Teaching methods for modelling problems and students' task-specific enjoyment, value, interest and self-efficacy expectations

Educational Studies in Mathematics

Volumn 79, Issue 2, 2012, Pages 215-237

  Schukajlow, Stanislaw ^a   Leiss, Dominik ^b   Pekrun, Reinhard ^c   Blum, Werner ^a   Müller, Marcel ^a   Messner, Rudolf ^a  

^a UNIVERSITY OF KASSEL   (Germany)

^b LEUPHANA UNIVERSITY OF LÜNEBURG   (Germany)

^c UNIVERSITY OF MUNICH   (Germany)

Author keywords

Affect; Enjoyment; Modelling problems; Self efficacy; Self regulation; Teaching methods; Word problems

Indexed keywords

EID: 84855346366     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-011-9341-2     Document Type: Article

References (84)

1. Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84, 261-271.
2. Bandura, A. (2003). Self-efficacy: The exercise of control (6th ed.). New York: Freeman.
3. Betz, N. E., & Hackett, G. (1983). The relationship of mathematics self-efficacy expectations to the selection of science-based college majors. Journal of Vocational Behavior, 23(3), 329-345.
4. Blum, W., Galbraith, P. L., Henn, W., & Niss, M. (2007). Mathematical modelling and applications in mathematics education. New York: Springer.
5. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning mathematical modelling (pp. 15 -30). New York: Springer.
6. Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example "Sugarloaf" and the DISUM Project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12)-Education, engineering and economics (pp. 222-231). Horwood: Chichester.
7. 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, 37-68.
8. Bong, M. (2002). Predictive utility of subject-, task-, and problem-specific self-efficacy judgments for immediate and delayed academic performances. Journal of Experimental Education, 70(2), 133-162.
9. Borromeo Ferri, R. (2007). Individual modelling routes of pupils-Analysis of modelling problems in mathematical lessons from a cognitive perspective. In C. Haines (Ed.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 260-270). Chichester: Horwood Publishing.
10. Brophy, J. E., & Good, T. L. (1986). Teacher behavior and student achievement. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 328-375). New York: Macmillan.
11. Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155-159.
12. Eccles, J. S., & Wigfield, A. (1995). In the mind of the actor: The structure of adolescents' academic achievement task value and expectancy-related beliefs. Personality and Social Psychology Bulletin, 21, 215-225.
13. Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109-132.
14. Efklides, A., & Volet, S. (2005). Emotional experiences during learning: Multiple, situated and dynamic. Learning and Instruction, 15(5), 377-380.
15. Fennema, E. H. (1989). The study of affect and mathematics: A proposed genetic model for research. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 205-219). New York: Springer.
16. Fraser, B. J., Walberg, H. J., Welch, W. W., & Hattie, J. (1987). Syntheses of educational productivity research. International Journal of Educational Research, 11, 147-252.
17. Frenzel, A. C., Jullien, S., & Pekrun, R. (2006). Thomas hat 60 Euro gespart. oder 1/4x + 60 = x. Freude und Angst beim Bearbeiten von Text- und Rechenaufgaben. Mathematik Lehren, 57-59.
18. Frenzel, A. C., Pekrun, R., & Goetz, T. (2007). Perceived learning environment and students' emotional experiences: A multilevel analysis of mathematics classrooms. Learning and Instruction, 17, 478-493.
19. Galbraith, P. L., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 143-162.
20. Gläser-Zikuda, M., Fuß, S., Laukenmann, M., Metz, K., & Randler, C. (2005). Promoting students' emotions and achievement-Instructional design and evaluation of the ECOLE approach. Learning and Instruction, 15, 481-495.
21. Goetz, T., Frenzel, A. C., Pekrun, R., Hall, N. C., & Lüdtke, O. (2007). Between- and within-domain relations of students' academic emotions. Journal of Educational Psychology, 99, 715-733.
