Skip to main content
SpringerLink
Log in

How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety?

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

The study compares 140 third-grade Israeli students (lower and higher achievers) who were either exposed to self-regulated learning (SRL) supported by metacognitive questioning (the MS group) or received no direct SRL support (the N_MS group). We investigated: (a) mathematical problem solving performance; (b) metacognitive strategy use in three phases of the problem-solving process; and (c) mathematics anxiety. Findings indicated that the MS students showed greater gains in mathematical problem solving performance than the N_MS students. They reported using metacognitive strategies more often, and showed a greater reduction in anxiety. In particular, the lower MS achievers showed these gains in the basic and complex tasks, in strategy use during the on-action phase of the problem solving process and a decrease in negative thoughts. The higher achievers showed greater improvement in transfer tasks and an increase in positive thoughts towards mathematics. Both the theoretical and practical implications of this study are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety and performance. Journal of Experimental Psychology: General, 130(2), 224–237.

    Article  Google Scholar 

  • Azevedo, R., & Cromley, J. G. (2004). Does training of self-regulated learning facilitate student’s learning with hypermedia? Journal of Educational Psychology, 96(3), 523–535.

    Article  Google Scholar 

  • Bandura, A. (1988). Self-efficacy conception of anxiety. Anxiety Stress & Coping, 1(2), 77–98.

    Article  Google Scholar 

  • Brown, A. L., & Campione, J. C. (1994). Guided discovery in a community of learners. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory with classroom practice (pp. 229–270). Cambridge: MIT press.

    Google Scholar 

  • Cardelle-Elawar, M. (1995). Effects of metacognitive instruction on low achievers in mathematics problems. Teaching and Teacher Education, 11(1), 81–95.

    Article  Google Scholar 

  • Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362.

    Article  Google Scholar 

  • Desoete, A., & Roeyers, H. (2002). Off-line metacognition: A domain-specific retardation in young children with learning disabilities? Learning Disability Quarterly, 25(2), 123–139.

    Article  Google Scholar 

  • English, L. D. (1997). The development of fifth grade children’s problem posing abilities. Educational Studies in Mathematics, 34(3), 183–217.

    Article  Google Scholar 

  • Fuchs, L. S., Fuchs, D., Finelli, D. R., Courey, S. J., & Hamlett, C. L. (2004). Expanding schema-based transfer instruction to help third graders solve real-life mathematical problems. American Educational Research Journal, 41(2), 419–445.

    Article  Google Scholar 

  • Gierl, M. J., & Bisanz, J. (1994). Anxieties and attitudes related to mathematics in grade 3 and 6. Journal of Experimental Education, 63(2), 139–158.

    Article  Google Scholar 

  • Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, 33–46.

    Article  Google Scholar 

  • King, A. (1990). Enhancing peer interaction and learning in the classroom through reciprocal peer questioning. American Educational Research Journal, 27(4), 664–687.

    Google Scholar 

  • King, A. (1992). Comparison of self-questioning, summarizing, and notetaking-review as strategies for learning from lectures. American Educational Research Journal, 29(2), 303–323.

    Google Scholar 

  • Kramarski, B. (2004). Making sense of graphs: Does metacognitive instruction make a difference on students’ mathematical conceptions and alternative conceptions? Learning and Instruction, 14(6), 593–619.

    Article  Google Scholar 

  • Kramarski, B. (2008). Promoting teachers’ algebraic reasoning and self-regulation with metacognitive guidance. Metacognition and Learning, 3(2), 83–99.

    Article  Google Scholar 

  • Kramarski, B., & Gutman, M. (2006). How can self-regulated learning be supported in mathematical e-learning environments? Journal of Computer Assisted Learning, 22(1), 24–33.

    Article  Google Scholar 

  • Kramarski, B., & Hirsch, C. (2003). Using computer algebra systems in mathematical classrooms. Journal of Computer Assisted Learning, 19(1), 35–45.

    Article  Google Scholar 

  • Kramarski, B., & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: Effects of cooperative learning and metacognitive training. American Educational Research Journal, 40(1), 281–310.

    Article  Google Scholar 

  • Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive training on solving mathematical authentic tasks. Educational Studies in Mathematics, 49(2), 225–250.

