We examined the associations between the expressed mathematical beliefs of students and their self-regulated actions in solving mathematics problems. We conducted surveys and interviews that focused on students’ self-regulated problem solving and identified students’ self-reported beliefs about mathematics. Our findings suggest that even though students may possess rigid instrumental views about mathematics, they may still be able to achieve success by incorporating some general heuristics into their problem solving if they have first broadened their definition of mathematics to legitimize such activity. Instructional activities that allow students opportunities to share and defend their ideas for solving particular problems prior to actually solving them help students develop self-advocacy and contribute to a proactive sense of agency. Students need support to develop as self-regulated problem solvers. This can be achieved through coaching and one-on-one tutoring; however, it is difficult to achieve in classroom practice. For students to broaden their view of mathematics and what their role as a mathematical problem solver can be, they must be provided with ample problem-solving opportunities. Encouraging students to reflect on their problem solving helps promote the monitoring and assessment necessary for self-regulated learning to occur.
Get full access to this article
View all access options for this article.
References
1.
BanduraA. (1986). Social foundations of thought and action: A social cognitive theory. Englewood Cliffs, NJ: Prentice-Hall.
2.
BanduraA. (1997). Self-efficacy: The exercise of control. New York, NY: Freeman.
3.
BanduraA. (2006). Guide for constructing self-efficacy scales. In PajaresF.UrdanT. (Eds.), Adolescence and education, Vol. 5: Self-efficacy beliefs of adolescents (pp. 307–337). Greenwich, CT: Information Age.
4.
BeckerJ.ShimadaS. (2005). The open-ended approach: A new proposal for teaching mathematics. Reston, VA: National Council of Teachers of Mathematics.
5.
BrownS.WalterM. (2004). The art of problem posing (3rd ed.). Mahwah, NJ: Lawrence Erlbaum.
6.
CaiJ. (1994). A protocol-analytic study of metacognition in mathematical problem solving. Mathematics Education Research Journal, 6, 166–183.
7.
CarlsonM. (1997). Obstacles for college algebra students in understanding functions: What do high-performing students really know?The AMATYC Review, 19, 48–59.
8.
CifarelliV. V. (1998, March). Student portraits: A study of the mathematical beliefs and conceptions of college algebra students. Paper presented at the Western Region North Carolina Council of Teachers of Mathematics Conference, Charlotte, NC.
9.
CifarelliV. V.Goodson-EspyT. (2001). The role of mathematical beliefs in the problem solving actions of college algebra students. In van den Heuval-PanhuizenM. (Ed.), Proceedings of the 25th meeting of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 265–272). Utrecht, The Netherlands: The Freudenthal Institute.
10.
CobbP.SteffeL. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14, 83–94.
11.
CreswellJ. W.Plano ClarkV. L. (2007). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage.
12.
De CorteE.VerschaffelL.Op'T EyndeP. (2005). Self-regulation: A characteristic and a goal of mathematics education. In BoekaertsM.PintrichP. R.ZeidnerM. (Eds.), Handbook of self-regulation (pp. 687–726). Orlando, FL: Academic Press.
13.
EnglishL. (2003). Engaging students in problem posing in an inquiry-oriented mathematics classroom. In LesterF.CharlesR. (Eds.), Teaching mathematics through problem solving: Prekindergartengrade 6 (pp. 187–198). Reston, VA: National Council of Teachers of Mathematics.
14.
EricssonK. A.SimonH. A. (1993). Protocol analysis: Verbal reports as data (Rev. ed.). Cambridge, MA: The MIT Press.
15.
HallR.KiblerD.WengerE.TruxawC. (1989). Exploring the episodic structure of algebra story problem solving. Cognition & Instruction, 6, 223–283.
16.
HastingsN. B. (2006). Afresh start for collegiate mathematics: Rethinking the courses below calculus. Washington, DC: MAA Notes Series.
17.
KieranT. E.PirieS. E. B. (1991). Recursion and the mathematical experience. In SteffeL. P. (Ed.), Epistemological foundations of mathematical experience (pp. 78–101). New York, NY: Springer-Verlag.
18.
KloostermanP. (2002). Beliefs about mathematics and mathematics learning in the secondary school: Measurement and implications for motivation. In LederG. C.PehkonenE.TörnerG. (Eds.), Beliefs: A hidden variable in mathematics education (pp. 247–269). Dordrecht, The Netherlands: Kluwer Academic.
19.
LarsonR.HostetlerR. P.HodgkinsA. V. (2000). College algebra: Concepts and models (3rd ed.). Wilmington, MA: Houghton Mifflin.
20.
