(2), 124−139.CrossRefGoogle Scholar
  50. Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86(2), 193–203.CrossRefGoogle Scholar
  51. Pajares, F., & Schunk, D. (2001). Self-beliefs and school success: Self-efficacy, self-concept, and school achievement. In R. J. Riding & S. G. Rayner (Eds.), International perspectives of individual differences (pp. 239–266). Westport, CT: Ablex.Google Scholar
  52. Pantziara, M., & Philippou, G. N. (2015). Students’ motivation in the mathematics classroom. Revealing causes and consequences. International Journal of Science and Mathematics Education, 13(2), 385–411.  https://doi.org/10.1007/s10763-013-9502-0 CrossRefGoogle Scholar
  53. Parker, P. D., Marsh, H. W., Ciarrochi, J., Marshall, S., & Abduljabbar, A. S. (2014). Juxtaposing math self-efficacy and self-concept as predictors of long-term achievement outcomes. Educational Psychology, 34(1), 29–48.CrossRefGoogle Scholar
  54. Patrick, H., Ryan, A. M., & Kaplan, A. (2007). Early adolescents’ perceptions of the classroom social environment, motivational beliefs, and engagement. Journal ofEducational Psychology, 99, 83–98.CrossRefGoogle Scholar
  55. Phan, H. P. (2012). The development of English and mathematics self-efficacy: A latent growth curve analysis. Journal of Educational Research, 105, 196–209.CrossRefGoogle Scholar
  56. Pintrich, E. A., & Schrauben, B. (1992). Students’ motivational beliefs and their cognitive engagement in classroom academic tasks. In D. H. Schunk & J. L. Meece (Eds.), Student perceptions in the classroom (pp. 149–183). Hillsdale, NJ: Erlbaum.Google Scholar
  57. Pintrich, P. R. (1999). The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31(6), 459–470.CrossRefGoogle Scholar
  58. Reeve, J., & Jang, H. (2006). What teachers say and do to support students’ autonomy during a learning activity. Journal of Educational Psychology, 98, 209–218.CrossRefGoogle Scholar
  59. Rozek, C. S., Hyde, J. S., Svoboda, R. C., Hulleman, C. S., & Harackiewicz, J. M. (2015). Gender differences in the effects of a utility-value intervention to help parents motivate adolescents in mathematics and science. Journal of Educational Psychology, 107(1), 195–206.CrossRefGoogle Scholar
  60. Ryan, A. M., & Pintrich, P. R. (1997). Should I ask for help? The role of motivation and attitudes in adolescents’ help seeking in math class. Journal of Educational Psychology, 89(2), 329–341.CrossRefGoogle Scholar
  61. Ryan, R. M., & Connell, J. P. (1989). Perceived locus of causality and internalization: Examining reasons for acting in two domains. Journal of Personality and Social Psychology, 57, 749–761.CrossRefGoogle Scholar
  62. Ryan, R. M., & Deci, E. L. (2002). Overview of self-determination theory: An organismic dialectical perspective. In E. L. Deci & R. M. Ryan (Eds.), Handbook of self-determination research (pp. 3–33). Rochester, NY: University of Rochester Press.Google Scholar
  63. 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.CrossRefGoogle Scholar
  64. Schunk, D. H. (1985). Participation in goal setting: Effects on self-efficacy and skills of learning-disabled children. Journal of Special Education, 19, 307–317.CrossRefGoogle Scholar
  65. Senko, C., Hulleman, C. S., & Harackiewicz, J. (2011). Achievement goal theory at the crossroads: Old controversies, current challenges, and new directions. Educational Psychologist, 46(1), 26–27.CrossRefGoogle Scholar
  66. Singh, K., Granville, M., & Dika, S. (2002). Mathematics and science achievement: Effects of motivation, interest, and academic engagement. Journal of Educational Research, 95(6), 323–332.CrossRefGoogle Scholar
  67. Skaalvik, E. M. (1997a). Issues in research on self-concept. In M. Meahr & P. R. Pintrich (Eds.), Advances in motivation and achievement (Vol. 10, pp. 51–97). Greenwich, CT: JAI Press Inc.Google Scholar
