Teaching the problem-solving process in a progressive or in a simultaneous way: a question of making sense?
Main Article Content
Abstract
Over the past two decades, the perennial low success rates of elementary students in math problem-solving and the difficulties experienced by teachers in helping their students with this type of task has become quite a hot topic. In response, several instructional interventions aiming to develop an expert and reflexive approach to problem-solving have been designed. However, these interventions are based on two contrasting learning approaches, either teaching the components of the problem-solving process at the same time or teaching them one at the time. The two approaches have never been compared. Moreover, they have mainly been assessed in terms of cognitive outcomes. Yet, recent studies stress the importance of analyzing the cognitive, motivational and emotional processes involved in problem-solving learning together in order to gain a full understanding of the process. Addressing these limitations is essential to enhance our understanding of problem-solving learning and to design more effective interventions. This paper focuses on this issue by investigating whether it is preferable as regards cognitive, motivational and emotional outcomes, to teach the problem-solving process in all its complexity or one component at a time. This issue is handled both for novice and expert solvers. Data were gathered among 267 upper elementary students. Findings showed that both learning approaches support the short- and long-term acquisition of cognitive problem-solving strategies, regardless of the student’s profile. However, beneficial emotional and motivational outcomes occur only when the problem-solving process is taught in all its complexity, i.e., makes sense for the learner. Novice solvers made less use of the help seeking strategy and persisted more.
Article Details
How to Cite
Vanessa, H., & Catherine, V. N. (2018). Teaching the problem-solving process in a progressive or in a simultaneous way: a question of making sense?. Frontline Learning Research, 6(2), 39–65. https://doi.org/10.14786/flr.v6i2.333
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References
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Authors (in press).
Bassok, M. (2003). Analogical transfer in problem solving. In J. E. Davidson & R. J. Sternberg (Eds.), The psychology of problem solving (pp. 343-369). New York: Cambridge University Press.
Beswick, K. (2006). The importance of mathematics teachers' beliefs. The Australian Mathematics Teacher, 62(4), 17.
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics- ICTMA 12 (pp. 222-231). Chichester, UK: Horwood Publishing.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects. State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. doi: 10.1007/BF00302716.
Boekaerts, M. (1997). Self-Regulated Learning: a new concept embraced by researchers, policy makers, educators, teachers and students. Learning and Instruction, 7(2), 161-186. doi: 10.1016/S0959-4752(96)00015-1.
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-55. doi: 10.1007/s10649-012-9441-7.
Brand, S., Reimer, T., & Opwis, K. (2003). Effects of metacognitive thinking and knowledge acquisition in dyads on individual problem solving and transfer performance. Swiss Journal of Psychology, 62(4), 251-261. doi: 10.1016/j.learninstruc.2006.11.002
Brault-Labbé, A., & Dubé, L. (2008). Engagement, surengagement et sous-engagement académiques au collégial: pour mieux comprendre le bien-être des étudiants [Academic commitment, over-commitment and under-commitment at secondary school: understanding students’ wellbeing]. Revue des sciences de l’éducation, 34(3), 729-751. doi: 10.7202/029516ar.
Cosnefroy, L. (2004). Apprendre, faire mieux que les autres, éviter l’échec : l’influence de l’orientation des buts sur les apprentissages scolaires [Learning, doing better than others, avoiding failure: the influence of goal orientation on academic learning]. Revue Française de Pédagogie, 147(1), 107-128. doi: 10.3406/rfp.2004.3125.
Cumming, G. (2012). Understanding the new statistics. Effect sizes, confidence, intervals, and meta-analysis. New York, NY: Routledge.
De Corte, E., Depaepe, F., Op’t Eynde, P., & Verschaffel, L. (2011). Students’ self-regulation of emotions in mathematics: an analysis of meta-emotional knowledge and skills. ZDM, 43(4), 483-495.
De Corte, E., Verschaffel, L., & Masui, C. (2004). The CLIA-model: a framework for designing powerful learning environments for thinking and problem solving. European Journal of Psychology of Education, 19(4), 365-384.
Demonty, I., Blondin, C., Matoul, A., Baye, A., & Lafontaine, D. (2013). La culture mathématique à 15 ans. Premiers résultats de Pisa 2012 en Fédération Wallonie-Bruxelles [Mathematical knowledge at 15 years old. First results of Pisa 2012 in the Wallonia-Brussels Federation]. Les Cahiers des Sciences de l’Education, 34, 1-26.