22. Greene, B. A., DeBacker, T. K., Ravindran, B., & Krows, A. J. (1999). Goals, values, and beliefs as predictors of achievement and effort in high school mathematics classes. Sex Roles, 40(5-6), 421-458.
23. Greeno, J. G. (1989). Situations, mental models und generative knowledge. In D. Klahr & K. Kotovsky (Eds.), Complex information professing: The impact of Herbert A. Simon (pp. 285-318). Hillsdale, NJ: Ablex.
24. Hannula, M. S. (2007). Finnish research on affect in mathematics: Blended theories, mixed methods and some findings. Zentralblatt für Didaktik der Mathematik, 39, 197-203.
25. Hannula, M. S., Pantziara, M., Wæge, K., & Schlöglmann, W. (2009). Introduction. Multimethod approaches to the multidimensional affect in mathematics education. Paper presented at the CERME 6, Lyon.
26. Hänze, M., & Berger, R. (2007). Cooperative learning, motivational effects, and student characteristics: An experimental study comparing cooperative learning and direct instruction in 12th grade physics classes. Learning and Instruction, 17, 29-41.
27. Hattie, J., Biggs, J. B., & Purdie, N. (1996). Effects of learning skills interventions on student learning: A metaanalysis. Review of Educational Research, 66, 99-136.
28. Hoffman, B. & Spatariu, A. (2008). The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency. Contemporary Educational Psychology, 33(4), 875-893.
29. Köller, O., Baumert, J., & Schnabel, K. (2001). Does interest matter? The relationship between academic interest and achievement in mathematics. Journal for Research in Mathematics Education, 32(5), 448-470.
30. Krapp, A. (2000). Interest and human development during adolescence: An educational-psychological approach. In J. Heckhausen (Ed.), Motivational psychology of human development (pp. 109-128). Amsterdam: Elsevier.
31. Kuntze, S., & Reiss, K. (2006). Profile mathematikbezogener motivationaler Prädispositionen. Zusammenhänge zwischen Motivation, Interesse, Fähigkeitskonzepten und Schulleistungsentwicklung in verschiedenen Lernumgebungen. [Profiles of motivational dispositions. Interactions between motivation, interest, self concepts and achievement in different learning environments]. Mathematica Didactica, 29(2), 24-48.
32. Larson, R. W., & Richards, M. H. (1991). Boredom in the middle school years. Blaming schools versus blaming students. American Journal of Education, 99(4), 418-443.
33. Leder, G., Pehkonen, E., & Törner, G. (2002). Beliefs-A hidden variable in mathematics education? Dordrecht: Kluwer.
34. Leiss, D. (2007). Hilf mir es selbst zu tun. Franzbecker: Lehrerinterventionen beim mathematischen Modellieren. ["Help me to do it myself". Teachers' interventions in mathematical modelling prosesses]. Hildesheim: Franzbecker.
35. Leiss, D., & Blum, W. (2006). Beschreibung zentraler mathematischer Kompetenzen. [Discription of central mathematical competencies]. In W. Blum, C. Drüke-Noe, R. Hartung, & O. Köller (Eds.), Die Bildungsstandards Mathematik (pp. 33-50). Berlin: Cornelsen Scriptor.
36. Leiss, D., Blum, W., Messner, R., Müller, M., Schukajlow, S., & Pekrun, R. (2008). Modellieren lehren und lernen in der Realschule. [Teaching and learning of modelling in the middle track school]. Beiträge zum Mathematikunterricht (pp. 370-373). Münster: WTM Verlag.
37. Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling-Task analyses, student competencies, and teacher interventions. Journal für Mathematikdidaktik, 31(1), 119-141.
38. Lewis, M. W., Haviland-Jones, J. M., & Feldmann Barrett, L. (2008). Handbook of emotions (3rd ed.). New York: The Guilford Press.
39. 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.
40. Linnenbrink, E. A. (2007). The role of affect in student learning: A multi-dimensional approach to considering the interaction of affect, motivation, and engagement. In P. A. Schutz & R. Pekrun (Eds.), Emotion in education (pp. 107-124). London: Elsevier.
