Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies

Karina Joyce Wilkie

doi:10.12973/eurasia.2016.1260a

Full Text (PDF)

Karina Joyce Wilkie ¹ ^*

More Detail

¹ Monash University^* Corresponding Author

Abstract

Background:
Learning to solve more challenging mathematics problems using multiple strategies has been promoted by research and is a feature of numerous curricula. Yet teachers have been found to be reluctant to incorporate these tasks into their lessons predicting resistance from students.

Material and methods:
This study examined 87 senior secondary students’ reactions to a challenging quadratics task as part of their teachers’ participation in a design-based research project. It sought insights into students’ own perspectives on challenge and multiple strategies in mathematics teaching and learning, with the intent of understanding more about the cognitive, affective, and motivational aspects of this teaching approach.

Results:
In responding to open-ended prompts, the students reported diverse but generally positive reactions related to their interest in the task and its relevance for their learning. Two thirds reported that they liked learning strategies from peers, and two thirds liked learning multiple strategies from their teacher.

Conclusions:
Implications for considering secondary students’ preferences for learning, engagement, and motivation in mathematics lessons are discussed.

Keywords

challenging mathematics tasks
multiple solutions
achievement goals
engagement
motivation
quadratic functions

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, Volume 12, Issue 8, August 2016, 2061-2083

