An Exploration of the Cognitive, Motivational, Emotional and Regulatory Behaviours of Elementary-School Novice and Expert Problem Solvers

Abstract

Over the past two decades, the perennial low success rates of elementary students in mathematical problem solving and the difficulties experienced by teachers in meeting the various needs of their students with this type of task have become quite a hot topic. While there is a general consensus among education scholars about the crucial role played by cognitive, emotional and motivational self-regulatory processes in mathematical problem-solving learning and performance, so far, no study has looked simultaneously and finely at these three dimensions in specific profiles of students. That issue is the focus of this contribution. To gain fine-grained and complete understandings of the behaviours of “above average” and “below average” problem solvers, both research from educational psychology on emotion and motivation and the work done in mathematics education on the cognitive and metacognitive characteristics of these two learner profiles were called upon. This qualitative study conducted among 22 upper elementary students is based on a cross-analysis of their verbal and written output. The data revealed that inappropriate reading of the problem by “below average” learners masks a difficulty with taking all the relational calculations involved in the problem into account and a strong conception of the uselessness of the problem’s context. These behaviours do not improve during the solution process due to the absence of control and regulation strategies. Findings regarding “above-average” achievers make it possible to identify the most important cognitive, emotional, motivational and regulatory processes that go along with problem-solving expertise. Implications in terms of educational practices are also discussed.

Résumé

Au cours des deux dernières décennies, les faibles performances en résolution de problèmes mathématiques des élèves et les difficultés éprouvées par les enseignants à répondre à leurs besoins variés dans ce type de tâche sont devenues un sujet de plus en plus préoccupant. S'il existe un consensus général parmi les chercheurs en éducation sur le rôle crucial joué par les processus d'autorégulation cognitive, émotionnelle et motivationnelle dans l'apprentissage et la performance en résolution de problèmes mathématiques, aucune étude ne s'est penchée simultanément et finement sur ces trois dimensions auprès de profils spécifiques d’élèves. Cette question a fait l'objet de la présente contribution. Afin d'acquérir une compréhension fine et complète des comportements des élèves " au-dessus de la moyenne " et " en-dessous de la moyenne " en résolution de problèmes, nous avons convoqué à la fois les recherches en psychologie de l'éducation sur les émotions et la motivation, et les travaux en didactique des mathématiques sur les caractéristiques cognitives et métacognitives de ces deux profils d'apprenants. Cette étude qualitative menée auprès de 22 élèves en fin d’enseignement primaire repose sur une analyse croisée de leurs productions verbales et écrites. Les données montrent que la lecture inappropriée du problème par les résolveurs " en-dessous de la moyenne " masque à la fois une difficulté à prendre en compte l'ensemble des calculs relationnels impliqués dans le problème et une conception forte de l'inutilité du contexte du problème. Ces comportements n’évoluent pas au cours du processus de résolution en raison de l'absence de stratégies de contrôle et de régulation. Les résultats concernant les résolveurs "au-dessus de la moyenne" permettent d'identifier les processus cognitifs, émotionnels, motivationnels et régulateurs les plus importants pour accéder à l'expertise en résolution de problèmes. Les implications en termes de pratiques éducatives sont également abordées.

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Notes

  1. 1.

    The schools’ socio-economic index score classifies schools on a scale of 1 (the lowest index) to 20 (the highest index). It is calculated from five factors measured for each student: the per capita income, the level of qualification, the unemployment rate, the professional activities, and the housing conditions. The index score of each school is then defined on the basis of the average of the indices of its population.

  2. 2.

    Problem 1 is presented in Figure 11.

References

  1. Ader, E. (2019). What would you demand beyond learning? Teachers’ promotion of students’ self-regulated learning and metacognition. ZDM, 51(4), 613–624. https://doi.org/10.1007/s11858-019-01054-8

  2. Ahmed, W., Minnaert, A., van der Werf, G., & Kuyper, H. (2010). The Role of Competence and Value Beliefs in Students’ Daily Emotional Experiences: A Multilevel Test of a Transactional Model. Learning and Individual Differences, 20, 507–511. https://doi.org/10.1016/j.lindif.2010.03.005

  3. Allal, L. (2016). The co-regulation of student learning in an assessment for learning culture. In L. Allal, & D. Laveault (Eds.), Assessment for learning: Meeting the challenge of implementation (pp.259–273). Cham: Springer.

