Using Prompts to Empower Learners: Exploring Primary Students’ Attitudes Towards Enabling Prompts When Learning Mathematics Through Problem Solving

Authors

  • James Anthony Russo Monash University http://orcid.org/0000-0002-9855-7522
  • Michael Minas Consultant, Love Maths
  • Travis Hewish Teacher Department of Education, Victoria
  • Jessie McCosh Teacher Department of Education, Victoria

Keywords:

primary education, problem solving, challenging tasks, enabling prompts, instructional design, student attitudes, student autonomy

Abstract

Teaching mathematics through problem solving is central to contemporary approaches to mathematics instruction, whilst augmenting problem-solving tasks through enabling and extending prompts ensures that a diverse community of learners are provided with opportunities to be optimally challenged, supporting an inclusive classroom environment. However, it has been frequently assumed that teachers should determine when a student should access an enabling prompt, perhaps in part due to concerns that students might be reluctant to seek prompts themselves because of social stigma associated with help seeking. In this paper, we argue that getting students to access prompts of their own volition should be central to teaching mathematics in this manner. One hundred and thirty-two Year 3-6 students completed a questionnaire disclosing their attitudes towards enabling prompts in classroom environments where they were expected to access prompts themselves. Most students consistently reported that enabling prompts empowered them as learners, allowing them to both take responsibility for, and have success with, their mathematics learning. In particular, students valued being able to access prompts when they were stuck on a task, felt that prompts had the power to increase their understanding, and to approach mathematical tasks with more confidence. Students generally did not associate accessing enabling prompts with being ‘bad’ at mathematics and acknowledged that even strong mathematicians might use a prompt sometimes. There was almost no evidence of any stigma or embarrassment associated with accessing enabling prompts. The implication is that classroom teachers can rapidly establish a culture where students access enabling prompts themselves to support learning mathematics through problem solving. 

Author Biography

James Anthony Russo, Monash University

Dr James Russo

Lecturer

Faculty of Education

References

Abdu, R., & Schwarz, B. (2020). Split up, but stay together: Collaboration and cooperation in mathematical problem solving. Instructional Science, 48(3), 313-336. https://doi.org/10.1007/s11251-020-09512-7

Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., Russo, J., & Sullivan, P. (2019). Changing teacher practices while teaching with challenging tasks. In H. V. M. Graven, A. Essien, P.Vale (Ed.), Proceedings of 43rd Psychology of Mathematics Education conference (Vol. 2, pp. 105-112). Pretoria, South Africa: PME.

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101. https://doi.org/10.1191/1478088706qp063oa

Capraro R. M. & Slough, S. W. (2008). Why PBL? Why STEM? Why now? An introduction to STEM project-based learning: an integrated science, technology, engineering, and mathematics (STEM) approach. In R.M. Capraro, M.M. Capraro and J. Morgan (Eds.), STEM Project-Based Learning: An Integrated Science, Technology, Engineering and Mathematics (STEM) Approach, (pp. 1-5). Rotterdam, NLD: Sense Publishers. https://doi.org/10.1007/978-94-6209-143-6_1

César, M., & Santos, N. (2006). From exclusion to inclusion: Collaborative work contributions to more inclusive learning settings. European Journal of Psychology of Education, 21(3), 333-346. https://doi.org/10.1007/bf03173420

Cheeseman, J., Downton, A., & Livy, S. (2017). Investigating teachers’ perceptions of enabling and extending prompts. In A. Downton, S. Livy, & J. Hall (Eds.), 40 years on: We are still learning! Proceedings of the 40th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 141-148). Melbourne: MERGA.

Cheeseman, J., Clarke, D.M., Roche, A., & Walker, N. (2016). Introducing challenging tasks: Inviting and clarifying without explaining and demonstrating. Australian Primary Mathematics Classroom, 21(3), 3-7.

Clarke, D.M., Cheeseman, J., Roche, A., & Van Der Schans, S. (2014). Teaching strategies for building student persistence on challenging tasks: Insights emerging from two approaches to teacher professional learning. Mathematics Teacher Education and Development, 16(2), 46-70.

Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2001). Participating in classroom mathematical practices. The Journal of the Learning Sciences, 10(1-2), 113-163. https://doi.org/10.1207/s15327809jls10-1-2_6

Deci, E. L., Koestner, R., & Ryan, R. M. (1999). A meta-analytic review of experiments examining the effects of extrinsic rewards on intrinsic motivation. Psychological Bulletin, 125(6), 627-668. https://doi.org/10.1037//0033-2909.125.6.627

Deci, E. L., & Ryan, R. M. (2012). Self-determination theory. In P. A. M. Van Lange, A. W. Kruglanski, & E.T. Higgins (Eds.), Handbook of Theories of Social Psychology (Vol. 1; pp. 416–433). Thousand Oaks, CA: Sage.

