Who benefits from modelling tasks combined with experiments? Effects of students’ affective traits and learning situations on situational interest and feeling of competence
DOI:
https://doi.org/10.48489/quadrante.31452Keywords:
modelling, experiments, interest, feeling of competence, affect, exponential functionAbstract
Modelling is a key mathematical competence. However, previous research has found inconsistent results concerning students’ motivation regarding modelling. One frequently discussed approach to foster students’ motivation is to combine modelling tasks with scientific experiments. In this contribution, we analyse which students benefit from such tasks – in the sense of beneficial affective states like situational interest and feelings of competence – by taking into account different learning situations related to modelling tasks with and without experiment as well as students’ affective traits, namely individual interest and mathematical self-concept. Our results with 82 students indicate that students’ affective states do depend on both, the specific learning situation and their affective traits. Especially in the case of situational interest, an interaction of learning situation and individual interest exists: students with low individual interest in mathematics report most situational interest in conducting experiments but not in modelling their experimental data, while students with high individual interest are most interested in modelling without experiments. We discuss theoretical and practical implications of these results.
References
Arens, A. K., Trautwein, U., & Hasselhorn, M. (2011). Erfassung des Selbstkonzepts im mittleren Kindesalter: Validierung einer deutschen Version des SDQ I [Measuring self-concept in middle childhood: validation of a German version of the SDQ I]. Zeitschrift für Pädagogische Psychologie, 25, 131-144. https://doi.org/10.1024/1010-0652/a000030
Bednorz, D., Huget, J., & Kleine, M. (2021). Fördermöglichkeiten von Motivation, Interesse und Emotio-nen durch Modellierungsaufgaben [Fostering motivation, interest and emotions with modelling tasks]. mathematica didactica, 44(1), 1–20. https://doi.org/10.18716/ojs/md/2021.1212
Beumann, S. (2016). Versuch´s doch mal: Eine empirische Untersuchung zur Förderung von Motivation und Interesse durch mathematische Schülerexperimente [Just try it: an empirical study concerning the promotion of motivation and interest with mathematical experiments]. (Doctoral Dissertation) Ruhr-Universität Bochum. https://hss-opus.ub.ruhr-uni-bochum.de/opus4/frontdoor/index/index/year/2017/docId/5122
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering, and economics (pp. 222–231). Horwood. https://doi.org/10.1533/9780857099419.5.221
Bong, M., & Skaalvik, E. M. (2003). Academic self-concept and self-efficacy: How different are they really? Educational Psychology Review, 15(1), 1–40. https://doi.org/10.1023/A:1021302408382
Carreira, S., & Baioa, A. M. (2018). Mathematical modelling with hands-on experimental tasks: On the student’s sense of credibility. ZDM – Mathematics Education, 50(1–2), 201–215. https://doi.org/10.1007/s11858-017-0905-1
Czocher, J. A. (2018). How does validating activity contribute to the modeling process? Educational Studies in Mathematics, 99(2), 137–159. https://doi.org/10.1007/s10649-018-9833-4
Deci, E. L., & Ryan, R. M. (2000). The “What” and “Why” of goal pursuits: Human needs and the self-determination of behavior. Psychological Inquiry, 11(4), 227–268. https://doi.org/10.1207/S15327965PLI1104_01
Di Martino, P. (2019). Chapter 9: The Complex Relationship Between Mathematical Modeling and Attitude Towards Mathematics. In S. A. Chamberlin & B. Sriraman (Eds.), Affect in Mathematical Modeling (pp. 219–234). Springer. https://doi.org/10.1007/978-3-030-04432-9_14
Engel, J. (2011). Datenanalyse und Geometrie. Vom Zusammenspiel theoriegeleiteter und daten¬bezo¬ge-ner Modellierungen [Data-analysis and geometry. The interplay between theory based and data-driven modelling]. mathematica didactica, 34, 5–19. https://doi.org/10.18716/ojs/md/2011.1098
Galbraith, P. L., Stillman, G. A., & Brown, J. (2013). Turning ideas into modeling problems. In R. Lesh, P. L. Galbraith, C. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 133–144). Springer. https://doi.org/10.1007/978-94-007-6271-8_11
Ganter, S. (2013). Experimentieren - ein Weg zum Funktionalen Denken: Empirische Untersuchung zur Wirkung von Schülerexperimenten [Experiments – a way to functional thinking: an empirical study concerning the effect of student experiments]. Verlag Dr. Kovac.
Geisler, S., & Rach. S. (in press). Students’ situational interest concerning modelling tasks with experiments. In S. Beumann & S. Geisler (Eds.). Experimentieren im Mathematikunterricht - Aktuelle Ergebnisse aus Forschung und Praxis. WTM-Verlag.
Geisler, S. (accepted). Mathematical modelling with experiments: Students’ sense of validation and its relevance. Rivista di Matematica della Università di Parma.
Guderian, P., & Priemer, B. (2008). Interessenförderung durch Schülerlaborbesuche [Fostering interest by visiting out-of-school labs]. Physik Und Didaktik in Schule Und Hochschule, 7, 27–36.