  68. Skaalvik, E. M. (1997b). Self-enhancing and self-defeating ego orientation: Relations with task and avoidance orientation, achievement, self-perceptions, and anxiety. Journal of Educational Psychology, 89(1), 71.CrossRefGoogle Scholar
  69. Skaalvik, E. M., Federici, R. A., & Klassen, R. M. (2015). Mathematics achievement and self-efficacy: Relations with motivation for mathematics. International Journal of Educational Research, 72, 129–136.CrossRefGoogle Scholar
  70. Spinath, B., Spinath, F. M., Harlaar, N., & Plomin, R. (2006). Predicting school achievement from general cognitive ability, self-perceived ability, and intrinsic value. Intelligence, 4, 363–374.CrossRefGoogle Scholar
  71. Stankov, L., Lee, J., Luo, W., & Hogan, D. J. (2012). Confidence: A better predictor of academic achievement than self-efficacy, self-concept and anxiety? Learning and Individual Differences, 22, 747–758.CrossRefGoogle Scholar
  72. Sullivan, P., Clarke, D., & Clarke, B. (2009). Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching. Mathematics Education Research Journal, 21(1), 85–105.CrossRefGoogle Scholar
  73. Thomson, S., De Bortoli, L., & Buckley, S. (2013). PISA in brief: Highlights from the full Australian report: PISA 2012: How Australia measures up.Google Scholar
  74. Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validation study. Contemporary Educational Psychology, 34(1), 89–101.CrossRefGoogle Scholar
  75. Utsumi, M. C., & Mendes, C. R. (2000). Researching the attitudes towards mathematics in basic education. Educational Psychology, 2, 237–244.CrossRefGoogle Scholar
  76. Viljaranta, J., Lerkkanen, M.-K., Poikkeus, A.-M., Aunola, K., & Nurmi, J.-E. (2009a). Cross-lagged relations between task motivation and performance in arithmetic and literacy in kindergarten. Learning and Instruction, 19, 335–344.CrossRefGoogle Scholar
  77. Viljaranta, J., Nurmi, J.-E., Aunola, K., & Salmela-Aro, K. (2009b). The role of task values in adolescents’ educational tracks: A person-oriented approach. Journal of Research on Adolescence, 19(4), 786–798.CrossRefGoogle Scholar
  78. Watt, H. M. G. (2004). Development of adolescents’ self-perceptions, values, and task perceptions according to gender and domain in 7th-through 11th-grade Australian students. Child Development, 75(5), 1556–1574.CrossRefGoogle Scholar
  79. Watt, H. M. G. (2006). The role of motivation in gendered educational and occupational trajectories related to maths. Educational Research and Evaluation, 12(4), 305–322.CrossRefGoogle Scholar
  80. Wigfield, A., Eccles, J., Mac Iver, D., Reuman, D., & Midgley, C. (1991). Transitions at early adolescence: Changes in children’s domain-specific self-perceptions and general self-esteem across the transition to junior high school. Developmental Psychology, 27, 552–565.CrossRefGoogle Scholar
  81. Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of motivation. Contemporary Educational Psychology, 25, 68–81.CrossRefGoogle Scholar
  82. 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.CrossRefGoogle Scholar
  83. Wong, E. H., Wiest, D. J., & Cusick, L. B. (2002). Perceptions of autonomy support, parent attachment, competence and self-worth as predictors of motivational orientation and academic achievement: An examination of sixth-and-ninth-grade regular education students. Adolescence, 37, 255–266.PubMedGoogle Scholar
  84. Zeldin, A. L., & Pajares, F. (2000). Against the odds: Self-efficacy beliefs of women in mathematical, scientific, and technological careers. American Educational Research Journal, 37(1), 215–246.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Clarence Ng
    • 1
  • Brendan Bartlett
    • 2
  • Stephen N. Elliott
    • 3
  1. 1.Institute for Learning Sciences & Teacher EducationAustralian Catholic UniversityBrisbaneAustralia
  2. 2.Faculty of Education & ArtsAustralian Catholic UniversityVirginiaAustralia
  3. 3.Sanford School of Social and Family DynamicsArizona State UniversityTempeUSA

Personalised recommendations