RESEARCH PAPER
The role of affective learner characteristics for learning about abstract algebra: A multiple linear regression analysis
 
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Mathematics Education, Institute for Mathematics and Applied Computer Science, Stiftung Universität Hildesheim, Hildesheim, GERMANY
 
2
Physics Education, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, GERMANY
 
 
Publication date: 2022-08-31
 
 
EURASIA J. Math., Sci Tech. Ed 2022;18(10):em2157
 
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ABSTRACT
Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students’ abstract thinking. However, in addition to research on cognitive processes, learners’ affective characteristics have largely remained unexplored in the context of teaching and learning group theory to date. In this paper, we contribute to closing this gap: We report on an empirical study investigating n=143 students’ affective characteristics within a two-weeks course program–the Hildesheim teaching concept. In our study, this concept was used to introduce pre-service primary teachers into group theory. A multiple linear regression analysis reveals that neither mathematics-specific ability self-concept nor subject interest are significant predictors of the achieved conceptual understanding of group theory after the intervention indicating that group theory is not reserved for only the mathematically interested students or students with a high mathematics-specific self-concept.
 
REFERENCES (41)
1.
Baldinger, E. E. (2018). Learning mathematical practices to connect abstract algebra to high school algebra. In N. Wasserman (Eds.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 211-239). Springer. https://doi.org/10.1007/978-3-....
 
2.
Baumeister, R. F. (Ed.). (1999). The self in social psychology. Psychology Press.
 
3.
Bitzenbauer, P. (2020). Quantenoptik an Schulen. Studie im Mixed-Methods Design zur Evaluation des Erlanger Unterrichtskonzepts zur Quantenoptik [Quantum optics in schools. A mixed methods study to evaluate the Erlangen Teaching Concept of quantum optics]. Logos Verlag Berlin. https://doi.org/10.30819/5123.
 
4.
Chick, H. L., & Harris, K. (2007). Grade 5/6 teachers’ perceptions of algebra in the primary school curriculum. In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (pp. 127-134).
 
5.
Cohen, J. (1988). Statistical power analysis for the behavioral Sciences. Lawrence Erlbaum Associates.
 
6.
Cook, J. P. (2018). Monster-barring as a catalyst for bridging secondary algebra to abstract algebra. In N. Wasserman (Eds.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 47-70). Springer. https://doi.org/10.1007/978-3-....
 
7.
Even, R. (2011). The relevance of advanced mathematics studies to expertise in secondary school mathematics teaching: Practitioners’ views. ZDM Mathematics Education, 43, 941-950. https://doi.org/10.1007/s11858....
 
8.
Frymier, A. B., & Shulman, G. M. (1995). “What’s in it for me?”: Increasing content relevance to enhance students’ motivation. Communication Education, 44, 40-50.https://doi.org/10.1080/036345....
 
9.
Griesel, H. (1965). Die Leitlinie Menge-Struktur im gegenwärtigen Mathematikunterricht. [The guideline set-structure in contemporary mathematics classroom.] Der Mathematikunterricht, 1 [Mathematics Lesson], 40-53.
 
10.
Hemphill, J. F. (2003). Interpreting the magnitudes of correlation coefficients. American Psychologist, 58, 79-79. https://doi.org/10.1037/0003-0....
 
11.
Hidi, S. (1990). Interest and its contribution as a mental resource for learning. Review of Educational Research, 60, 549-571. https://doi.org/10.2307/117050....
 
12.
Hoffmann, L., Häußler, P., & Lehrke, M. (1998). Die IPN-Interessensstudie [The IPN interest study]. IPN. https://archiv.ipn.uni-kiel.de....
 
13.
Kirsch, A. (1965). Über die enaktive Repräsentation von Abbildungen, insbesondere Permutationen [About the enactive representation of maps, particularly permutations]. Didaktik der Mathematik [Ddidactics of Mathematics], 3, 169-194.
 
14.
Kutner, M. H., Nachtsheim, C. J., & Neter, J. (2004). Applied linear regression models. McGraw-Hill.
 
15.
Larsen, S. (2013a). A local instructional theory for the guided reinvention of the group and isomorphism concepts. The Journal of Mathematical Behaviour, 32, 712-725. https://doi.org/10.1016/j.jmat....
 
16.
Larsen, S. (2013b). A local instructional theory for the guided reinvention of the quotient group concept. The Journal of Mathematical Behaviour, 32, 726-742. https://doi.org/10.1016/j.jmat....
 
17.
Larsen, S. (2018). Struggling to disentangle the associative and commutative properties. For the Learning of Mathematics, 30, 37-42.
 
18.
Lee, Y., & Heid, M. K. (2018). Developing a structural perspective and its role in connecting school algebra and abstract algebra: A factorization example. In N. Wasserman (Eds.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 291-318). Springer. https://doi.org/10.1007/978-3-....
 
19.
Melhuish, K. (2015). The design and validation of a group theory concept inventory [PhD thesis, Portland State University].
 