  4. Artino, A. R. (2012). Academic self-efficacy: From educational theory to instructional practice. Perspectives on Medical Education, 1(2), 76–85. https://doi.org/10.1007/s40037-012-0012-5

  5. Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic bulletin & review, 14(2), 243–248. https://doi.org/10.3758/BF03194059

  6. Bakosh, L.S., Tobias Mortlock, J.M., Querstret, D., & Morison, L. (2018). Audio-guided mindfulness training in schools and its effects on academic attainment: Contributing to theory and practice. Learning and Instruction, 58, 34–41. https://doi.org/10.1016/j.learninstruc.2018.04.012

  7. Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.

    Google Scholar 

  8. Berger, J.-L., & Büchel, F. P. (2012). Métacognition et croyances motivationnelles : Un mariage de raison [Metacognition and motivational beliefs: a marriage of reason]. Revue française de pédagogie, 179, 95–128.

  9. Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Cham: Springer International Publishing.

    Google Scholar 

  10. Blum, W., Artigue, M., Mariotti, M.A., Sträßer, R., & Heuvel-Panhuizen, M.V.D. (2019). European didactic traditions in mathematics: Introduction and overview. Switzerland: Springer.

    Google Scholar 

  11. Bosnjak, A., Boyle, C., & Chodkiewicz, A.R. (2017). An intervention to retrain attribution using CBT: A piloy study. The Educational and Developmental Psychologist, 34(1), 19–30. https://doi.org/10.1017/edp.2017.1

  12. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.

  13. Cleary, T. J., Velardi, B., & Schnaidman, B. (2017). Effects of the Self-Regulation Empowerment Program (SREP) on middle school students’ strategic skills, self-efficacy, and mathematics achievement. Journal of School Psychology, 64, 28–42. https://doi.org/10.1016/j.jsp.2017.04.004

  14. Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46.

  15. Colognesi, S., & Van Nieuwenhoven, C. (2016). La métacognition comme tremplin pour l’apprentissage de l’écriture [Metacognition as a springboard for learning how to write]. In S. Cartier, & B. Noël (Eds.), De la métacognition à l’apprentissage autorégulé [From metacognition to self-regulated learning] (pp.111–126). Bruxelles : De Boeck.

  16. Côté, I., Trottier-Cyr, R-P., Lavoie, K., & Pagé, G. (2018). <<Veux-tu participer à ma recherche?>>: principes, enjeux et stratégies concernant l’assentiment des enfants dans le processus de recherche [Do you want to participate in my research?: principles, issues and strategies regarding children’s consent in the research process]. In A. Marin, B. Eysermann, & M.T. Giroux (Eds.), Recrutement et consentement en recherche: réalités et défis éthiques [Research recruitment and consent: ethical realities and challenges] (pp. 127–145). Sherbrooke: EDUS.

  17. Daly, L. A., Haden, S. C., Hagins, M., Papouchis, N., & Ramirez, P.M. (2015). Yoga and emotion regulation in high school students: A randomized controlled trial. Evidence-Based Complementary and Alternative Medicine, 794928, 1–8.

    Article  Google Scholar 

  18. De Corte, E., Mason, L., Depaepe, F., & Verschaffel, L. (2011). Self-regulation of mathematical knowledge and skills. In B. Zimmerman, & D. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp. 155–172). New-York: Routledge.

  19. Depaepe, F., De Corte, E., & Verschaffel, L. (2015). Students’ non-realistic mathematical modeling as drawback of teachers’ beliefs about and approaches to word problem solving. In B. Pepin, & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 137–156). Springer International Publishing.

  20. Desoete, A., & De Craene, B. (2019). Metacognition and mathematics education: an overview. ZDM Mathematics Education, 51(4), 565–575. https://doi.org/10.1007/s11858-019-01060-w

  21. Dewolf, T., Van Dooren, W., & Verschaffel, L. (2011).Upper elementary school children’s understanding and solution of a quantitative problem inside and outside the mathematics class. Learning and Instruction, 21(6), 770–780. https://doi.org/10.1016/j.learninstruc.2011.05.003

    Article  Google Scholar 

  22. Efklides, A. (2011). Interactions of metacognition with motivation and affect in self-regulated learning: The MASRL model. Educational Psychologist, 46, 6–25. https://doi.org/10.1080/00461520.2011.538645

  23. Eisenmann, P., Novotná, J., Pribyl, J., & Brehovský, J. (2015). The development of a culture of problem solving with secondary students through heuristic strategies. Mathematics Education Research Journal, 27(4), 535–562. https://doi.org/10.1007/s13394-015-0150-2

  24. Elia, I., Van den Heuvel-Panhuizen, M. & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM - The International Journal on Mathematics Education, 41, 605–618. https://doi.org/10.1007/s11858-009-0184-6

  25. Ericsson, K.A. (2008). Deliberate practice and acquisition of expert performance: a general overview. Academic Emergency Medecine,15, 988–994.