Demonty, I., & Fagnant, A. (2014). Tâches complexes en mathématiques : difficultés des élèves et exploitations collectives en classe [Complex mathematical tasks: students difficulties and whole-class practice]. Education et Francophonie, 42(2), 173-189. doi : 10.7202/1027912ar.
Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers' approaches towards word problem solving: elaborating or restricting the problem context. Teaching and Teacher education, 26(2), 152-160. doi: 10.1016/j.tate.2009.03.016.
Durlak, J. A., & DuPre, E. P. (2008). Implementation matters: a review of research on the influence of implementation on program outcomes and the factors affecting implementation. American Journal of Community Psychology, 41(3-4), 327. doi : 10.1007/s10464-008-9165-0.
Fagnant, A. & Demonty, I. (2005). Résoudre des problèmes : pas de problème ! Guide méthodologique et documents reproductibles. 10/12ans [Solving problems: no problem ! Methodological guide and reproducible documents. 10/12 years]. Brussels : De Boeck.
Fagnant, A., Demonty, I., & Lejonc, M. (2003). La résolution de problèmes : un processus complexe de « modélisation mathématique » [Problem-solving: a complex process of “mathematical modeling”]. Bulletin d’informations pédagogiques, 54, 29-39.
Fayol, M. (2006). Un esprit pour apprendre [A mind to learn]. In E. Bourgeois & G. Chapelle (Eds.), Apprendre et faire apprendre [To learn and to teach] (pp.53-67). Paris: PUF.
Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th edition). London: SAGE Publications.
Fredricks, J. A., & McColskey, W. (2012). The measurement of student engagement: a comparative analysis of various methods and student self-report instruments. In S.L., Christenson, A.L. Reschly, & C. Wylie, Handbook of research on student engagement (pp. 763-782). Springer US.
Hampel, P., Meier, M., & Kümmel, U. (2008). School-based stress management training for adolescents: longitudinal results from an experimental study. Journal of Youth and Adolescence, 37(8), 1009-1024. doi: 10.1007/s10964-007-9204-4.
Hohn, R., & Frey, B. (2002). Heuristic training and performance in elementary mathematical problem solving. The Journal of Educational Research, 95(6), 374-380. doi: 10.1080/00220670209596612.
Kanfer, R., Ackerman, P. L., & Heggestad, E. D. (1996). Motivational skills & self-regulation for learning: a trait perspective. Learning and individual differences, 8(3), 185-209. doi: 10.1016/S1041-6080(96)90014-X.
Lester, F.K, Garofalo, J., & Kroll, D. (1989). The role of metacognition in mathematical problem solving: a study of two grade seven classes (Final report to the National Science Foundation, NSF Project). Bloomington: Indiana University, Mathematics Education Development Center.
Linnenbrink, E.A. (2006). Emotion research in education: theoretical and methodological perspectives on the integration of affect, motivation, and cognition. Educational Psychology Review, 18(4), 307-314. doi: 10.1007/s10648-006-9028-x.
Mevarech, Z.R. & Amrany, C. (2008). Immediate and delayed effects of meta-cognitive instruction on regulation of cognition and mathematics achievement. Metacognition and Learning, 3(2), 147-157. doi : 10.1007/s11409-008-9023-3.
Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: a multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34(2), 365-394. doi: 10.3102/00028312034002365.
Muir, T., Beswick, K., & Williamson, J. (2008). “I’m not very good at solving problems”: an exploration of students’ problem solving behaviours. The Journal of Mathematical Behavior, 27(3), 228-241. doi: 10.1016/j.jmathb.2008.04.003.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2010). Why is teaching with problem solving important to student learning? Reston: National Council of Teachers of Mathematics.
Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14(3), 510–520. doi: 10.1037/0278-7393.14.3.510.
OECD (2014). Pisa 2012 Results. What students know and can do. Student performance in mathematics, reading and science (Volume I, revised edition). Paris: OECD Publishing.
OECD (2016). Pisa 2015 Results. Excellence and equity in education (Volume I). Paris: OECD Publishing.
Op’t Eynde, P., De Corte, E., & Mercken, I. (2004). Pupils (meta)emotional knowledge and skills in the mathematics classroom. Unpublished document presented at the American Educational Research Association (AERA), San Diego.
Pekrun, R. (2014). Emotions and learning. Educational Practices Series. Belley, France: International Academy of Education.
Pekrun, R., Goetz, T., Daniels, L. M., Stupnisky, R. H., & Perry, R. P. (2010). Boredom in achievement settings: control-value antecedents and performance outcomes of a neglected emotion. Journal of Educational Psychology, 102(3), 531-549. doi: 10.1037/a0019243.