DiNapoli, J. (2019). Persevering toward what? Investigating the relationship between ninth-grade students’ achievement goals and perseverant actions on an algebraic task. International Electronic Journal of Mathematics Education, 14(3), 435-453. https://doi.org/10.29333/iejme/5747

Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia: Psychology Press.

Gadanidis, G., Borba, M., Hughes, J., & Lacerda, H. (2016). Designing aesthetic experiences for young mathematicians: A model for mathematics education reform. International Journal for Research in Mathematics Education, 6(2), 225-244.

Gervasoni, A., & Peter-Koop, A. (2020). Inclusive mathematics education. Mathematics Education Research Journal, 32(1), 1-4. https://doi.org/10.1007/s13394-020-00315-0

Han, S., Rosli, R., Capraro, M. M., & Capraro, R. M. (2016). The effect of science, technology, engineering and mathematics (STEM) project based learning (PBL) on students’ achievement in four mathematics topics. Journal of Turkish Science Education, 13, 3-29. https://doi.org/10.12973/tused.10168a

Ingram, N., Holmes, M., Linsell, C., Livy, S., McCormick, M., & Sullivan, P. (2019). Exploring an innovative approach to teaching mathematics through the use of challenging tasks: A New Zealand perspective. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-019-00266-1

Kyriacou, C. (2001). Teacher stress: Directions for future research. Educational Review, 53(1), 27-35. https://doi.org/10.1080/00131910124115

Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University Press.

Lee, C. I. (2017). An appropriate prompts system based on the Polya method for mathematical problem-solving. EURASIA Journal of Mathematics Science and Technology Education, 13(3), 893-910. https://doi.org/10.12973/eurasia.2017.00649a

Lee, Y., Capraro, R. M., & Bicer, A. (2019). Affective mathematics engagement: A comparison of STEM PBL versus non-STEM PBL instruction. Canadian Journal of Science, Mathematics and Technology Education, 19(3), 270-289. https://doi.org/10.1007/s42330-019-00050-0

Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving behavior. In D. B. McLeod & V. M. Adams (Eds.), Affect and Mathematical Problem Solving: A New Perspective (pp. 75-88). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3614-6_6

Livy, S., Muir, T., & Sullivan, P. (2018). Challenging tasks lead to productive struggle!. Australian Primary Mathematics Classroom, 23(1), 19-24.

McGhie-Richmond, D., & de Bruin, C. (2015). Tablets, tweets and talking text: The role of technology in inclusive pedagogy. In J. M. Deppeler, T. Loreman, and R.A. L. Smith (Eds.). Inclusive pedagogy Across the Curriculum: International Perspectives on Inclusive Education, Volume 7, (pp. 211-234). Bingley, UK: Emerald Group Publishing. https://doi.org/10.1108/s1479-363620150000007017

Minas, M. (2019). Using enabling prompts to effectively support teaching with challenging tasks. Australian Primary Mathematics Classroom, 24(4), 12-16.

Polya, G. (1957). How to Solve It: A New Aspect of Mathematical Method: Princeton University Press.

Punch, K. F., & Tuetteman, E. (1996). Reducing teacher stress: The effects of support in the work environment. Research in Education, 56(1), 63-72. https://doi.org/10.1177/003452379605600105

Reeve, J., Deci, E. L., & Ryan, R. M. (2004). Self-determination Theory: A dialectical framework for understanding sociocultural influences on student motivation. In D. M. McInerney & S. Van Etten (Eds.), Big Theories Revisited (pp. 31–60). Greenwich, CT: Information Age.

Reeve, J., & Jang, H. (2006). What teachers say and do to support students' autonomy during a learning activity. Journal of Educational Psychology, 98(1), 209-218. https://doi.org/10.1037/0022-0663.98.1.209

Roche, A., & Clarke, D.M. (2014). Teachers Holding Back from Telling: A Key to Student Persistence on Challenging Tasks. Australian Primary Mathematics Classroom, 19(4), 3-8.

Roche, A., & Clarke, D.M. (2015). Describing the nature and effect of teacher interactions with students during seat work on challenging tasks. In M. Marshman, V. Geiger, & A. Bennison (Eds.). Mathematics Education in the Margins: Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia, (pp. 532–539). Sunshine Coast: MERGA.

Rollard, R. G. (2012). Synthesizing the Evidence on Classroom Goal Structures in Middle and Secondary Schools A Meta-Analysis and Narrative Review. Review of Educational Research, 82(4), 396-435. https://doi.org/10.3102/0034654312464909

Russo, J. (2018). The challenges of teaching with challenging tasks: Developing prompts. In G. FitzSimons (Ed.), Proceedings of the 55th Annual Conference of the Mathematics Association of Victoria (pp. 91-96). Melbourne, Australia: MAV.