https://doi.org/10.12973/eurasia.2016.1260a

Publication date: 02 Jul 2016

Article Views: 2743

Article Downloads: 1496

Open Access References How to cite this article

References

Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84, 261-271.
Anthony, G. (1996). Classroom instructional factors affecting mathematics students’ strategic learning behaviours. Paper presented at the 19th Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), University of Melbourne.
Australian Curriculum Assessment and Reporting Authority. (2009, January, 2011). The Australian curriculum: Mathematics. Retrieved October 1, 2011, from http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
Bingolbali, E. (2011). Multiple solutions to problems in mathematics teaching : do teachers really value them? Australian Journal of Teacher Education, 36(1), 18-31. doi: 10.14221/ajte.2011v36n1.2
Brophy, J. (2005). Goal theorists should move on from performance goals. Educational Psychologist, 40(3), 167-176. doi: 10.1207/s15326985ep4003_3
Clough, P., & Nutbrown, C. (2007). A student’s guide to methodology (2nd ed.). London: Sage.
Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307-333). Mahwah, NJ: Lawrence Erlbaum Associates.
Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142. doi:10.3102/01623737025002119
Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, CA: Sage.
Davis, P. J., Hersh, R., & Marchisotto, E. A. (1995). The mathematical experience (Study ed.). Boston: Birkhäuser.
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.
Dweck, C. S. (2007). Boosting achievement with messages that motivate. Education Canada, 47(2), 6-10.
Dweck, C. S. (2010). Mind-Sets and Equitable Education. Principal Leadership, 10(5), 26-29.
Elliot, A. J. (1999). Approach and avoidance motivation and achievement goals. Educational Psychologist, 34(3), 169-189. doi: 10.1207/s15326985ep3403_3
Elliot, A. J. (2008). Approach and avoidance motivation. In A. J. Elliot (Ed.), Handbook of approach and avoidance motivation (Vol. 1, pp. 3-14): Taylor & Francis.
Elliot, A. J., & Murayama, K. (2008). On the measurement of achievement goals: Critique, illustration, and application. Journal of Educational Psychology, 100(3), 613-628. doi: 10.1037/0022-0663.100.3.613
Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A Longitudinal Study of Learning to Use Children’s Thinking in Mathematics Instruction. Journal for Research in Mathematics Education, 27(4), 403-434. doi: 10.2307/749875
Flutter, J., & Rudduck, J. (2004). Consulting pupils: What's in it for schools? London: Routledge Falmer.
Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148-170. doi: 10.2307/749608
Fujii, T. (2014). Understanding the concept of variable through whole-class discussions: the community of inquiry from a Japanese perspective. In F. K. S. Leung, K. Park, D. Holton & D. Clarke (Eds.), Algebra teaching around the world (pp. 129-148). Rotterdam: Sense Publishers.
Guberman, R., & Leikin, R. (2013). Interesting and difficult mathematical problems: Changing teachers’ views by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56. doi: 10.1007/s10857-012-9210-7
Hesse-Biber, S. N. (2010). Mixed methods research: Merging theory with practice. New York: Guilford Press.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom Mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on Mathematics teaching and learning (Vol. 1, pp. 371-404). Charlotte, NC: National Council of Teachers of Mathematics, Information Age Publishing.
Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116. doi: 10.2307/30034933
Hulleman, C. S., Schrager, S. M., Bodmann, S. M., & Harackiewicz, J. M. (2010). A meta-analytic review of achievement goal measures: Different labels for the same constructs or different constructs with similar labels? Psychological Bulletin, 136(3), 422-449. doi: 10.1037/a0018947
Jang, L., & Liu, W. (2012). 2 × 2 Achievement goals and achievement emotions: a cluster analysis of students’ motivation. European Journal of Psychology of Education, 27(1), 59- 76. doi: 10.1007/s10212-011-0066-5
Jitendra, A., Star, J. R., Starosta, K., Leh, J. M., Sood, S., Caskie, G., . . . Mack, T. R. (2009). Improving seventh grade students’ learning of ratio and proportion: the role of schemabased instruction. Contemporary Educational Psychology, 34, 250-264. doi: 10.1016/j.cedpsych.2009.06.001
Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349-371. doi: 10.2307/27822710
Leikin, R., Levav-Waynberg, A., & Mednikov, L. (2006). Implementation of multiple solution connecting tasks: Do students’ attitudes support teachers’ reluctance? Focus on Learning Problems in Mathematics, 28(1), 1-22.
Lynch, K., & Star, J. R. (2014). Teachers’ views about multiple strategies in middle and high school mathematics. Mathematical Thinking and Learning, 16(2), 85-108. doi: 10.1080/10986065.2014.889501
Marsh, H. W. (2006). Self-concept theory, measurement and research into practice: The role of self-concept in educational psychology. Paper presented at the 25th Vernon-Wall Lecture, Annual Meeting of the Education Section of the British Psychological Society, Durham University.
Martin, Andrew J. (2013). Goal orientation. In J. Hattie & E. M. Anderman (Eds.), International guide to student achievement (pp. 353-355). New York, NY: Routledge.
Megowan-Romanowicz, M. C., Middleton, J. A., Ganesh, T., & Joanou, J. (2013). Norms for participation in a middle school mathematics classroom and its effect on student motivation. Middle Grades Research Journal, 8(1), 51-76.
Middleton, J. A. (1999). Curricular influences on the motivational beliefs and practice of two middle school mathematics teachers: A follow-up study. Journal for Research in Mathematics Education, 30(3), 349.