20.
Melhuish, K. (2019). The group theory concept assessment: A tool for measuring conceptual understanding in introductory group theory. International Journal of Research in Undergraduate Mathematics Education, 5, 359-393. https://doi.org/10.1007/s40753....
 
21.
Melhuish, K., & Fagan, J. (2018). Connecting the group theory concept assessment to core concepts at the secondary level. In N. Wasserman (Eds.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 19-45). Springer. https://doi.org/10.1007/978-3-....
 
22.
Michael, J. R. (1983). The stabilized probability plot. Biometrika, 70(1), 11-17. https://doi.org/10.1093/biomet....
 
23.
Pawek, C. (2009). Schülerlabore als interessensfördernde außerschulische Lernumgebungen für Schülerinnen und Schüler aus der Mittel-und Oberstufe [Student labs as interest-promoting out-of-school learning environments for middle and high school students] [PhD thesis, Christian-Albrecht-University Kiel].
 
24.
Pramasdyahsari, A. S., Setyawati, R. D., & Albab, I. U. (2020). How group theory and school mathematics are connected: An identification of mathematics in-service teachers. Journal of Physics Conference Series, 1663, 012068. https://doi.org/10.1088/1742-6....
 
25.
Schraw, G., Flowerday, T., & Lehman, S. (2001). Increasing situational interest in the classroom. Educational Psychology Review, 13, 211-224. https://doi.org/10.1023/A:1016....
 
26.
Steiner, H. (1966). Einfache Verknüpfungsgebilde als Vorfeld der Gruppentheorie [Simple magmas prior to group theory]. Der Mathematikunterricht [Mathematics Lesson], 2, 5-18.
 
27.
Stoetzer, M.-W. (2017). Regressionsanalyse in der empirischen Wirtschafts-und Sozialforschung–Eine nichtmathematische Einführung mit SPSS und Stata. [Regression analysis in empirical economics and social research–a non-mathematical introduction with SPSS and Strata.] Springer. https://doi.org/10.1007/978-3-....
 
28.
Suominen, A. L. (2018). Abstract algebra and secondary school mathematics connections as discussed by mathematicians and mathematics educators. In N. Wasserman (Eds.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 149-173). Springer. https://doi.org/10.1007/978-3-....
 
29.
Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory. Springer. https://doi.org/10.1007/978-1-....
 
30.
Vainikainen, M.-P., Salmi, H., & Thuneberg, H. (2015). Situational interest and learning in a science center mathematics exhibition. Journal of Research in STEM Education, 1, 15-29. https://doi.org/10.51355/jstem....
 
31.
Veith, J. M., & Bitzenbauer, P. (2022). What group theory can do for you: From Magmas to abstract thinking in school mathematics. Mathematics, 10(5), 703. https://doi.org/10.3390/math10....
 
32.
Veith, J. M., Bitzenbauer, P., & Girnat, B. (2022a). Towards describing student learning of abstract algebra: Insights into learners’ cognitive processes from an acceptance survey. Mathematics, 10(7), 1138. https://doi.org/10.3390/math10....
 
33.
Veith, J. M., Bitzenbauer, P., & Girnat, B. (2022b). Assessing learners’ conceptual understanding of introductory group theory using the CI²GT: Development and analysis of a concept inventory. Education Sciences, 12(6), 376. https://doi.org/10.3390/educsc....
 
34.
Veith, J. M., Bitzenbauer, P., & Girnat, B. (2022c). Exploring learning difficulties in abstract algebra: The case of group theory. Education Sciences, 12(8), 516. https://doi.org/10.3390/educsc....
 
35.
Wasserman, N. H. (2014). Introducing algebraic structures through solving equations: Vertical content knowledge for K-12 mathematics teachers. PRIMUS, 24, 191-214. https://doi.org/10.1080/105119....
 
36.
Wasserman, N. H. (2016). Abstract algebra for algebra teaching: Influencing school mathematics instruction. Canadian Journal of Science, Mathematics and Technology Education, 16, 28-47. https://doi.org/10.1080/149261....
 
37.
Wasserman, N. H. (2017). Making sense of abstract algebra: Exploring secondary teachers’ understandings of inverse functions in relation to its group structure. Mathematical Thinking and Learning, 19, 181-201. https://doi.org/10.1080/109860....
 
38.
Wasserman, N. H. (2018). Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers. Springer. https://doi.org/10.1007/978-3-....
 
39.
Weber, K., & Larsen, S. (2018). Teaching and learning group theory. In M. P. Carlson, & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 139-151). https://doi.org/10.5948/UPO978....
 
40.
Winkelmann, J. (2015). Auswirkungen auf den Fachwissenszuwachs und auf affektive Schülermerkmale durch Schüler-und Demonstrationsexperimente im Physikunterricht [Effects on subject knowledge gain and affective student characteristics of student experiments in physics classrooms], Logos Verlag.
 
41.
Zaslavsky, O., & Peled, I. (1996). Inhibiting factors in generating examples by mathematics teachers and student teachers: The case of binary operation. Journal for Research in Mathematics Education, 27, 67-78. https://doi.org/10.2307/749198.
 
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