Russo, J. (2020). Designing and scaffolding rich mathematical learning experiences with challenging tasks. Australian Primary Mathematics Classroom, 25(1), 3-10.

Russo, J., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Sullivan, P. (2019). Teaching with challenging tasks in the first years of school: What are the obstacles and how can teachers overcome them?. Australian Primary Mathematics Classroom, 24(1), 11-18.

Russo, J., & Hopkins, S. (2019). Teachers’ perceptions of students when observing lessons involving challenging tasks. International Journal of Science and Mathematics Education, 17(4), 759-779 https://doi.org/10.1007/s10763-018-9888-9

Russo, J., & Minas, M. (2020). Student attitudes towards learning mathematics through challenging, problem solving tasks: “It’s so hard –in a good way”. Manuscript submitted for publication.

Skaalvik, E. M., & Skaalvik, S. (2015). Job satisfaction, stress and coping strategies in the teaching profession-What do teachers say? International Education Studies, 8(3), 181-192. https://doi.org/10.5539/ies.v8n3p181

Shernoff, E. S., Mehta, T. G., Atkins, M. S., Torf, R., & Spencer, J. (2011). A qualitative study of the sources and impact of stress among urban teachers. School Mental Health, 3(2), 59-69. https://doi.org/10.1007/s12310-011-9051-z

Smith, K., George, S., & Mansfield, J. (2020). What do primary teachers think about stem education? Exploring cross-cultural perspectives. In A. Fitzgerald, C. Haeusler, & L. Pfeiffer (Eds.), STEM Education in Primary Classrooms: Unravelling Contemporary Approaches in Australia and New Zealand (1st ed., pp. 115-130). Routledge. https://doi-org.ezproxy.lib.monash.edu.au/10.4324/9780429277689-8

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. https://doi.org/10.1080/10986060802229675

Sullivan, P. (2007). Teaching mixed ability mathematics classes. In S. Close, D.Corcoran, & T.Dooley (Eds.), Proceedings of the Second National Conference on Research in Mathematics Education, (pp. 372-383). Dublin: St Patrick's.

Sullivan, P., Askew, M., Cheeseman, J., Clarke, D.M., Mornane, A., Roche, A., & Walker, N. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education, 18(2), 123-140. https://doi.org/10.1007/s10857-014-9279-2

Sullivan, P., Aulert, A., Lehmann, A., Hislop, B., Shepherd, O., & Stubbs, A. (2013). Classroom culture, challenging mathematical tasks and student persistence. In V. Steinle, L. Ball, & C. Bardini (Eds.), Proceedings of the 36th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 618-625). Melbourne, VIC: MERGA.

Sullivan, P., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Russo, J. (2020). Ways that relentless consistency and task variation contribute to teacher and student mathematics learning. In A. Coles (Ed.), For the Learning of Mathematics Monograph 1: Proceedings of a symposium on learning in honour of Laurinda Brown (pp 32-37). (pp. 32-37). Canada: FLM Publishing Association.

Sullivan, P., Borcek, C., Walker, N., & Rennie, M. (2016). Exploring a structure for mathematics lessons that initiate learning by activating cognition on challenging tasks. The Journal of Mathematical Behavior, 41, 159-170. https://doi.org/10.1016/j.jmathb.2015.12.002

Sullivan, P., Mousley, J., & Jorgensen, R. (2009). Tasks and pedagogies that facilitate mathematical problem solving. In B. Kaur, Y. B. Har & M. Kapur (Eds.), Mathematical Problem Solving : Yearbook 2009 (pp. 17–42). Singapore: World Scientific Publishing Co. https://doi.org/10.1142/9789814277228_0002

Sullivan, P., Mousley, J. & Zevenbergen, R. (2006a). Developing Guidelines for Teachers Helping Students Experiencing Difficulty in Learning Mathematics. In P. Grootenboer, R. Zevenbergen & M. Chinnappan, (Eds.), Proceedings of the29th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 496–503), Canberra, July.

Sullivan, P., Mousley, J., & Zevenbergen, R. (2006b). Teacher actions to maximize mathematics learning opportunities in heterogeneous classrooms. International Journal of Science and Mathematics Education, 4(1), 117-143. https://doi.org/10.1007/s10763-005-9002-y

Wilburne, J. M., & Dause, E. (2017). Teaching self-regulated learning strategies to low-achieving fourth-grade students to enhance their perseverance in mathematical problem solving. Investigations in Mathematics Learning, 9(1), 38-52. https://doi.org/10.1080/19477503.2016.1245036

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2020-10-05

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