Middleton, J. A. (2013). Introduction/editorial: the problem of motivation in the middle grades. Middle Grades Research Journal, 8(1), xi-xiii.
Middleton, J., & Jansen, A. (2011). Motivation matters and interest counts: Fostering engagement in mathematics. Reston, VA: National Council of Teachers of Mathematics.
Middleton, J. A., & Toluk, Z. (1999). First steps in the development of an adaptive theory of motivation. Educational Psychologist, 34(2), 99-112. doi: 10.1207/s15326985ep3402_3
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
O’Toole, J., & Beckett, D. (2010). Educational research: Creative thinking & doing. Melbourne: Oxford University Press.
Ohtani, M. (2014). Construction zone for the understanding of simultaneous equations: An analysis of one Japanese teachers’ strategy of reflecting on a task in a lesson sequence. In F. K. S. Leung, K. Park, D. Holton & D. Clarke (Eds.), Algebra teaching around the world (pp. 113-128). Rotterdam: Sense Publishers.
Pintrich, C. H., & Schunk, D. (2002). Motivations in education: Theory, research, and applications (2nd ed.). Upper Saddle River, NJ: Prentice Hall.
Putwain, D. W., & Symes, W. (2011). Teachers’ use of fear appeals in the Mathematics classroom: Worrying or motivating students? British Journal of Educational Psychology, 81(3), 456-474. doi: 10.1348/2044-8279.002005
Rittle-Johnson, B., & Star, J. R. (2007). Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge? An Experimental Study on Learning to Solve Equations. Journal of Educational Psychology, 99(3), 561-574. doi: 10.1037/0022- 0663.99.3.561
Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836-852. doi: 10.1037/a0016026
Schiefele, Ulrich , & Csikszentmihalyi, Mihaly (1995). Motivation and ability as factors in Mathematics experience and achievement. Journal for Research in Mathematics Education, 26(2), 163-181.
Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. T. F. (2005). Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. The Journal of Mathematical Behavior, 24(3–4), 287-301. doi: http://dx.doi.org/10.1016/j.jmathb.2005.09.009
Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage.
Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: The case of equation solving. Learning and Instruction, 18(6), 565-579. doi: http://dx.doi.org/10.1016/j.learninstruc.2007.09.018
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell. Mathematical Thinking and Learning, 10(4), 313-340. doi: 10.1080/10986060802229675
Stein, M. K., & Lane, S. (1996). Instructional Tasks and the Development of Student Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project. Educational Research and Evaluation, 2(1), 50-80. doi: 10.1080/1380361960020103
Sullivan, P., Askew, M., Cheeseman, J., Clarke, D., Mornane, A., Roche, A., & Walker, N. (2014). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 1-18. doi: 10.1007/s10857-014-9279-2
Sullivan, P., Clarke, D., Clarke, B., & O’Shea, H. (2009). Exploring the relationship between teacher actions and student learning. 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. 185-193). Thessaloniki.
Sullivan, P., & Mornane, A. (2014). Exploring teachers’ use of, and students’ reactions to, challenging mathematics tasks. Mathematics Education Research Journal, 26(2), 193- 213. doi: 10.1007/s13394-013-0089-0
Sullivan, P., Tobias, S., & McDonough, A. (2006). Perhaps the decision of some students not to engage in learning mathematics in school is deliberate. Educational Studies in Mathematics, 62(1), 81-99. doi: 10.1007/s10649-006-1348-8
Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Teacher Education, 10(4-6), 217-237. doi: 10.1007/s10857-007-9038-8
Tzur, R. (2008). A researcher perplexity: Why do mathematical tasks undergo metamorphosis in teacher hands? In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PME-NA (Vol. 1, pp. 139-147). Morelia, México: International Group for the Psychology of Mathematics Education.
Wolcott, H. F. (2009). Writing up qualitative research (3rd ed.). Thousand Oaks, CA: Sage.
Woodward, J., Beckmann, S., Driscoll, M., Franke, M. L., Herzig, P., Jitendra, A., . . . Ogbuehi, P. (2012). Improving mathematical problem solving in Grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Zazkis, R., & Leikin, R. (2007). Generating examples: From pedagogical tool to a research tool. For the Learning of Mathematics, 27(2), 15-21. doi: 10.2307/40248566

How to cite this article

APA

Wilkie, K. J. (2016). Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies. Eurasia Journal of Mathematics, Science and Technology Education, 12(8), 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a

Vancouver

Wilkie KJ. Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies. EURASIA J Math Sci Tech Ed. 2016;12(8):2061-83. https://doi.org/10.12973/eurasia.2016.1260a

AMA

Wilkie KJ. Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies. EURASIA J Math Sci Tech Ed. 2016;12(8), 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a

Chicago

Wilkie, Karina Joyce. "Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies". Eurasia Journal of Mathematics, Science and Technology Education 2016 12 no. 8 (2016): 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a

Harvard

Wilkie, K. J. (2016). Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies. Eurasia Journal of Mathematics, Science and Technology Education, 12(8), pp. 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a

MLA

Wilkie, Karina Joyce "Rise or Resist: Exploring Senior Secondary Students’ Reactions to Challenging Mathematics Tasks Incorporating Multiple Strategies". Eurasia Journal of Mathematics, Science and Technology Education, vol. 12, no. 8, 2016, pp. 2061-2083. https://doi.org/10.12973/eurasia.2016.1260a