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Do Students Enjoy Computing a Triangle’s Side? Enjoyment and Boredom While Solving Problems with and Without a Connection to Reality from Students’ and Pre-Service Teachers’ Perspectives

Macht Schülern das Berechnen einer Dreiecksseite Spaß? Freude und Langeweile beim Bearbeiten von Aufgaben mit und ohne Realitätsbezug aus Sicht von Schülern und Lehramtsstudierenden

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Abstract

When students solve mathematical problems, they can have emotional responses, which in turn can influence their motivation and achievement. It is part of a teacher’s professional competence to accurately judge and take into consideration students’ emotions with the goal of optimizing student learning. The current study was aimed at investigating students’ task-specific emotions and pre-service teachers’ judgments of students’ emotions. The research questions were: (1) Do the extents to which students experience enjoyment and boredom differ for problems with and without a connection to reality? (2) Do pre-service teachers’ judgments of students’ task-specific enjoyment and boredom differ for problems with and without a connection to reality? (3) Can pre-service teachers accurately judge students’ task-specific enjoyment and boredom for problems with and without a connection to reality? To answer these research questions, 100 ninth graders were asked to rate the extents to which they experienced enjoyment and boredom while solving mathematical problems. In addition, 163 pre-service teachers were asked to judge fictitious ninth graders’ enjoyment and boredom with respect to the same mathematical problems. Results indicated that students experienced the same levels of enjoyment and boredom when solving problems with and without a connection to reality. However, pre-service teachers predicted that students would experience more enjoyment and less boredom when solving problems with a connection to reality. In addition, findings indicated that pre-service teachers had trouble accurately judging students’ task-specific emotions and that the ability to make accurate judgments varied greatly amongst pre-service teachers. Implications for teaching practice and teacher education are discussed.

Zusammenfassung

Die Bearbeitung von mathematischen Aufgaben kann emotionale Reaktionen in Schülern auslösen, die wiederum deren Motivation und Leistung beeinflussen. Die Fähigkeit, diese Schüleremotionen korrekt einzuschätzen und in der Unterrichtsgestaltung zu berücksichtigen, ist Teil der professionellen Kompetenz eines Lehrers und dient dazu, das Lernen zu optimieren. In dieser Studie wurden die aufgabenbezogenen Schüleremotionen und Einschätzungen von Lehramtsstudierenden zu Schüleremotionen untersucht. Die Forschungsfragen lauten: (1) Unterscheidet sich das Ausmaß des Erlebens von Freude und Langeweile von Schülern bei der Bearbeitung von Aufgaben mit und ohne Realitätsbezug? (2) Unterscheiden sich die Einschätzungen von Lehramtsstudierenden im Hinblick auf das Erleben von Freude und Langeweile durch Schüler bei Aufgaben mit und ohne Realitätsbezug? (3) Können Lehramtsstudierende das Erleben von Freude und Langweile von Schülern bei Aufgaben mit und ohne Realitätsbezug korrekt einschätzen? Um diese Forschungsfragen zu beantworten, wurden 100 Schüler der neunten Jahrgangsstufe zu Freude und Langeweile bei der Bearbeitung von mathematischen Aufgaben befragt. Zudem wurden 163 Lehramtsstudierende gebeten, Freude und Langeweile von fiktiven Neuntklässlern für dieselben Aufgaben einzuschätzen. Die Ergebnisse zeigen, dass die Schüler ein gleiches Maß an Freude und Langeweile bei der Bearbeitung von Aufgaben mit und ohne Realitätsbezug erleben. Die Lehramtsstudierenden jedoch erwarten, dass die Schüler mehr Freude und weniger Langeweile beim Lösen der Aufgaben mit Realitätsbezug erleben würden. Außerdem weisen die Ergebnisse darauf hin, dass Lehramtsstudierende Schwierigkeiten haben, die aufgabenspezifischen Schüleremotionen korrekt einzuschätzen und dass die Fähigkeit, korrekte Einschätzungen abzugeben, stark zwischen den Lehramtsstudierenden variiert. Konsequenzen für die Unterrichtspraxis und die Lehrerbildung werden diskutiert.

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Notes

  1. Problems without a connection to reality emerged as more difficult to solve for students than problems with a connection to reality in this study (Rellensmann and Schukajlow 2017, based on the same samples as the present study). When we controlled for task difficulty, all effects maintained their direction and statistical significance.