41. Linnenbrink-Garcia, L., & Pekrun, R. (2011). Students' emotions and academic engagement. Introduction to the special issue. Contemporary Educational Psychology, 36, 1-3.
42. Ma, X., & Kishor, N. (1997). Attitude toward self, social factors, and achievement in mathematics: A meta-analytic review. Educational Psychology Review, 9(2), 89-120.
43. Malmivuori, M.-L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63, 149-164.
44. Marcou, A. & Lerman, S. (2007). Changes in students' motivational beliefs and performance in a self-regulated mathematical problem-solving environment. Paper presented at the CERME 5, Cyprus.
45. McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics, teaching and learning (pp. 575-596). New York: Macmillan.
46. Metallidou, P., & Vlachou, A. (2010). Children's self-regulated learning profile in language and mathematics: The role of task value beliefs. Psychology in the Schools, 47(8), 776-788.
47. Murphy, T. H., & Alexander, A. (2000). Motivational exploration of motivation terminology. Contemporary Educational Psychology, 25, 3-53.
48. Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 1-32). New York: Springer.
49. Nurmi, J.-E., & Aunola, K. (2005). Task-motivation during the first school years: A person-oriented approach to longitudinal data. Learning and Instruction, 15(2), 103-122.
50. Op't Eynde, P., De Corte, E., & Verschaffel, L. (2006). "Accepting emotional complexity": A socio-constructivist perspective on the role on the role of emotions in the mathematics classroom. Educational Studies in Mathematics, 63, 193-207.
51. Pajares, F., & Graham, L. (1999). Self-Efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24, 124-139.
52. Panaoura, A., Demetriou, A. & Gagatsis, A. (2009). Mathematical modeling, self-representation and self-regulation. Paper presented at the CERME 6, Lyon.
53. Panaoura, A., Gagatsis, A., & Demetriou, A. (2009). An intervention to the metacognitive performance: Self-regulation in mathematics and mathematical modeling. Acta Didactica Universitatis Comenianae Mathematics, 9, 63-79.
54. Pekrun, R., Elliot, A. J., & Maier, M. A. (2009). Achievement goals and achievement emotions: Testing a model of their joint relations with academic performance. Journal of Educational Psychology, 101, 115-135.
55. Pekrun, R., Goetz, T., Daniels, L. M., Stupnisky, R. H., & Perry, R. P. (2010). Boredom in achievement settings: Exploring control-value antecedents and performance outcomes of a neglected emotion. Journal of Educational Psychology, 102(3), 531-549.
56. Pekrun, R., Goetz, T., Titz, W., & Perry, R. P. (2002a). Academic emotions in students' self-regulated learning and achievement: A program of qualitative and quantitative research. Educational Psychologist, 37(2), 91-105.
57. Pekrun, R., Goetz, T., Titz, W., & Perry, R. P. (2002b). Positive emotions in education. In E. Frydenberg (Ed.), Beyond coping: Meeting goals, visions, and challenges (pp. 149-174). Oxford, UK: Elsevier.
58. Pekrun, R., vom Hofe, R., Blum, W., Frenzel, A. C., Goetz, T., & Wartha, S. (2007). Development of mathematical competencies in adolescence: The PALMA longitudinal study. In M. Prenzel (Ed.), Studies on the educational quality of schools. The final report on the DFG Priority Programme (pp. 17-37). Münster, Germany: Waxmann.
59. Pietsch, J., Walker, R., & Chapman, E. (2003). The relationship among self-concept, self-efficacy, and performance in mathematics during secondary school. Journal of Educational Psychology, 95(3), 589-603.
60. Pintrich, P. R. (1999). The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31, 459-470.
61. Pintrich, P. R., & DeGroot, E. V. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82(1), 33-40.
62. Pollak, H. (1979). The interaction between mathematics and other school subjects. New trends in mathematics teaching IV (pp. 232-248). Paris: UNESCO.
63. Rasch, D., & Guiar, V. (2004). The robustness of parametric statistical methods. Psychology Science, 46, 175-208.