  26. 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]. Bruxelles : De Boeck.

    Google Scholar 

  27. Feldman, D. B., & Kubota, M. (2015). Hope, self-efficacy, optimism, and academic achievement: Distinguishing constructs and levels of specificity in predicting college grade-point average. Learning and Individual Differences, 37, 210–216. https://doi.org/10.1016/j.lindif.2014.11.022

  28. Fereday, J., & Muir-Cochrane, E. (2006). Demonstrating rigor using thematic analysis: a hybrid approach of inductive and deductive coding and theme development. International Journal of Qualitative Methods, 5(1), 80–92. https://doi.org/10.1177/160940690600500107

  29. Fitzpatrick, C.L., Hallett, D., Morrissey, K.R., Yildiz, N.R., Wynes, R., & Ayesu, F. (2019). Response sentences, examples, and authenticity do not help children solve real wor(l)d problem. Learning and Instruction, 61, 111–125. https://doi.org/10.1016/j.learninstruc.2018.10.002

  30. Focant, J., & Gregoire, J. (2008). Les stratégies d’autorégulation cognitive: une aide à la résolution de problèmes arithmétiques [Cognitive self-regulation strategies: an aid to solve arithmetic problems]. In M. Crahay, L. Verschaffel, E. De Corte, & J. Gregoire (Eds.), Enseignement et apprentissages des mathématiques. Que disent les recherches psychopédagogiques? [Teaching and learning mathematics. What does psycho-pedagogical research tell us?] (pp 201–221). Brussels: De Boeck.

  31. Fong, C. J., Acee, T. W., & Weinstein, C. E. (2016). A person-centered investigation of achievement motivation goals and correlates of community college student achievement and persistence. Journal of College Student Retention: Research, Theory & Practice, 20(3), 369–387. https://doi.org/10.1177/1521025116673374

  32. Gallagher, M. W., Marques, S. C., & Lopez, S. J. (2016). Hope and the academic trajectory of college students. Journal of Happiness Studies, 18(2), 341–352. https://doi.org/10.1007/s10902-016-9727-z

  33. Gamo, S., Taabane, L., & Sander, E. (2011). Rôle de la nature des variables dans la résolution de problèmes additifs complexes [Role of the nature of variables in solving complex additive problems]. L’Année Psychologique, 111(4), 613–640.

  34. Goetz, T., Haag, L., Lipnevitch, A. A., Keller, M. M., Frenzel, A. C., & Collier, P. M. (2014). Between-domain relations of students’ academic emotions and their judgments of school domain similarity. Frontiers in Psychology, 5(1153), 1–14. https://doi.org/10.3389/fpsyg.2014.01153

  35. Graham, S., & Williams, C. (2009). An attributional approach to motivation in school. In K.R. Wentzel, & A. Wigfield (Eds.), Handbook of motivation at school (pp. 11–34). New-York: Routledge.

  36. Grether, T., Sowislo, J. F., & Wiese, B. S. (2018). Top-down or bottom-up? Prospective relations between general and domain-specific self-efficacy beliefs during a work-family transition. Personality and Individual Differences, 121, 131–139. https://doi.org/10.1016/j.paid.2017.09.021.

  37. Gurcay, D., Ferah, & H. O. (2018). High school students’ critical thinking related to their metacognitive self-regulation and physics self-efficacy beliefs. Journal of Education and Training Studies, 6(4), 125–130. https://doi.org/10.11114/jets.v6i4.2980

  38. Haeffel, G.J. (2010). When self-help is no help: traditional cognitive skills training does not prevent depressive symptoms in people who ruminate. Behavior Research and Therapy, 48(2), 152–157. https://doi.org/10.1016/j.brat.2009.09.016

  39. Hagena, M., Leiss, D., & Schwippert, K. (2017). Using reading strategy training to foster students’ mathematical modelling competencies: Results of a Quasi-Experimental Control Trial. Eurasia Journal of Mathematics Science and Technology Education, 13(7b), 4057–4085.

    Article  Google Scholar 

  40. Hanin, V. & Van Nieuwenhoven, C. (2016a). Evaluation d’un dispositif pédagogique visant le développement de stratégies cognitives et métacognitives en résolution de problème en première secondaire. Evaluer. Journal international de Recherche en Education et Formation, 2(1), 53–88.

  41. Hanin, V. & Van Nieuwenhoven, C. (2016b). The influence of motivational and emotional factors in mathematical learning in secondary education. European Review of Applied Psychology, 66(3), 127-138.