Pekrun, R., Goetz, T., & Frenzel, A.C. (2005). Achievement Emotions Questionnaire-Mathematics (AEQ-M). User’s Manual. Unpublished document. University de Munich, Munich.
Piaget, J. (1978). Success and understanding. Cambridge: Harvard University Press.
Pollock, E., Chandler, P., & Sweller, J. (2002). Assimilating complex information. Learning and Instruction, 12(1), 61-86. doi: 10.1016/S0959-4752(01)00016-0.
Polya, G. (1957). How to solve it (2nd ed.). Princeton. NJ: Princeton University Press.
Pool, L., & Qualter, P. (2012). Improving emotional intelligence and emotional self-efficacy through a teaching intervention for university students. Learning and individual differences, 22 (3), 306-312. doi: 10.1016/j.lindif.2012.01.010.
Prawat, R. S., & Anderson, A. L. (1994). The affective experiences of children during mathematics. The Journal of Mathematical Behavior, 13(2), 201-222. doi: 10.1016/0732-3123(94)90024-8.
Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New-York: Macmillan.
Sweller, J. (1999). Instructional designs in technical areas. Melbourne: ACER.
Sweller, J., van Merrienboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10 (3), 251–296. doi: 10.1023/A:1022193728205.
Van der Sandt, S. (2007). Research framework on mathematics teacher behaviour: Koehler and Grouws' framework revisited. Eurasia Journal of mathematics, Science & Technology, 3(4), 343-350.
Van Merriënboer, J. J., & Sweller, J. (2005). Cognitive load theory and complex learning: recent developments and future directions. Educational Psychology Review, 17(2), 147-177. doi: 10.1007/s10648-005-3951-0.
Veenman, M.V.J., Van Hout-Wolters, B., & Afflerbach, P. (2006). Metacognition and learning: conceptual and methodological considerations. Metacognition Learning, 1(1), 3-14. doi: 10.1007/s11409-006-6893-0.
Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modeling and problem solving in the elementary school. A teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28(5), 577-601. doi: 10.2307/749692.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, Hollande: Swets & Zeitlinger.
Verschaffel, L., Greer, B., & Van Dooren, W. (2008). La résolution de problèmes [Problem solving]. In A. Van Zanten (Ed.), Dictionnaire de l’éducation [Dictionary of education] (pp 588-590). Paris : P.U.F., Presses universitaires de France.
Wilkins, J. L. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139-164. doi : 10.1007/s10857-007-9068-2.
Zimmerman, B.J. (2011). Motivational sources and outcomes of self-regulated learning and performance. In B. Zimmerman, & D. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp.49-64). New-York: Routledge.
Allal, L. (2007). Régulations des apprentissages: orientations conceptuelles pour la recherche et la pratique en éducation [Regulation of learning: conceptual guidelines for research and practice in education]. In L. Allal, & L. Mottier Lopez (Eds.), Régulation des apprentissages en situation scolaire et en formation [Regulation of learning in educational and instructional situations] (pp. 7-24). Brussels: De Boeck.
Anderson, J.R. (1981). Cognitive skills and their acquisition. Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
Authors. (2016a).
Authors. (2016b).
Authors (2017).
Authors (in press).
Bassok, M. (2003). Analogical transfer in problem solving. In J. E. Davidson & R. J. Sternberg (Eds.), The psychology of problem solving (pp. 343-369). New York: Cambridge University Press.
Beswick, K. (2006). The importance of mathematics teachers' beliefs. The Australian Mathematics Teacher, 62(4), 17.
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics- ICTMA 12 (pp. 222-231). Chichester, UK: Horwood Publishing.
Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects. State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. doi: 10.1007/BF00302716.
Boekaerts, M. (1997). Self-Regulated Learning: a new concept embraced by researchers, policy makers, educators, teachers and students. Learning and Instruction, 7(2), 161-186. doi: 10.1016/S0959-4752(96)00015-1.
Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-55. doi: 10.1007/s10649-012-9441-7.
Brand, S., Reimer, T., & Opwis, K. (2003). Effects of metacognitive thinking and knowledge acquisition in dyads on individual problem solving and transfer performance. Swiss Journal of Psychology, 62(4), 251-261. doi: 10.1016/j.learninstruc.2006.11.002
Brault-Labbé, A., & Dubé, L. (2008). Engagement, surengagement et sous-engagement académiques au collégial: pour mieux comprendre le bien-être des étudiants [Academic commitment, over-commitment and under-commitment at secondary school: understanding students’ wellbeing]. Revue des sciences de l’éducation, 34(3), 729-751. doi: 10.7202/029516ar.