References

  • Ahmed, W., van der Werf, G., Kuyper, H., & Minnaert, A. (2013). Emotions, self-regulated learning, and achievement in mathematics: a growth curve analysis. Journal of Educational Psychology, 105(1), 150–161.

    Article  Google Scholar 

  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Dubberke, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47, 133–180.

    Article  Google Scholar 

  • Behrmann, L., & Souvignier, E. (2013). The relation between teachers’ diagnostic sensitivity, their instructional activities, and their students’ achievement gains in reading. Zeitschrift für Pädagogische Psychologie, 27, 283–293.

    Article  Google Scholar 

  • Beswick, K. (2011). Putting context in context: an examination of the evidence for the benefits of ‘contextualised’ tasks. International Journal of Science and Mathematics Education, 9(2), 367–390.

    Article  Google Scholar 

  • 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: intellectual and attitudinal challenges (pp. 73–96). Cham: Springer.

    Google Scholar 

  • Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (2007). Modelling and applications in mathematics education. The 14th ICMI study. New York: Springer.

    Book  Google Scholar 

  • Boaler, J. (1993). The role of contexts in the mathematics classroom: Do they make mathematics more “real”? For the Learning of Mathematics, 13(2), 12–17.

    Google Scholar 

  • Brown, M., Brown, P., & Bibby, T. (2008). “I would rather die”: reasons given by 16-year-olds for not continuing their study of mathematics. Research in Mathematics Education, 10(1), 3–18. https://doi.org/10.1080/14794800801915814.

    Article  Google Scholar 

  • Brunner, M., Anders, Y., Hachfeld, A., & Krauss, S. (2013). The diagnostic skills of mathematics teachers. In Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 229–248). New York: Springer.

    Chapter  Google Scholar 

  • Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., et al. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal for Research in Mathematics Education, 45(4), 419–459.

    Article  Google Scholar 

  • Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: an integrative model for teacher preparation. Journal of Teacher Education, 44, 263–272.

    Article  Google Scholar 

  • Dienes, Z. (2014). Using Bayes to get the most out of non-significant results. Frontiers in psychology, 5, 781.

    Article  Google Scholar 

  • Eccles, J. S., Adler, T. F., Futterman, R., Goff, S., Kaczala, C., & Meece, J. L. (1983). Expectancies, values, and academic behaviors. In J. T. Spencer (Ed.), Achievement and achievement motivation (pp. 75–146). San Francisco: Freeman.

    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, 135, 57–59.

    Google Scholar 

  • 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 

  • Frenzel, A. C., Goetz, T., Ludtke, O., Pekrun, R., & Sutton, R. E. (2009). Emotional transmission in the classroom: exploring the relationship between teacher and student enjoyment. Journal of Educational Psychology, 101(3), 705–716.

    Article  Google Scholar 

  • Fried, L. (2011). Teaching teachers about emotion regulation in the classroom. Australian Journal of Teacher Education, 36(3), 1.

    Article  Google Scholar 

  • Galbraith, P. L., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM—The International Journal on Mathematics Education, 38(2), 143–162.

    Article  Google Scholar 

  • Givvin, K. B., Stipek, D. J., Salmon, J. M., & MacGyvers, V. L. (2001). In the eyes of the beholder: students’ and teachers’ judgments of students’ motivation. Teaching and Teacher Education, 17(3), 321–331.

    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(4), 715.

    Article  Google Scholar 

  • Goetz, T., Frenzel, A. C., Stoeger, H., & Hall, N. C. (2010). Antecedents of everyday positive emotions: an experience sampling analysis. Motivation and Emotion, 34(1), 49–62.

    Article  Google Scholar 

  • Goldin, G. A. (2014). Perspectives on emotion in mathematical engagement, learning, and problem solving. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 391–414). New York: Routledge.

    Google Scholar 

  • Große, C. S. (2014). Learning to solve story problems—supporting transitions between reality and mathematics. European Journal of Psychology of Education, 29(4), 619–634.

    Article  Google Scholar 

  • Harackiewicz, J. M., Tibbetts, Y., Canning, E., & Hyde, J. S. (2014). Harnessing values to promote motivation in education. Motivational interventions, 18, 71–105.

    Article  Google Scholar 

  • Helmke, A., & Schrader, F.-W. (1987). Interactional effects of instructional quality and teacher judgement accuracy on achievement. Teaching and Teacher Education, 3(2), 91–98.

    Article  Google Scholar 

  • Hiebert, J., Gallimore, R., Garnier, H., Givvin, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries. Results from the TIMSS 1999 video study. Washington, DC: NCES.