  42. Hanin, V. & Van Nieuwenhoven, C. (2018a). Teaching the problem-solving process in a progressive or a simultaneous way: a question of making sense? Frontline Learning Research, 6(2), 39–65.

  43. Hanin, V. & Van Nieuwenhoven, C. (2018b). Evaluation d’un dispositif d’enseignement apprentissage en résolution de problèmes mathématiques: Evolution des comportements cognitifs, métacognitifs, motivationnels et émotionnels d’un résolveur novice et expert. Evaluer. Journal international de Recherche en Education et Formation, 4(1), 37–66.

  44. Hanin, V. & Van Nieuwenhoven, C. (2018c). Developing an expert and reflexive approach to problem-solving: the place of emotional knowledge and skills. Psychology, 9(2), 280–309.

  45. Hanin, V. & Van Nieuwenhoven, C. (2019). Emotional and motivational relationship of elementary students to mathematical problem-solving: a person centered approach. European Journal of Psychology of Education, 34(4), 705–730.

    Article  Google Scholar 

  46. Hanin, V. & Van Nieuwenhoven, C. (2020). From perceived competence to emotion regulation: Assessment of the effectiveness of a trainingprogram among upper elementary students. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-020-00481-6.pdf

  47. Hanin, V., Grégoire, J., Mikolajczak, M., Fantini-Hauwel, & Van Nieuwenhoven, C. (2017). Children’s Emotion Regulation Scale in Mathematics (CERS-M): development and validation of a self-reported instrument. Psychology, 8(13), 2240–2275.

  48. Hannula, M.S. (2019). Young learners’ mathematics-related affect: a commentary on concepts, methods, and developmental trends. Educational Studies in Mathematics, 100(3), 309–316. https://doi.org/10.1007/s10649-018-9865-9

  49. Hattie, J. A. C., & Donoghue, G. M. (2016). Learning strategies: A synthesis and conceptual model. Nature Partner Journals Science of Learning, 1(16013), 1–13. https://doi.org/10.1038/npjscilearn.2016.13

    Article  Google Scholar 

  50. Holm, M. E., Hannula, M. S., & Björn, P. M. (2017). Mathematics-related emotions among Finnish adolescents across different performance levels. Educational Psychology, 37, 205–218. https://doi.org/10.1080/01443410.2016.1152354.

  51. Houdement, C. (2011). Connaissances cachées en résolution de problèmes arithmétiques ordinaires à l’école [Hidden knowledge in traditional arithmetical problem solving tasks at school]. Annales de Didactique des Sciences cognitives, 16, 67–96.

  52. Hyry-Beihammer, E. K., & Hascher, T. (2015). Multi-grade teaching practices in Austrian and Finnish primary schools. International Journal of Educational Research, 74(1), 104–113. https://doi.org/10.1016/j.ijer.2015.07.002

  53. Ince, E. (2018). An overview of problem-solving studies in physics education. Journal of Education and Learning, 7(4), 191–200.

  54. Jindal-Snape, D., Cantali, D., MacGillivray, S. & Hannah, E. (2019). Primary-Secondary Transitions: A Systematic Literature Review. Social Research Series. Edinburgh, Scotland: Scottish Government.

    Google Scholar 

  55. Karabenick, S. A. (2003). Seeking help in large college classes: A person-centered approach. Contemporary Educational Psychology, 28(1), 37– 58. https://doi.org/10.1016/S0361-476X(02)00012-7

  56. Kirkegaard Thomsen, D.K. (2006). The association between rumination and negative affect: a review. Cognition and Emotion, 20(8), 1216–1235. https://doi.org/10.1080/02699930500473533

  57. Kurki, K., Järvelä, S., Mykkänen, A., & Määttä, E. (2015). Investigating children’s emotion regulation in socio-emotionally challenging classroom situations. Early Child Development and Care, 185(8), 1238–1254. https://doi.org/10.1080/03004430.2014.988710

  58. Lajoie, C., & Bednarz, N. (2014). La résolution de problèmes mathématiques au Québec : évolution des rôles assignés par les programmes et des conseils donnés aux enseignants [Mathematical problem solving in Quebec: evolution of curriculum-defined roles and advice to teachers]. Education et Francophonie, 42(2), 7–23.

  59. Lothaire, S., Dumay, X., & Dupriez, V. (2012). Pourquoi les enseignants quittent-ils leur école? Revue de la littérature scientifique relative au turnover des enseignants [Why do teachers leave school? Review of the scientific literature on teacher turnover]. Revue française de pédagogie. Recherches en éducation, 4(181), 99–126.