Cosnefroy, L. (2004). Apprendre, faire mieux que les autres, éviter l’échec : l’influence de l’orientation des buts sur les apprentissages scolaires [Learning, doing better than others, avoiding failure: the influence of goal orientation on academic learning]. Revue Française de Pédagogie, 147(1), 107-128. doi: 10.3406/rfp.2004.3125.
Cumming, G. (2012). Understanding the new statistics. Effect sizes, confidence, intervals, and meta-analysis. New York, NY: Routledge.
De Corte, E., Depaepe, F., Op’t Eynde, P., & Verschaffel, L. (2011). Students’ self-regulation of emotions in mathematics: an analysis of meta-emotional knowledge and skills. ZDM, 43(4), 483-495.
De Corte, E., Verschaffel, L., & Masui, C. (2004). The CLIA-model: a framework for designing powerful learning environments for thinking and problem solving. European Journal of Psychology of Education, 19(4), 365-384.
Demonty, I., Blondin, C., Matoul, A., Baye, A., & Lafontaine, D. (2013). La culture mathématique à 15 ans. Premiers résultats de Pisa 2012 en Fédération Wallonie-Bruxelles [Mathematical knowledge at 15 years old. First results of Pisa 2012 in the Wallonia-Brussels Federation]. Les Cahiers des Sciences de l’Education, 34, 1-26.
Demonty, I., & Fagnant, A. (2014). Tâches complexes en mathématiques : difficultés des élèves et exploitations collectives en classe [Complex mathematical tasks: students difficulties and whole-class practice]. Education et Francophonie, 42(2), 173-189. doi : 10.7202/1027912ar.
Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers' approaches towards word problem solving: elaborating or restricting the problem context. Teaching and Teacher education, 26(2), 152-160. doi: 10.1016/j.tate.2009.03.016.
Durlak, J. A., & DuPre, E. P. (2008). Implementation matters: a review of research on the influence of implementation on program outcomes and the factors affecting implementation. American Journal of Community Psychology, 41(3-4), 327. doi : 10.1007/s10464-008-9165-0.
Fagnant, A. & Demonty, I. (2005). Résoudre des problèmes : pas de problème ! Guide méthodologique et documents reproductibles. 10/12ans [Solving problems: no problem ! Methodological guide and reproducible documents. 10/12 years]. Brussels : De Boeck.
Fagnant, A., Demonty, I., & Lejonc, M. (2003). La résolution de problèmes : un processus complexe de « modélisation mathématique » [Problem-solving: a complex process of “mathematical modeling”]. Bulletin d’informations pédagogiques, 54, 29-39.
Fayol, M. (2006). Un esprit pour apprendre [A mind to learn]. In E. Bourgeois & G. Chapelle (Eds.), Apprendre et faire apprendre [To learn and to teach] (pp.53-67). Paris: PUF.
Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th edition). London: SAGE Publications.
Fredricks, J. A., & McColskey, W. (2012). The measurement of student engagement: a comparative analysis of various methods and student self-report instruments. In S.L., Christenson, A.L. Reschly, & C. Wylie, Handbook of research on student engagement (pp. 763-782). Springer US.
Hampel, P., Meier, M., & Kümmel, U. (2008). School-based stress management training for adolescents: longitudinal results from an experimental study. Journal of Youth and Adolescence, 37(8), 1009-1024. doi: 10.1007/s10964-007-9204-4.
Hohn, R., & Frey, B. (2002). Heuristic training and performance in elementary mathematical problem solving. The Journal of Educational Research, 95(6), 374-380. doi: 10.1080/00220670209596612.
Kanfer, R., Ackerman, P. L., & Heggestad, E. D. (1996). Motivational skills & self-regulation for learning: a trait perspective. Learning and individual differences, 8(3), 185-209. doi: 10.1016/S1041-6080(96)90014-X.
Lester, F.K, Garofalo, J., & Kroll, D. (1989). The role of metacognition in mathematical problem solving: a study of two grade seven classes (Final report to the National Science Foundation, NSF Project). Bloomington: Indiana University, Mathematics Education Development Center.
Linnenbrink, E.A. (2006). Emotion research in education: theoretical and methodological perspectives on the integration of affect, motivation, and cognition. Educational Psychology Review, 18(4), 307-314. doi: 10.1007/s10648-006-9028-x.