    Article  Google Scholar 

  • Kramarski, B., & Michalsky, M. (2009). Investigating preservice teachers’ professional growth in self-regulated learning environments. Journal of Educational Psychology, 101(1), 161–175.

    Article  Google Scholar 

  • Kramarski, B., & Mizrachi, N. (2006). Online discussion and self-regulated learning: Effects of instructional methods on mathematical literacy. Journal of Educational Research, 99(4), 218–230.

    Article  Google Scholar 

  • Kramarski, B., & Zoldan, S. (2008). Using errors as springboards for enhancing mathematical reasoning with three metacognitive approaches. Journal of Educational Research, 102(2), 137–151.

    Article  Google Scholar 

  • Lester, F. K., & Kehle, P. E. (2003). From problem solving to modeling: the evolution of thinking about research on complex mathematical activity. In R. Lesh & H. Doer (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 501–517). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Lin, X., Schwartz, D. L., & Hatano, G. (2005). Toward teachers’ adaptive metacognition. Educational Psychologist, 40(4), 245–255.

    Article  Google Scholar 

  • Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5), 520–540.

    Article  Google Scholar 

  • McLeod, D. B. (1993). Research on affect in mathematics education: A reconceptualisation. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). London: Macmillan.

    Google Scholar 

  • Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34(2), 365–395.

    Google Scholar 

  • Midgley, C., Maehr, M., Hruda, L., Anderman, E., Anderman, L., Freeman, K., et al. (2000). Manual for the patterns of adaptive learning scales. Ann Arbor: University of Michigan.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.

  • Naveh-Benjamin, M. (1991). A comparison of training programs intended for different types of test-anxious students: Further support for an information-processing model. Journal of Educational Psychology, 83(1), 134–391.

    Article  Google Scholar 

  • Naveh-Benjamin, M., McKeachie, W. J., & Lin, Y. G. (1987). Two types of test-anxious students: Support for an information processing model. Journal of Educational Psychology, 79, 131–136.

    Article  Google Scholar 

  • Richardson, E., & Suinn, R. M. (1972). The mathematics anxiety rating scale: Psychometric data. Journal of Counseling Psychology, 19(6), 551–554.

    Article  Google Scholar 

  • Richardson, F. C., & Woolfolk, R. L. (1980). Mathematics anxiety. In I. G. Sarason (Ed.), Test anxiety: Theory, research, and applications. Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Sarason, I. G. (1980a). Test anxiety: Theory, research, and applications. Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Sarason, I. G. (1980b). Test anxiety, worry, and cognitive interference. In R. Schwarzer (Ed.), Self-related cognitions in anxiety and motivation (pp. 19–35). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 165–197). New York: MacMillan.

    Google Scholar 

  • Schraw, G., Crippen, K. J., & Hartley, K. (2006). Promoting self-regulation in science education: Metacognition as part of a broader perspective on learning. Research in Science Education, 36(1/2), 111–139.

    Article  Google Scholar 

  • Sherman, B. F., & Wither, D. P. (2003). Mathematics anxiety and mathematics achievement. Mathematics Education Research Journal, 15(2), 138–150.

    Google Scholar 

  • Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521–539.

    Article  Google Scholar 

  • Skemp, R. R. (1986). The psychology of learning mathematics (2nd ed.). London: Penguin Books.

    Google Scholar 

  • Slavin, R. E. (1996). Research on cooperative learning and achievement: What we know, what we need to know. Contemporary Educational Psychology, 21(1), 43–69.

    Article  Google Scholar 

  • Stodolsky, S. S. (1985). Telling math: Origins of math aversion and anxiety. Educational Psychologist, 20(2), 125–133.

    Article  Google Scholar 

  • Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285.

    Article  Google Scholar 

  • Tobias, S. (1978). Overcoming math anxiety. New York: Norton.

    Google Scholar 

  • Tobias, S. (1987). Math anxiety. Science, 237(4822), 1556.

    Article  Google Scholar 

  • Tobias, S., & Weissbrod, C. (1980). Anxiety and mathematics: An update. Harvard Educational Review, 50(1), 63–70.

    Google Scholar 

  • Vacc, N. N. (1993). Teaching and learning mathematics through classroom discussion. Arithmetic Teacher, 41(2), 225–227.