64. Reusser, K., & Stebler, R. (1997). Every word problem has a solution. The social rationality of mathematical modelling at school. Learning and Instruction, 7(4), 309-327.
65. Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55, 68-78.
66. Schiefele, U. (1996). Topic interest, text representation, and quality of experience. Contemporary Educational Psychology, 21, 3-18.
67. Schiefele, U., Krapp, A., & Schreyer, I. (1993). Metaanalyse von Interesse und schulischer Leistung. [A metaanalysis of the interaction between scholastic interest and scholastic achievement]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 25, 120-148.
68. Schiefele, U., & Schreyer, I. (1994). Intrinsische Lernmotivation und Lernen. Ein Überblick zu Ergebnissen der Forschung. [Intrinsic motivation to learn and learning: A review of recent research findings]. Zeitschrift für Pädagogische Psycholgie, 8, 1-13.
69. Schukajlow, S., Blum, W., Messner, R., Pekrun, R., Leiss, D., & Müller, M. (2009). Unterrichtsformen, erlebte Selbständigkeit, Emotionen und Anstrengung als Prädiktoren von Schüler-Leistungen bei anspruchsvollen mathematischen Modellierungsaufgaben. [Teaching methods, perceived self-regulation, emotions, and effort as predictors for students' performance while solving mathematical modelling tasks]. Unterrichtswissenschaft, 37(2), 164-186.
70. Schunk, D. B. (1989). Self-efficacy and achievement behaviors. Educational Psychology Review, 1(3), 173-207.
71. Schunk, D. B., & Zimmerman, B. J. (2003). Self-regulation and learning. In: W. M. Reynolds & G. E. Miller (eds.), Vol. 7, pp. 59-78. Wiley: New York.
72. Schutz, P. A., & Pekrun, R. (2007). Emotion in education. San Diego, CA: Academic.
73. Seegers, G., & Boekaerts, M. (1993). Task motivation and mathematics achievement in actual task situations. Learning and Instruction, 3(2), 133-150.
74. Seidel, T., Rimmele, R., & Prenzel, M. (2003). Gelegenheitsstrukturen beim Klassengespräch und ihre Bedeutung für die Lemmotivation-Videoanalysen in Kombination mit Schülerselbsteinschätzungen. [Opportunities for learning in whole class communication and their importance for the motivation to learn. Analyses of videos combined with students' self-assesment]. Unterrichtswissenschaft, 31(2), 142-165.
75. Seidel, T., & Shavelson, R. J. (2007). Teaching effectiveness research in the past decade: The role of theory and research design in disentangling meta-analysis results. Review of Educational Research, 77(4), 454-499.
76. Skaalvik, E. M., & Skaalvik, S. (2008). Self-concept and self-efficacy in mathematics: Relation with mathematics motivation and achievement. In F. M. Olsson (Ed.), New developments in the psychology of motivation (pp. 105-127). NY, US: Nova.
77. Slavin, R. E., Hurley, E. A., & Chamberlain, A. (2003). Cooperative learning and achievement: Theory and research. In W. M. Reynolds & G. E. Miller (Eds.), Handbook of psychology: Educational psychology (Vol. 7, pp. 177-198). New York: Wiley.
78. Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validation study. Contemporary Educational Psychology, 34, 89-101.
79. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse: Swets and Zeitlinger.
80. Webb, N. M., & Palincsar, A. S. (1996). Group processes in the classroom. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 841-873). New York: Macmillan.
81. Wigfield, A., & Eccles, J. S. (1992). The development of achievement task values: A theoretical analysis. Developmental Review, 12, 1-46.
82. Wigfield, A., & Eccles, J. S. (2000). Expectancy-value theory of achievement motivation. Contemporary Educational Psychology, 25, 68-81.
83. Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational studies in mathematics, 63(2), 113-122.
84. Zimmerman, B. J., & Martinez-Pons, M. (1990). Student differences in self-regulated learning: Relating grade, sex, and giftedness to self-efficacy and strategy use. Journal of Educational Psychology, 82, 51-59.