Mevarech, Z.R. & Amrany, C. (2008). Immediate and delayed effects of meta-cognitive instruction on regulation of cognition and mathematics achievement. Metacognition and Learning, 3(2), 147-157. doi : 10.1007/s11409-008-9023-3.
Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: a multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34(2), 365-394. doi: 10.3102/00028312034002365.
Muir, T., Beswick, K., & Williamson, J. (2008). “I’m not very good at solving problems”: an exploration of students’ problem solving behaviours. The Journal of Mathematical Behavior, 27(3), 228-241. doi: 10.1016/j.jmathb.2008.04.003.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2010). Why is teaching with problem solving important to student learning? Reston: National Council of Teachers of Mathematics.
Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of Experimental Psychology: Learning, Memory, and Cognition, 14(3), 510–520. doi: 10.1037/0278-7393.14.3.510.
OECD (2014). Pisa 2012 Results. What students know and can do. Student performance in mathematics, reading and science (Volume I, revised edition). Paris: OECD Publishing.
OECD (2016). Pisa 2015 Results. Excellence and equity in education (Volume I). Paris: OECD Publishing.
Op’t Eynde, P., De Corte, E., & Mercken, I. (2004). Pupils (meta)emotional knowledge and skills in the mathematics classroom. Unpublished document presented at the American Educational Research Association (AERA), San Diego.
Pekrun, R. (2014). Emotions and learning. Educational Practices Series. Belley, France: International Academy of Education.
Pekrun, R., Goetz, T., Daniels, L. M., Stupnisky, R. H., & Perry, R. P. (2010). Boredom in achievement settings: control-value antecedents and performance outcomes of a neglected emotion. Journal of Educational Psychology, 102(3), 531-549. doi: 10.1037/a0019243.
Pekrun, R., Goetz, T., & Frenzel, A.C. (2005). Achievement Emotions Questionnaire-Mathematics (AEQ-M). User’s Manual. Unpublished document. University de Munich, Munich.
Piaget, J. (1978). Success and understanding. Cambridge: Harvard University Press.
Pollock, E., Chandler, P., & Sweller, J. (2002). Assimilating complex information. Learning and Instruction, 12(1), 61-86. doi: 10.1016/S0959-4752(01)00016-0.
Polya, G. (1957). How to solve it (2nd ed.). Princeton. NJ: Princeton University Press.
Pool, L., & Qualter, P. (2012). Improving emotional intelligence and emotional self-efficacy through a teaching intervention for university students. Learning and individual differences, 22 (3), 306-312. doi: 10.1016/j.lindif.2012.01.010.
Prawat, R. S., & Anderson, A. L. (1994). The affective experiences of children during mathematics. The Journal of Mathematical Behavior, 13(2), 201-222. doi: 10.1016/0732-3123(94)90024-8.
Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370). New-York: Macmillan.
Sweller, J. (1999). Instructional designs in technical areas. Melbourne: ACER.
Sweller, J., van Merrienboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10 (3), 251–296. doi: 10.1023/A:1022193728205.
Van der Sandt, S. (2007). Research framework on mathematics teacher behaviour: Koehler and Grouws' framework revisited. Eurasia Journal of mathematics, Science & Technology, 3(4), 343-350.
Van Merriënboer, J. J., & Sweller, J. (2005). Cognitive load theory and complex learning: recent developments and future directions. Educational Psychology Review, 17(2), 147-177. doi: 10.1007/s10648-005-3951-0.
Veenman, M.V.J., Van Hout-Wolters, B., & Afflerbach, P. (2006). Metacognition and learning: conceptual and methodological considerations. Metacognition Learning, 1(1), 3-14. doi: 10.1007/s11409-006-6893-0.
Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modeling and problem solving in the elementary school. A teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28(5), 577-601. doi: 10.2307/749692.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, Hollande: Swets & Zeitlinger.
Verschaffel, L., Greer, B., & Van Dooren, W. (2008). La résolution de problèmes [Problem solving]. In A. Van Zanten (Ed.), Dictionnaire de l’éducation [Dictionary of education] (pp 588-590). Paris : P.U.F., Presses universitaires de France.
Wilkins, J. L. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139-164. doi : 10.1007/s10857-007-9068-2.
Zimmerman, B.J. (2011). Motivational sources and outcomes of self-regulated learning and performance. In B. Zimmerman, & D. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp.49-64). New-York: Routledge.