    Google Scholar 

  • Veenman, M. V. J., Kerseboom, L., & Imthorn, C. (2000). Test anxiety and metacognitive skillfulness: Availability versus production deficiencies. Anxiety Stress and Coping, 13(4), 391–412.

    Article  Google Scholar 

  • Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3–14.

    Article  Google Scholar 

  • Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets & Zeitlinger.

    Google Scholar 

  • Von Glasersfeld, E. (1991). Radical constructivism in mathematics education. Dordrecht: Kluwer.

    Google Scholar 

  • White, B. Y., & Frederiksen, J. R. (1998). Inquiry, modeling and metacognition: Making science accessible to all students. Cognition and Instruction, 16(1), 3–118.

    Article  Google Scholar 

  • White, B. Y., & Frederiksen, J. R. (2000). Metacognitive facilitation: An approach to making scientific inquiry accessible to all. In J. L. Minstrell & E. H. Van-Zee (Eds.), Inquiry into inquiry learning and teaching in science (pp. 331–370). Washington, DC: American Association for the Advancement of Science.

    Google Scholar 

  • Wigfield, A., & Eccles, J. S. (1989). Test anxiety in elementary and secondary school students. Educational Psychologist, 24(2), 159–183.

    Article  Google Scholar 

  • Zeidner, M. (1998). Test anxiety: The state of the art. New York: Plenum Press Boekaerts.

    Google Scholar 

  • Zimmerman, B. J. (2000). Attainment of self-regulated: A social cognitive perspective. In M. Boekaerts, P. Pintrich, & M. Zeidner (Eds.), Handbook of self-regulation: Research and applications (pp. 13–39). Orlando: Academic Press.

    Chapter  Google Scholar 

  • Zohar, A. (2004). Hogher order thinking in science classrooms: Students’ learning and teachers’ professional development. Netherlands: Kluwer.

    Google Scholar 

  • Zohar, A., & David, A. B. (2008). Explicit teaching of meta-strategic knowledge in authentic classroom situations. Metacognition Learning, 3(1), 59–82.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Education, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Bracha Kramarski, Izik Weisse & Inbal Kololshi-Minsker

Authors
  1. Bracha Kramarski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Izik Weisse
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Inbal Kololshi-Minsker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bracha Kramarski.

Appendices

Appendix 1: Sample problem with metacognitive questioning and expected answers for the metacognitive guidance

“Planning a Trip”

For the end of the year, the “Noam” school’s principal organized a trip for the third grade students. How many children were originally supposed to go on the trip if 88 students joined the trip and 19 students stayed at home?

1. What is the problem about? Describe the problem in your own words. List the mathematical terms/operations and underline the question.

2. What is the solution strategy? Why?

Expected ways of solutions suggested by students:

a. Mapping all the mathematical terms and operations in a table.

At the beginning

Action

In the end

Original

Stayed

Joined

?

19

88

Explanation: In order to calculate the number of students who were originally supposed to go on the trip, we should add the number of students who stayed at home to the number of students who joined the trip.

19 + 88 = 107 students

b. Present the solution in another way.

1.

figure a

2. Using a number line:

figure b

3. What is similar/different between the present task and the tasks we solved previously?

In the previous tasks, the keyword “stayed” indicated the “subtraction operation”. However, in the current task, this term indicated the “addition operation”.

4. Reflective question: Do I understand the problem? Does the result make sense?

Yes. We were asked for the whole number of students (107), so the answer should be bigger than each of the components (88; 19).

Appendix 2: Examples of basic, complex and transfer tasks

1. Basic tasks

How many children attended the party if we know that 13 children went home in the middle of the party and 27 children left at the end of the party? Show your work.

2. Complex tasks

Write three different questions that can be using the information below.

Dan, Shai and Gila took turns at a new game. Shai scored ten points less than Dan, Gila scored twice as many points as Shai, and Dan scored thirty points.

3. Transfer tasks

a. Dan builds a model with small hearts in several stages

figure c

How many hearts will be in the fourth stage, the sixth stage and the 25th stage? Explain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kramarski, B., Weisse, I. & Kololshi-Minsker, I. How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety?. ZDM Mathematics Education 42, 179–193 (2010). https://doi.org/10.1007/s11858-009-0202-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-009-0202-8

Keywords

Search

Navigation