Habig, S., Blankenburg, J., van Vorst, H., Fechner, S., Parchmann, I., & Sumfleth, E. (2018). Context characteristics and their effects on students’ situational interest in chemistry. International Journal of Science Education, 40(10), 1154-1175. https://doi.org/10.1080/09500693.2018.1470349
Halverscheid, S. (2008). Building a local conceptual framework for epistemic actions in a modelling environment with experiments. ZDM–The International Journal on Mathematics Education, 40(2), 225–234. https://doi.org/10.1007/s11858-008-0088-x
Hidi, S., & Renninger, K. A. (2006). The four-phase model of interest development. Educational Psychologist, 41(2), 111–127. https://doi.org/10.1207/s15326985ep4102_4
KMK (2012). Bildungsstandards im Fach Mathematik für die Allgemeine Hochschulreife [National Standards for Mathematics]. https://www.kmk.org/fileadmin/veroeffentlichungen_beschluesse/2012/2012_10_18-Bildungsstandards-Mathe-Abi.pdf
Krapp, A. (2005). Basic needs and the development of interest and intrinsic motivational orientations. Learning and Instruction, 15(5), 381–395. https://doi.org/10.1016/j.learninstruc.2005.07.007
Krapp, A. (2007). An educational-psychological conceptualisation of interest. International Journal for Educational and Vocational Guidance, 7(1), 5–21. https://doi.org/10.1007/s10775-007-9113-9
Krawitz, J., & Schukajlow, S. (2018). Do students value modelling problems, and are they confident they can solve such problems? Value and self-efficacy for modelling, word, and intra-mathematical problems. ZDM - Mathematics Education, 50(1–2), 143–157. https://doi.org/10.1007/s11858-017-0893-1
Krug, A., & Schukajlow, S. (2013). Problems with and without connection to reality and students’ task-specific interest. In A. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3) (pp. 209–216). IGPME.
Ludwig, M. & Oldenburg, R. (2007). Lernen durch Experimentieren. Handlungsorientierte Zugänge zur Mathematik [Learning through Experiments]. mathematik lehren 141, 4–11.
National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common core state standards for mathematics. Council of Chief State School Officers.
Niss, M. (1994). Mathematics in Society. In R. Biehler, R. W. Scholz, R. Sträßer, & B. Winkelmann (Eds.). Didactics of Mathematics as a Scientific Discipline (pp. 367–378). Kluwer Academic Publishers.
Ochsen, S., Bernholt, S., Bernholt, A., & Parchmann, I. (2021). Eine Mikroanalyse von Chemieunterricht-Einsatz und Perzeption von Triggern für situationales Interesse [A Microanalysis of Chemistry Lessons – Use and Perception of Triggers for Situational Interest]. Zeitschrift für Didaktik der Naturwissenschaften, 27, 1–15. https://doi.org/10.1007/s40573-020-00122-x
OECD. (2017). PISA 2015 assessment and analytical framework. OECD Publishing.
Parhizgar, Z., & Liljedahl, P. (2019). Teaching modelling problems and its effects on students’ enga¬ge-ment and attitude toward mathematics. In S. A. Chamberlin & B. Sriraman (Eds.), Affect in Mathe-matical Modeling (pp. 235–256). Springer. https://doi.org/10.1007/978-3-030-04432-9_15
Rakoczy, K., Buff, A., & Lipowsky, F. (2005). Befragungsinstrumente [Instruments of measurement]. In E. Klieme, C. Pauli & K. Reusser (Eds.), Dokumentation der Erhebungs- und Auswertungsinstrumente zur schweizerisch-deutschen Videostudie "Unterrichtsqualität, Lernverhalten und mathematisches Verständnis" (Teil 1). GFPF/DIPF.
Rellensmann, J., Schukajlow, S., Blomberg, J., & Leopold, C. (2021). Does strategic knowledge matter? Effects of strategic knowledge about drawing on students’ modeling competencies in the domain of geometry. Mathematical Thinking and Learning, 25(3), 296–316. https://doi.org/10.1080/10986065.2021.2012741
Schukajlow, S., & Krug, A. (2014a). Do multiple solutions matter? Prompting multiple solutions, interest, competence, and autonomy. Journal for Research in Mathematics Education, 45(4), 497–533. https://doi.org/10.5951/jresematheduc.45.4.0497
Schukajlow, S., & Krug, A. (2014b). Are interest and enjoyment important for students’ performance? In Nicol, C., Oesterle, S., Liljedahl, P., & Allan, D. (Eds.) Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 5 (pp. 129-136). IGPME.
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 expec¬-ta¬tions. Educational Studies in Mathematics, 79, 215–237. https://doi.org/10.1007/s10649-011-9341-2
Schulze Elfringhoff, M., & Schukajlow, S. (2021). What makes a modelling problem interesting? Sources of situational interest in modelling problems. Quadrante: Revista de Investigação Em Educação Matemática, 30(1), 8–30. https://doi.org/10.48489/quadrante.23861
van Tuijl, C., & van der Molen, J. H. (2016). Study choice and career development in STEM fields: An overview and integration of the research. International Journal of Technology and Design Education, 26, 159–183. https://doi.org/10.1007/s10798-015-9308-1
Willems, A. S. (2011). Bedingungen des situationalen Interesses im Mathematikunterricht – eine mehrebenenanalytische Perspektive [Conditions of situational interests in mathematics lessons – a multilevel perspective]. Waxmann.
Zell, S. (2010). Fächerübergreifende Elemente im Mathematikunterricht zur Förderung von mathematical literacy [Interdiciplinary elements in mathematics lessons to foster mathematical literacy]. Franzbecker.
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