  60. Marcoux, G. (2014). Résolution de problèmes arithmétiques dans le cadre d’une approche par compétences: ordre des tâches et parts d’influence de quelques facteurs cognitifs et motivationnels [Solving arithmetical problems in a competency-based approach: chronology of tasks and role of some cognitive and motivational factors]. Les cahiers des Sciences de l’Éducation, 36, 67–114.

  61. Mary, C., Theis, L., & Martin, V. (2018). Faire réfléchir sur les opérations : quels défis pour l’enseignement ? Bulletin AMQ, 58(2), 26–43.

  62. McRae, K. (2016). Cognitive emotion regulation: a review of theory and scientific findings. Current Opinion in Behavioral Sciences, 10, 119–124. https://doi.org/10.1016/j.cobeha.2016.06.004

  63. Meusen-Beekman, K. D., Joosten-ten Brinke, D., & Boshuizen, H. P. A. (2016). Effects of formative assessments to develop self-regulation among sixth grade students: Results from a randomized controlled intervention. Studies in Educational Evaluation, 51,126–136. doi: https://doi.org/10.1016/j.stueduc.2016.10.008.

    Article  Google Scholar 

  64. Monteiro, V., Peixoto, F., Mata, L., & Sanches, C. (2017). Mathematics: I don’t like it! I like it! Very much, a little, not at all … social support and emotions in students from 2nd and 3rd cycles of education. Analise Psicologica, 35(3), 281–296. https://doi.org/10.14417/ap.1156

    Article  Google Scholar 

  65. Morshedian, M., Hemmati, F., & Sotoudehnama, E. (2017). Training EFL learners in self-regulation of reading: implementing an SRL model. Reading & Writing Quartely, 33(3), 290–303. https://doi.org/10.1080/10573569.2016.1213147

    Article  Google Scholar 

  66. Mottier Lopez, L., Blanc, C., Dechamboux, L., & Couchepin, C. (2017). Les héritages de Jean Cardinet : regards à partir de trois recherches doctorales sur l’évaluation des apprentissages des élèves en classe [Jean Cardinet’s legacies: insights from three doctoral research studies on the evaluation of students’ learning in the classroom]. E-Jiref, 3(3), 51–67.

  67. Muenks, K., Wigfield, A., & Eccles, J. S. (2018). I can do this! The development and calibration of children’s expectations for success and competence beliefs. Developmental Review, 48, 24–39.

  68. 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. https://doi.org/10.1016/j.jmathb.2008.04.003

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

    Google Scholar 

  70. Ohtani, K., & Hisasaka, T. (2018). Beyond intelligence: A meta-analytic review of the relationship among metacognition, intelligence, and academic performance. Metacognition Learning, 13(2), 179–212. https://doi.org/10.1007/s11409-018-9183-8

  71. Ozsoy, G. & Ataman, A. (2009). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67–82.

  72. Parker, P. D., van Zanden, B., & Parker, R. B. (2017). Girls get smart, boys get smug: Historical changes in gender differences math, English, and academic social comparison and achievement. Learning and Instruction, 54, 125–137. https://doi.org/10.1016/j.learninstruc.2017.09.002

  73. Passolunghi, M. C., Cargnelutti, E., & Pellizzoni, S. (2019). The relation between cognitive and emotional factors and arithmetic problem-solving. Educational Studies in Mathematics, 100(3), 271–290. https://doi.org/10.1007/s10649-018-9863-y

  74. Patrick, H., Kaplan, A., & Ryan, A. M. (2011). Positive classroom motivational environments: Convergence between mastery goal structure and classroom social climate. Journal of Educational Psychology, 103(2), 367–382. https://doi.org/10.1037/A0023311

  75. Peixoto, F., Sanches, C., Mata, L. & Monteiro, V. (2017). « How do you feel about math? »: relationships between competence and value appraisals, achievement emotions and academic achievement. European Journal of Psychology of Education, 32(3), 385–405. https://doi.org/10.1007/s10212-016-0299-4

  76. Pekrun, R., Lichtenfeld, S., Marsh, H. W., Murayama, K., & Goetz, T. (2017). Achievement emotions and academic performance: a longitudinal model of reciprocal effects. Child Development, 88(5), 1653–1670. https://doi.org/10.1111/cdev.12704

  77. Pringle, A., McLennan, J., Bateman, P., & Smith, M. (2018). The power of positive touch: A qualitative and quantitative study of the impact of daily peer massage in five primary schools in Nottinghamshire. Journal Interactive Learning Environments, 18, 343–357. https://doi.org/10.1080/02643944.2018.1528627

  78. Priolet, M. (2014). Enseignement-apprentissage de la résolution de problèmes numériques à l’école élémentaire : un cadre didactique basé sur une approche systémique [Teaching-learning numerical problem solving in elementary school: a didactic framework based on a systemic approach]. Education & Didactique, 8(2), 59–86. https://doi.org/10.4000/educationdidactique.1948

  79. Saboya, M., Hitt, F., & Bednarz, N. (2015). Le contrôle exercé en algèbre: conceptualisation et analyses en résolution de problèmes [Control in algebra: conceptualization and analysis in problem solving]. Annales de Didactique et de Sciences cognitives, 20, 61–100.

