Abstract
In this chapter, the author reflects on his professional experiences that span more than five decades working in mathematics education as mathematics teacher and mathematics education researcher. He draws on experience from working in schools, teacher education, and a university department of mathematical sciences, latterly leading a national centre for excellence in higher education. Reflecting on this experience and engagement in mathematics teaching developmental research and supporting evidence from published sources, it is asserted that many students in higher education would enjoy improved learning experiences of mathematics if there were a transformation of teaching approaches. Framing the argument within Community of Practice Theory, the author sets out obstacles that need to be overcome if there is to be an effective collaboration and knowledge exchange between mathematics education researchers/teaching developers and mathematicians/mathematics teachers in higher education. In the second part of the chapter, consideration is given to the types of intervention in teaching approaches that might make a positive difference to students’ experiences. This begins with a brief summary of a small part of what is known about learning mathematics. Attention to two key issues in teaching is recommended, providing constructive feedback to students, and approaching teaching in a way that promotes students’ active engagement with the mathematics to be learned.
This chapter title is the vision statement of MatRIC, Centre for Research, Innovation and Coordination of Mathematics Teaching, which is the background for this reflective essay.
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Notes
- 1.
I refer to higher education mathematics teachers rather than the simpler, mathematician or mathematics researcher because many academics teaching mathematics in higher education have backgrounds in other disciplines with substantial mathematical content such as physics, engineering, or economics. Further, I refer to “teaching and teachers” as embracing practices and practitioners who may adopt a variety of instructional approaches including lecturing, mentoring, supervising, etc.
- 2.
Supporting evidence for this assertion is also emerging from the analysis of a Norwegian survey of active learning approaches used in higher education mathematics classes. The findings are yet to be published; a preliminary report from the survey is available; see Bjørkestøl et al. (2021).
- 3.
I admit that I am making an unsupportable generalisation here, and I therefore acknowledge that many HEMTs are interested to learn about, inquire into, and make sense of theories espoused by MERs.
- 4.
In the school-focused mathematics teaching development research, we referred to the university-based participants as “didacticians” because we wanted to emphasise that all participants, whether based in school or university, were researchers.
- 5.
- 6.
I want to allow one of the reviewers of this chapter to have a voice at this point. “I agree that mathematicians may not like some of the theories (I guess we all have our own preferred ones), but in my experience, they also enjoy employing them and using them as a lens. Sharing suitable theories with them enables the community to communicate and share the same language. We hope that in the future, through productive collaboration, more theories (that are tailored to our needs) would emerge from these CoPs.”
- 7.
More about “metacognition” follows below.
- 8.
This is not the place to reiterate extensive and deep philosophical arguments behind these assertions. I will simplistically add that they are based upon whether mind and cognition are purely biological products of an individual organism, or social-cultural artefacts that emerge temporarily as amalgamations of the individual and social in a particular socio-cultural context. For more on this, I refer the reader to Cobb (1994) and Lerman (1996, 2010).
- 9.
A crucial issue for teachers is how students might be motivated towards and facilitated in such critical engagement.
- 10.
There is a growing literature describing efforts to develop students’ motivation and meaningful engagement in undergraduate mathematics, especially based on the setting of non-routine projects. One good entry point to this literature is the collection of papers “Transitions in undergraduate mathematics education” (Croft et al., 2015).
- 11.
“Pain of” avoids the mixing of the metaphor of “magic pill”; however, fundamentally I believe that if the engagement is motivated by intrinsic interest, a belief in one’s own self-efficacy, and a deep approach to learning, sustained effort in learning mathematics and grappling with the challenges is not a matter of pain, it is a cause for joy!
- 12.
RUME: Research in Undergraduate Mathematics Education, a Special Interest Group of the Mathematical Association of America, holds an annual conference, http://sigmaa.maa.org/rume/Site/News.html
INDRUM: International Network for Didactics Research in University Mathematics, https://indrum2020.sciencesconf.org/
CERME: Congress of the European Society for Research in Mathematics Education (ERME) https://www.mathematik.uni-dortmund.de/~erme/ (INDRUM is a “Topic Conference” or ERME).
- 13.
- 14.
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Goodchild, S. (2023). Students Enjoying Transformed and Improved Learning Experiences of Mathematics in Higher Education. In: Stewart, S. (eds) Mathematicians' Reflections on Teaching. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-34295-0_5
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