Skip to main content
SpringerLink
Log in

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

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed before and after a ten-lesson teaching unit promoting modelling competency related to the topics “Pythagoras’ theorem” and “linear functions”. The study aimed to answer the following research questions: (1) Do students’ enjoyment, value, interest and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems, including a “directive”, teacher-centred instruction and an “operative-strategic”, more student-centred instruction emphasising group work and strategic scaffolding by the teacher? The findings show that there were no differences in students’ enjoyment, interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial effects.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Ames, C. (1992). Classrooms: Goals, structures, and student motivation. Journal of Educational Psychology, 84, 261–271.

    Article  Google Scholar 

  • Bandura, A. (2003). Self-efficacy: The exercise of control (6th ed.). New York: Freeman.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Blum, W., Galbraith, P. L., Henn, W., & Niss, M. (2007). Mathematical modelling and applications in mathematics education. New York: Springer.

    Book  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 155–159.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53, 109–132.

    Article  Google Scholar 

  • Efklides, A., & Volet, S. (2005). Emotional experiences during learning: Multiple, situated and dynamic. Learning and Instruction, 15(5), 377–380.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Leder, G., Pehkonen, E., & Törner, G. (2002). Beliefs—A hidden variable in mathematics education? Dordrecht: Kluwer.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lewis, M. W., Haviland-Jones, J. M., & Feldmann Barrett, L. (2008). Handbook of emotions (3rd ed.). New York: The Guilford Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Linnenbrink-Garcia, L., & Pekrun, R. (2011). Students' emotions and academic engagement. Introduction to the special issue. Contemporary Educational Psychology, 36, 1–3.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Malmivuori, M.-L. (2006). Affect and self-regulation. Educational Studies in Mathematics, 63, 149–164.

    Article  Google Scholar 

  • 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.

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Murphy, T. H., & Alexander, A. (2000). Motivational exploration of motivation terminology. Contemporary Educational Psychology, 25, 3–53.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pajares, F., & Graham, L. (1999). Self-Efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24, 124–139.

    Article  Google Scholar 

  • Panaoura, A., Demetriou, A. & Gagatsis, A. (2009). Mathematical modeling, self-representation and self-regulation. Paper presented at the CERME 6, Lyon.

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pintrich, P. R. (1999). The role of motivation in promoting and sustaining self-regulated learning. International Journal of Educational Research, 31, 459–470.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pollak, H. (1979). The interaction between mathematics and other school subjects. New trends in mathematics teaching IV (pp. 232–248). Paris: UNESCO.

    Google Scholar 

  • Rasch, D., & Guiar, V. (2004). The robustness of parametric statistical methods. Psychology Science, 46, 175–208.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Schiefele, U. (1996). Topic interest, text representation, and quality of experience. Contemporary Educational Psychology, 21, 3–18.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Schunk, D. B. (1989). Self-efficacy and achievement behaviors. Educational Psychology Review, 1(3), 173–207.

    Article  Google Scholar 

  • 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.

  • Schutz, P. A., & Pekrun, R. (2007). Emotion in education. San Diego, CA: Academic.

    Google Scholar 

  • Seegers, G., & Boekaerts, M. (1993). Task motivation and mathematics achievement in actual task situations. Learning and Instruction, 3(2), 133–150.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validation study. Contemporary Educational Psychology, 34, 89–101.

    Article  Google Scholar 

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

    Google Scholar 

  • 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.

    Google Scholar 

  • Wigfield, A., & Eccles, J. S. (1992). The development of achievement task values: A theoretical analysis. Developmental Review, 12, 1–46.

    Article  Google Scholar 

  • Wigfield, A., & Eccles, J. S. (2000). Expectancy–value theory of achievement motivation. Contemporary Educational Psychology, 25, 68–81.

    Article  Google Scholar 

  • Zan, R., Brown, L., Evans, J., & Hannula, M. S. (2006). Affect in mathematics education: An introduction. Educational studies in mathematics, 63(2), 113–122.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Kassel, Kassel, Germany

    Stanislaw Schukajlow, Werner Blum, Marcel Müller & Rudolf Messner

  2. Leuphana University of Lüneburg, Lüneburg, Germany

    Dominik Leiss

  3. University of Munich, Munich, Germany

    Reinhard Pekrun

Authors
  1. Stanislaw Schukajlow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dominik Leiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Reinhard Pekrun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Werner Blum
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Marcel Müller
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Rudolf Messner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stanislaw Schukajlow.

Additional information

The research project DISUM has been funded by the German Research Foundation [Deutsche Forschungsgemeinschaft] since 2005.

Appendix

Appendix

Modelling problem (topic “linear functions”)

figure a

A part of test-book

Task 1

figure b

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schukajlow, S., Leiss, D., Pekrun, R. et al. Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educ Stud Math 79, 215–237 (2012). https://doi.org/10.1007/s10649-011-9341-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-011-9341-2

Keywords

Search

Navigation