  80. Sander, E., Levrat, B., Brissiaud, R., Porcheron, P., & Richard, R. (2003). Conceptualisation et propriétés sémantiques des situations dans la résolution de problèmes arithmétiques: rapport d’étape. Ministère de la Recherche: appel d’offres 2002, École et Sciences Cognitives: les apprentissages et leurs dysfonctionnements. Université Paris 8.

  81. Savelsbergh, E. R., Prins, G. T., Rietbergen, C., Fechner, S., Vaes-sen, B. E., Draijer, J. M., et al. (2016). Effects of innovative science and mathematics teaching on student attitudes and achievement: A meta-analytic study. Educational Research Review, 19, 158–172. https://doi.org/10.1016/j.edurev.2016.07.003

  82. Schenke, K., Lam, A. C., Conley, A. M., & Karabenick, S. (2015). Adolescents’ help seeking in mathematics classrooms: Relations between achievement and perceived classroom environmental influences over one school year. Contemporary Educational Psychology, 41,133–146. https://doi.org/10.1016/j.cedpsych.2015.01.003

  83. Schukajlow, S., Kolter, J., & Blum, W. (2015). Scaffolding mathematical modelling with a solution plan. ZDM Mathematics Education, 47(7), 1241–1254. https://doi.org/10.1007/s11858-015-0707-2

  84. Schukajlow, S., Rakoczy, K., & Pekrun, R. (2017). Emotions and motivation in mathematics education: theoretical considerations and empirical contributions. ZDM, 49(3), 307–322. https://doi.org/10.1007/s11858-017-0864-6

  85. Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: A survey on the current state-of-the-art. ZDM Mathematics Education, 50(1–2), 5–18. https://doi.org/10.1007/s11858-018-0933-5

  86. Sewasew, D., Schroeders, U., Schiefer, I. M., Weirich, S., & Artelt, C. (2018). Development of sex differences in math achievement, self-concept, and interest from grade 5 to 7. Contemporary Educational Psychology, 54, 55–65. https://doi.org/10.1016/j.cedpsych.2018.05.003

  87. Shilo, A., & Kramarski, B. (2019). Mathematical-metacognitive discourse: how can it be developed among teachers and their students? Empirical evidence from a videotaped lesson andtwo case studies. ZDM Mathematics Education, 51(4), 625–640.

  88. Simons, D. J., Shoda, Y. & Lindsay, D. S. (2017) Constraints on generality (COG): A proposed addition to all empirical papers. Perspectives on Psychological Science, 12(6), 1123–1128. https://doi.org/10.1177/1745691617708630

  89. Skaalvik, E. M. (2018). Mathematics anxiety and coping strategies among middle school students: relations with students’ achievement goal orientations and level of performance. Social Psychology of Education, 21(3), 709–723. https://doi.org/10.1007/s11218-018-9433.

  90. Smit, K., de Brabander, C. J., Boekaerts, M., & Martens, R. L. (2017). The self-regulation of motivation: Motivational strategies as mediator between motivational beliefs and engagement for learning. International Journal of Educational Research, 82, 124–134. https://doi.org/10.1016/j.ijer.2017.01.006

  91. Smy, V., Cahillane, M., & MacLean, P. (2016). Sensemaking and metacognitive prompting in ill-structured problems. The International Journal of Information and Learning Technology, 33(3), 186–199. https://doi.org/10.1108/IJILT-10-2015-0027

  92. Szumski, G., & Karwowski, M. (2019). Exploring the Pygmalion effect: the role of teacher expectations, academic self-concept, and class context in students’ math achievement. Contemporary Educational Pychology, 59, 1–10. https://doi.org/10.1016/j.cedpsych.2019.101787

  93. Tornare, E., Czajkowski, N. O., & Pons, F. (2015). Children’s emotions in math problem solving situations: Contributions of self-concept, metacognitive experiences, and performance. Learning and Instruction, 39, 88–96. https://doi.org/10.1016/j.learninstruc.2015.05.011

  94. Tzohar-Rozen, M., & Kramarski, B. (2017). Meta-cognition and meta-affect in young students: does it make a difference on mathematical problem solving? Teachers College Record, 119(13), 1–24.

