Matematikundervisning på universitetet
whiteboards, tilfældige grupper og problemløsningsopgaver
DOI:
https://doi.org/10.7146/dut.v20i37.143339Abstract
The university's mathematics education is typically structured around lectures with one-way communication, followed by tutorial sessions where students engage in problem-solving. This study presents an investigation in which an instructor, across two different engineering mathematics classes, experimented with new teaching practices developed by Peter Liljedahl. These practices include introducing classes with open problem-solving tasks, employing randomly selected three-person groups during instruction, and using vertical, non-permanent whiteboard surfaces during group work.
Throughout the semester, data has been systematically collected in the form of teaching observations, evaluation surveys, and instructor interviews. The results of the article illuminate various potential benefits of this approach but also identify some challenges. This contributes to a deeper understanding of the dynamics that arise during the implementation of these innovative teaching methods and their impact on both the teaching process and students' social affiliations and learning of mathematics at the university.
References
Andreassen, H. (1999). Begrundelser for matematikundervisningen i den lærde skole hhv. gymnasiet (Doctoral dissertation, Roskilde Universitetscenter, Institut for Studiet af Matematik og Fysik
Bayer, M., Plauborg, H., & Andersen, J. (2007). Aktionslæring: Læring i og af praksis. Hans Reitzels Forlag.
Bergmann, J., & Sams, A. (2012). Flip your classroom: Reach every student in every class every day. International society for technology in education.
Burdman, P., Baker, M., & Henderson, F. (2021). Charting a new course: Investigating barriers on the calculus pathway to STEM. Just Equations. justequations. org/resource/charting-a-new-course-investigating-barriers-on-the-calculuspathway-to-stem.
Duch, H. (Ed.) (2023). Gruppearbejde på ungdoms- og videregående uddannelser. Frydenlund.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Oliver, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth: Heinemann.
Ivankova, N. V. (2015). Mixed methods applications in action research. Sage
Kutnick, P., & Blatchford, P. (2014). Effective group work in primary school classrooms. Dordrecht: Springer Science & Business Media. https://doi.org/10.1007/978-94-007-6991-5
Lauridsen, E., & Dohn, N. B. (2017). Implicitte forudsætninger i gruppearbejde. Dansk Pædagogisk Tidsskrift, (1), 80-89.
Laursen, S., Andrews, T., Stains, M., Finelli, C. J., Borrego, M., McConnell, D., Johnson, E., Foote, K., Ruedi, B., & Malcom, S. (2019). Levers for change: An assessment of progress on changing STEM instruction. Washington, DC: American Association for the Advancement of Science. https://www.aaas.org/resources/levers-change-assessment-progress-changing-stem-instruction
LeSage, A., Friedlan, J., Tepylo, D., & Kay, R. (2021). Supporting at-Risk University Business Mathematics Students: Shifting the Focus to Pedagogy. International Electronic Journal of Mathematics Education, 16(2), em0635. https://doi.org/10.29333/iejme/10893
Leyva, L. A., Quea, R., Weber, K., Battey, D., & López, D. (2020). Detailing Racialized and Gendered Mechanisms of Undergraduate Precalculus and Calculus Classroom Instruction. Cognition and Instruction, 39(1), 1-34. https://doi.org/10.1080/07370008.2020.1849218
Liljedahl, P. (2014). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (eds.) Transforming Mathematics Instruction: Multiple Approaches and Practices. New York, NY: Springer. https://doi.org/10.1007/978-3-319-04993-9_8
Liljedahl, P. (2016). Building Thinking Classrooms: Conditions for Problem-Solving. In: Felmer, P., Pehkonen, E., Kilpatrick, J. (eds) Posing and Solving Mathematical Problems. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-28023-3_21
Liljedahl, P. (2019). Conditions for Supporting Problem Solving: Vertical Non-permanent Surfaces. In: Liljedahl, P., Santos-Trigo, M. (eds) Mathematical Problem Solving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-10472-6_13
Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin press.
Papert, S. (1980). Computers for children. Mindstorms: Children, computers, and powerful ideas, Basic Books, Inc Publishers.
Pruner, M., & Liljedahl, P. (2021). Collaborative problem solving in a choice-affluent environment. ZDM-Mathematics Education, 53, 753-770. https://doi.org/10.1007/s11858-021-01232-7
Reimer, D., & Andersen, I. G. (2022). Frafald fra de videregående uddannelser: Forklaringer, mekanismer og løsninger. Aalborg Universitetsforlag.
Schindler, M., & Bakker, A. (2020). Affective field during collaborative problem posing and problem solving: A case study. Educational Studies in Mathematics, 105(3), 303-324. https://doi.org/10.1007/s10649-020-09973-0
Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (Reprint). Journal of education, 196(2), 1-38. https://doi.org/10.1177/002205741619600202
Sfard, A. (2008). Thinking as communicating. Human development, the growth of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Stains, M., Harshman, J., Barker, M. K., Chasteen, S. V., Cole, R., DeChenne-Peters, S. E., ... & Young, A. M. (2018). Anatomy of STEM teaching in North American universities. Science, 359 (6383), 1468-1470. https://doi.org/10.1126/science.aap8892
Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80. https://doi.org/10.1080/1380361960020103
Syddansk Universitet (2023). Bærende principper for undervisning, https://www.sdu.dk/da/om_sdu/institutter_centre/c_unipaedagogik/baerende_principper
Yackel, E., & Rasmussen, C. (2002). Beliefs and norms in the mathematics classroom. In G.C. Leder, E Pehkonen, & G. Törner, Beliefs (Eds): A hidden variable in mathematics education? (pp. 313-330). Dordrecht: Springer Netherlands. https://doi.org/10.1007/0-306-47958-3_18
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