    Book  Google Scholar 

  • Jordan, A., Krauss, S., Löwen, K., Blum, W., Neubrand, M., Brunner, M., et al. (2008). Aufgaben im COACTIV-Projekt: Zeugnisse des kognitiven Aktivierungspotentials im deutschen Mathematikunterricht [Tasks in the COACTIV project: Evidence of the potential for cognitive activation in German mathematics instruction]. Journal für Mathematik-Didaktik, 29(2), 83–107.

    Article  Google Scholar 

  • Kahneman, D. (2003). A perspective on judgment and choice: mapping bounded rationality. American Psychologist, 58(9), 697.

    Article  Google Scholar 

  • Kaiser-Meßmer, G. (1986). Anwendungen im Mathematikunterricht [Applications in mathematics classrooms]. Bad Salzdetfurth: Franzbecker.

    Google Scholar 

  • Karing, C., Dörfler, T., & Artelt, C. (2015). How accurate are teacher and parent judgements of lower secondary school children’s test anxiety? Educational Psychology, 35(8), 909–925.

    Article  Google Scholar 

  • Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs. ZDM—The International Journal on Mathematics Education, 40, 873–892.

    Article  Google Scholar 

  • Kultusministerkonferenz (2003). Bildungsstandards im Fach Mathematik für den mittleren Schulabschluss [Educational standards in mathematics for the intermediate secondary school certificate]. München: Luchterhand.

    Google Scholar 

  • Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285–311.

    Article  Google Scholar 

  • McElvany, N., Schroeder, S., Hachfeld, A., Baumert, J., Richter, T., Schnotz, W., et al. (2009). Diagnostische Fähigkeiten von Lehrkräften bei der Einschätzung von Schülerleistungen und Aufgabenschwierigkeiten bei Lernmedien mit instruktionalen Bildern [Teachers’ diagnostic skills to judge student performance and task difficulty when learning materials include instructional pictures]. Zeitschrift für Pädagogische Psychologie, 23(34), 223–235.

    Article  Google Scholar 

  • 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 

  • Mega, C., Ronconi, L., & De Beni, R. (2014). What makes a good student? How emotions, self-regulated learning, and motivation contribute to academic achievement. Journal of Educational Psychology, 106(1), 121.

    Article  Google Scholar 

  • Muthén, B. O., & Satorra, A. (1995). Complex sample data in structural equation modeling. Sociological Methodology, 25, 267–316.

    Article  Google Scholar 

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

    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 

  • Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Street mathematics and school mathematics. Cambridge: Cambridge University Press.

    Google Scholar 

  • Ostermann, A., Leuders, T., & Nückles, M. (2015). Wissen, was Schülerinnen und Schülern schwer fällt. Welche Faktoren beeinflussen die Schwierigkeitseinschätzung von Mathematikaufgaben? [Knowing what students know. Which factors influence teachers’ estimation of task difficulty?]. Journal für Mathematik-Didaktik, 36(1), 45–76.

    Article  Google Scholar 

  • Pekrun, R. (2006). The control-value theory of achievement emotions: assumptions, corollaries, and implications for educational research and practice. Educational Psychology Review, 18, 315–341.

    Article  Google Scholar 

  • Pekrun, R., & Linnenbrink-Garcia, L. (2014). International handbook of emotions in education. New York: Routledge.

    Google Scholar 

  • Pekrun, R., Goetz, T., Titz, W., & Perry, R. P. (2002). 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., Frenzel, A. C., Götz, T., & Perry, R. P. (2007). The control-value theory of achievement emotions: an integrative approach to emotions. In P. A. Schutz & R. Pekrun (Eds.), Emotion in education (pp. 13–36). Amsterdam: Academic Press.

    Chapter  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., Hall, N. C., Goetz, T., & Perry, R. P. (2014). Boredom and academic achievement: testing a model of reciprocal causation. Journal of Educational Psychology, 106(3), 696.

    Article  Google Scholar 

  • Plessner, H., & Czenna, S. (2008). The benefits of intuition. In H. Plessner, C. Betsch & T. Betsch (Eds.), Intuition in judgment and decision making (pp. 251–266). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Praetorius, A.-K., & Südkamp, A. (2017). Eine Einführung in das Thema der diagnostischen Kompetenz von Lehrkräften [An introduction to the issue of teachers’ diagnostic competence]. In A. Südkamp & A.-K. Praetorius (Eds.), Diagnostische Kompetenz von Lehrkräften—Theoretische und methodische Weiterentwicklungen [Diagnostic competence of teachers—Theoretical and methodological developments] (pp. 13–18). Münster: Waxmann.