  95. Van den Berg, M., Bosker, R. J., & Suhre, C. J. (2018). Testing the effectiveness of classroom formative assessment in Dutch primary mathematics education. School Effectiveness and School Improvement, 29(3), 339–361. https://doi.org/10.1080/09243453.2017.1406376

  96. Van Loon, M., de Bruin, A., Leppink, J., & Roebers, C. (2017). Why are children overconfident? Developmental differences in the implementation of accessibility cues when judging concept learning. Journal of Experimental Child Psychology, 158, 77–94. https://doi.org/10.1016/j.jecp.2017.01.008

  97. Vantourout, M., & Goasdoué, R. (2014). Approches et validité psycho-didactiques des évaluations [Psycho-didactic approaches and validity of assessments]. Éducation & Formation, e-302, 139–15.

  98. Veenman, M. V. J., & Van Cleef, D. (2019). Measuring metacognitive skills for mathematics: students’ self-reports versus on-line assessment methods. ZDM Mathematics Education, 51(4), 691–701. https://doi.org/10.1007/s11858-018-1006-5

  99. Vergnaud, G. (1975). Calcul relationnel et représentation calculable. Bulletin de psychologie, 28(315), 378-387.

    Google Scholar 

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

    Google Scholar 

  101. Vickery, C.E., & Dorjee, D., (2015). Mindfulness training in primary schools decreases negative affect and increases meta-cognition in children. Frontiers in Psychology, 6, 1–13. https://doi.org/10.3389/fpsyg.2015.02025

  102. Vierhaus, M., Lohaus, A., & Wild, E. (2016). The development of achievement emotions and coping/emotion regulation from primary to secondary school. Learning and Instruction, 42, 12–21. doi: https://doi.org/10.1016/j.learninstruc.2015.11.002.

  103. Weiner, B. (2010). The development of an attribution-based theory of motivation: a history of ideas. Educational Psychologist, 45(1), 28–36. https://doi.org/10.1080/00461520903433596.

  104. Weinstein, R.S. (2018). Pygmalion at 50: harnessing its power and application in schooling. Educational Research and Evaluation, 24(3-5), 346–365. https://doi.org/10.1080/13803611.2018.1550842

    Article  Google Scholar 

  105. Wigfield, A., Klauda, S.L., & Cambria, J. (2011). Influences on the development of academic self-regulatory processes. In B. Zimmerman, & D. Schunk (Eds.), Handbook of self-regulation of learning and performance (pp.33–48). New-York: Routledge.

  106. Willig, C. (2013). Introducing qualitative research in psychology (3th ed.). Buckingham, UK: Open University Press.

    Google Scholar 

  107. Wolters, C.A. (2003). Regulation of motivation: Evaluating an underemphasized aspect of self-regulated learning. Educational Psychologist, 38(4), 189-205. doi: https://doi.org/10.1207/S15326985EP3804_1

    Article  Google Scholar 

  108. Wolters, C. A., & Mueller, S. A. (2010). Motivation regulation. In P. P. B. McGaw (Ed.), International encyclopedia of education (3rd ed., pp. 631–635). Oxford: Elsevier.

  109. Yin, R.K. (2011). Qualitative Research from Start to Finish. The Guilford Press, NewYork.

    Google Scholar 

  110. You, S., Lim, S. A. No, U., & Dang, M. (2016). Multidimensional aspects of parental involvement in Korean adolescents’ schooling: a mediating role of general and domain specific self-efficacy. Educational Psychology, 36, 916–934. https://doi.org/10.1080/01443410.2015.1025

    Article  Google Scholar 

  111. Zimmerman, B. J. (2008). Investigating self-regulation and motivation: Historical background, methodological development, and future prospects. American Educational Research Journal, 45(1), 166–183.

    Article  Google Scholar 

  112. Zimmerman, B. J., Schunk, D. H., & DiBenedetto, M. K. (2017). The role of self-efficacy and related beliefs in self-regulation of Learning and Performance. In A. J. Elliot, C.S. Dweck, & D.S. Yeager (Eds.), Handbook of competence and motivation (2nd ed., pp. 313–333). New York, NY: Guilford Press.