Mathematical Association of America. (2007). CRAFTY guidelines for college algebra. Washington, DC: Author.
21.
Op'T EyndeP.De CorteE.VerschaffelL. (2002). Framing students' mathematics related beliefs: A quest for conceptual clarity and a comprehensive categorization. In LederG. C.PehkonenE.TörnerG. (Eds.), Beliefs: A hidden variable in mathematics education (pp. 13–37). Dordrecht, The Netherlands: Kluwer Academic.
22.
PajaresF. (1996a). Role of self-efficacy beliefs in the mathematical problem solving of gifted students. Contemporary Educational Psychology, 21, 325–344.
23.
PajaresF. (1996b). Self-efficacy beliefs in academic settings. Review of Educational Research, 66, 533–578.
24.
PajaresF. (1999). Current directions in self-efficacy research. In MaehrM.PintrichP. R. (Eds.), Advances in motivation and achievement (pp. 1–49). Greenwich, CT: JAI.
25.
PajaresF. (2006). Self-efficacy during childhood and adolescence. In PajaresF.UrbanT. (Eds.), Adolescence and education, Vol. 5: Self-efficacy beliefs of adolescents (pp. 339–367). Greenwich, CT: Information Age.
26.
PajaresF.MillerD. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86, 193–203.
27.
PiagetJ. (1970). Genetic epistemology (3rd ed.). New York, NY: Columbia University Press.
28.
QuillenM. A. (2004). Relationships among prospective elementary teachers' beliefs about mathematics, mathematics content knowledge, and previous mathematics course experiences (Unpublished master's thesis). Virginia Polytechnic Institute and State University, Blacksburg, VA.
29.
RothW. M. (2005). Doing qualitative research: Praxis of method. Dordrecht, The Netherlands: Sense.
30.
SchoenfeldA. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
31.
SchoenfeldA. (1992). Learning to think mathematically: Problem-solving, metacognition, and sense making in mathematics. In GrouwsD. A. (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York, NY: Macmillan.
32.
SchwarzN. (1999). Self-reports: How the questions shape the answers. American Psychologist, 54, 93–105.
33.
SilverE. A. (1982, September). Thinking about problem solving: Toward an understanding of metacognitive aspects of mathematical problem solving. Paper presented at the Conference on Thinking, Suva, Fiji.
Underwood-GreggD.YackelE. B. (2000). Supporting students' conceptualization of algebraic expressions and operations using composite units. In FernandezM. L. (Ed.), Proceedings of the 22nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 147152). Columbus, OH: ERIC Clearinghouse for Science, Math, and Environmental Education.
37.
UsherE. L.PajaresF. (2006). Sources of academic and self-regulatory efficacy beliefs of entering middle school students. Contemporary Educational Psychology, 31, 125–141.
38.
UsherE. L.PajaresF. (2008). Self-efficacy for self regulated learning: A validation study. Educational and Psychological Measurement, 68, 443–463.
39.
von GlasersfeldE. (1991). Radical constructivism in mathematics education. Dordrecht, The Netherlands: Kluwer Academic.
40.
WheatleyG. H. (2004, February). Mathematics learning from a philosophic and psychological perspective. Paper presented at the annual conference of the Research Council on Mathematics Learning, Oklahoma City, OK.
41.
WongN.MartonF.WongK.LamC. (2002). The lived space of mathematics learning. Journal of Mathematical Behavior, 21, 25–50.
42.
YackelE. B. (1984). Mathematical beliefs survey. West Lafayette, IN: Purdue University.
43.
YackelE. B.RasmussenC. (2002). Beliefs and norms in the mathematics classroom. In LederG. C.PehkonenE.TörnerG. (Eds.), Beliefs: A hidden variable in mathematics education (pp. 313–330). Dordrecht, The Netherlands: Kluwer Academic.
44.
ZimmermanB. J. (1995). Self-regulation involves more than metacognition: A social cognitive perspective. Educational Psychologist, 29, 217–221.
45.
ZimmermanB. J. (2002). Becoming a self-regulated learner: An overview. Theory Into Practice, 41, 64–70.
46.
ZimmermanB. J. (2005). Attaining self-regulation: A social cognitive perspective. In BoekaertsM.PintrichP. R.ZeidnerM. (Eds.), Handbook of self-regulation (pp. 13–39). Orlando, FL: Academic Press.
47.
ZimmermanB. J.ClearyT. J. (2006). Adolescents' development of personal agency: The role of self-efficacy beliefs and self-regulatory skill. In PajaresF.UrdanT. (Eds.), Adolescence and education, Vol. 5: Self-efficacy beliefs of adolescents (pp. 45–69). Greenwich, CT: Information Age.