    Google Scholar 

  • Praetorius, A.-K., Drexler, K., Rösch, L., Christophel, E., Heyne, N., Scheunpflug, A., et al. (2015). Judging students’ self-concepts within 30s? Investigating judgement accuracy in a zero-acquaintance situation. Learning and Individual Differences, 37, 231–236.

    Article  Google Scholar 

  • Rellensmann, J., & Schukajlow, S. (2017). Does students’ interest in a mathematical problem depend on the problem’s connection to reality? An analysis of students’ interest and pre-service teachers’ judgments of students’ interest in problems with and without a connection to reality. ZDM Mathematics Education, 49(3), 367–378. https://doi.org/10.1007/s11858-016-0819-3.

    Article  Google Scholar 

  • Schukajlow, S. (2011). Mathematisches Modellieren. Schwierigkeiten und Strategien von Lernenden als Bausteine einer lernprozessorientierten Didaktik der neuen Aufgabenkultur [Mathematical modelling. Difficulties and strategies of learners as a means for a learning process-oriented didactic of problem posing]. Münster: Waxmann.

    Google Scholar 

  • Schukajlow, S. (2015). Effects of enjoyment and boredom on students’ interest in mathematics and vice versa. In K. Beswick, T. Muir & J. Wells (Eds.), Proceedings of the joint meeting of PME 39 (Vol. 4, pp. 137–144). Hobart: PME.

    Google Scholar 

  • Schukajlow, S., & Rakoczy, K. (2016). The power of emotions: can enjoyment and boredom explain the impact of individual preconditions and teaching methods on interest and performance in mathematics? Learning and Instruction, 44, 117–127.

    Article  Google Scholar 

  • Schukajlow, S., Leiss, D., Pekrun, R., Blum, W., Müller, M., & Messner, R. (2012). Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations. Educational Studies in Mathematics, 79(2), 215–237.

    Article  Google Scholar 

  • Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89(3), 393–417.

    Article  Google Scholar 

  • Spinath, B. (2005). Akkuratheit der Einschätzung von Schülermerkmalen durch Lehrer und das Konstrukt der diagnostischen Kompetenz [Accuracy of teacher judgments on student characteristics and the construct of diagnostic competence]. Zeitschrift für Pädagogische Psychologie, 19(1/2), 85–95.

    Article  Google Scholar 

  • Stender, P., & Kaiser, G. (2015). Scaffolding in complex modelling situations. ZDM Mathematics Education, 47(7), 1255–1267.

    Article  Google Scholar 

  • Südkamp, A., Kaiser, J., & Möller, J. (2012). Accuracy of teachers’ judgments of students’ academic achievement: a meta-analysis. Journal of Educational Psychology, 104(3), 743.

    Article  Google Scholar 

  • van Tilburg, W. A. P., & Igou, E. R. (2012). On boredom: lack of challenge and meaning as distinct boredom experiences. Motivation and Emotion, 36, 181–194.

    Article  Google Scholar 

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

    Google Scholar 

  • Verschaffel, L., Van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problems as exercises in mathematical modelling. Journal für Mathematik-Didaktik, 31, 9–29.

    Article  Google Scholar 

  • Vorhölter, K. (2009). Sinn im Mathematikunterricht: Zur Rolle von mathematischen Modellierungsaufgaben bei der Sinnkonstruktion von Schülerinnen und Schülern [Personal meaning in the mathematics instruction: On the role of mathematical modelling problems for students construction of meaning]. Vol. 27. Opladen: Budrich.

    Google Scholar 

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  1. Department of Mathematics, University of Münster, Fliednerstr. 21, 48149, Münster, Germany

    Johanna Rellensmann & Stanislaw Schukajlow

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  1. Johanna Rellensmann
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  2. Stanislaw Schukajlow
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Correspondence to Johanna Rellensmann.

Appendix

Appendix

1.1 Sample Problem with a Connection to Reality: Football Pitch (Schukajlow et al. 2012)

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Rellensmann, J., Schukajlow, S. Do Students Enjoy Computing a Triangle’s Side? Enjoyment and Boredom While Solving Problems with and Without a Connection to Reality from Students’ and Pre-Service Teachers’ Perspectives. J Math Didakt 39, 171–196 (2018). https://doi.org/10.1007/s13138-017-0123-y

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