    Google Scholar 

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Appendices

Appendix 1. Example of an analysis of the verbal explanations of one learner

figurea

Appendix 2. Pooling of the individual analyses and first coding attempt

  Task difficulty (P1) and inference regarding P2 Goal setting: external demand/personal goal (P2) Self-efficacy belief (P2) Planning (P2)
Below average - Tom: Ouf, je suis sûr que j’ai raté, c’est vraiment dur. Je vais essayer de bien m’appliquer, je vais bien lire pour comprendre comment faire le calcul, je vais essayer de bien faire le problème.
- Rose : c’était difficile, je pense que j’ai raté. Je vais essayer de ne pas baisser les bras, s’il y a quelque chose que je comprends pas, je vais le relire plusieurs fois, pour bien me concentrer. Je veux obtenir une bonne réponse.
Julie : ouf, je l’ai trouvé moyen, je sais pas trop, je réussis pas trop donc euh… Moi j’ai envie d’y arriver cette fois. Je vais fort me concentrer, je vais bien lire pour bien comprendre.
(…)
Tom: moi, j’ai compris que Mathieu prend un bonbon, puis, Sarah prend un bonbon et à la fin Sarah prend 5 bonbons. Moi, je veux comprendre le problème, arriver à trouver ce que je dois faire.
Rose: Mathieu et Sarah prennent chacun un bonbon à tour de rôle et Sarah en prend 5 en plus. Je voudrais faire de bons calculs et tout ça.
Julie : euh après que madame a lu le problème, ben je viens de le relire une fois, j’ai un peu compris qu’il fallait savoir combien il y avait de bonbons en tout dans le paquet. Voilà… J’ai envie d’arriver à résoudre ce problème. (…)
Tom : Des difficultés ? moi, je bloque tout le temps sur les problèmes. Ouf, je sais pas trop trop… Moi, je suis vraiment pas fort en problèmes.
Rose : Moi, j’ai des problèmes dans tout math, donc euh… Moi, j’ai tout le temps faux en problème, je suis vraiment pas très forte, donc euh…
Julie : j’arrive jamais à faire les problèmes, je suis vraiment pas forte en problèmes.
(…)
Tom (P2): là je vais faire mon calcul, fin… euh… je vais calculer.
Rose (P2): ben, moi, je vais relire pour voir quel calcul il faut faire et après, je vais… Ben après, je… je sais pas encore trop.
Julie : ben, je vais… Je vais… en fait, je sais pas encore très bien. En fait, j’ai pas très bien compris.
(…)
Above average Hugo: pour moi, ils sont tous aussi faciles parce que je suis fort en problèmes. Comme ça a bien marché, je vais faire pareil pour le deuxième problème.
Claire: pour moi ils sont tous de même niveau de facilité. Je vais faire comme j’ai fait pour le problème 1. Bien lire, bien comprendre, prendre bien mon temps pour avoir juste. (…)
Hugo: ce que j’ai compris c’est que Sarah va prendre chaque fois un bonbon en plus que Mathieu et qu’il faut savoir le nombre de bonbons qu’il y a dans le sachet et faire en sorte qu’il y ait 5 bonbons d’écart. Mon objectif est d’avoir la bonne réponse.
Claire : Ce que j'ai compris, c'est que chaque enfant va prendre 1 bonbon de plus que l'autre à chaque fois et que Mathieu commence. Et, il faut savoir combien de bonbons il y a au total dans le paquet. Mon objectif c’est d’arriver à une réponse qui est bonne.
(…)
Hugo: je ne pense pas rencontrer de difficulté parce que je suis bon en problèmes.
Claire : je vais pas avoir de difficulté parce que je suis assez forte dans tout math.
(…)
Hugo : je vais faire un tableau avec Mathieu et Sarah et je vais à chaque fois rajouter 2 bonbons, fin je vais rajouter le nombre de bonbons adéquat et à chaque fois regarder qu’il y ait un bonbon de différence et dès que Sarah elle aura 5 bonbons en plus, je vais additionner le tout.
Claire : je vais dessiner deux enfants et je vais mettre en dessous les bonbons, +1, +2, +3, etc. (…)
  1. P1: marbles game; P2: greedy child; P3: at the restaurant. Colour-coding was used to distinguish different theoretical dimensions within the same verbatim extract. Keywords have been put in bold

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Hanin, V., Van Nieuwenhoven, C. An Exploration of the Cognitive, Motivational, Emotional and Regulatory Behaviours of Elementary-School Novice and Expert Problem Solvers. Can. J. Sci. Math. Techn. Educ. 20, 312–341 (2020). https://doi.org/10.1007/s42330-020-00092-9

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Keywords

  • Novice and expert problem solver
  • Self-regulation cycle
  • Upper elementary school mathematics
  • Emotional regulation strategies
  • Self-efficacy belief