Innovative Pathways to Mathematics Education
Mathematics education is evolving in exciting and unexpected ways, pushing beyond traditional boundaries into social, creative, and sensory dimensions of learning. This month’s featured articles showcase diverse approaches, from exploring sociopolitical reasoning to creative teaching practices and sensory engagement, redefining what it means to learn and teach mathematics. Notably, the recent publications of SFU Mathematics Education faculty members exemplify and strengthen international collaborations, as well as contribute to developing the new generation of scholars by co-authoring papers with postdoctoral fellows and graduate students.
Some of the most innovative research in mathematics education argues for extending teaching and learning into human realms, including social contexts, emotions, creativity, and even physical sensation. According to Dr. Sean Chorney and co-authors of “Conceptualizing Reasoning Practices in the Context of Sociomathematical Issues” (2024), mathematical reasoning should consider social and political aspects that shape our world. By extending socioscientific reasoning (SSI) to mathematics education, mathematics teachers can connect learning with a social issue.
In this study, the SSI framework provides insight into how mathematics may inform students’ deliberations and judgements as they work with a pressing social problem: fairness in elections. To conceptualize how “sociomathematical reasoning” informs mathematical education, Dr. Chorney and his team examined undergraduate students’ notions about creating fair maps for elections and their justifications for why particular redistricting proposals are, or are not, fair. The findings suggest that mathematical reasons were “interwoven with students’ own opinions and stances as well as mixing with contextual factors that led to an overall comprehensive awareness,” including empathy and ethical concerns. In this case, the students’ reasoning “was not separate from their own personal feelings or sense of fairness.”
Another pathway toward teaching and learning mathematical reasoning is scriptwriting. This 2023 article, co-authored by Dr. Peter Liljedahl in The Journal of Mathematics Teacher Education, describes using scriptwriting as part of a classroom simulation. Offering an extensive literature review surveying student mathematical reasoning and the role teachers play in developing this competency, the paper details how scriptwriting, as envisioned and developed by SFU Faculty of Education professor Dr. Rina Zazkis, building on initial collaboration with Dr. Nathalie Sinclair and Dr. Peter Liljedahl, serves “the dual function. . . of helping prospective teachers prepare for instruction as well as serving as a diagnostic tool in teacher education.”
This study explores how the “moves” prospective teachers employ in their scriptwriting tasks provide a deeper understanding of how and why these teachers plan to support students’ mathematical reasoning. Based on a fictional classroom-level task requiring teachers to justify their response to solving a multiplication problem, the scripts include writing a dialogue among three students working on the problem and then completing the dialogue as if they were the teacher responding. Analysis of the simulation indicated the teachers tended to move students down a specific path with leading questions rather than focusing on “conceptual understanding.” This insight underscores how scriptwriting as a methodology offers opportunities to consider the various moves prospective teachers envision for classroom interaction before they face actual students.
In fact, scriptwriting has a rich history of use in mathematics education, as Dr. Rina Zazkis and co-author Dr. Andrew Kercher explain in “Scriptwriting as a Catalyst for Linking Undergraduate and School Mathematics” (in press). Their focus here, however, is on the benefits for mathematics teacher educators of using scripting tasks to prepare their student teachers. Student-written scripts extend Dr. Zazkis’ concept of the lesson play—originally “a more robust” form of preparing for instruction where teachers anticipated when they would need to respond to students—into creating a “hypothetical mathematical dialogue that is already underway.”
Surveying a number of studies using scripting tasks for teaching mathematics, this article shows how scriptwriting can help teachers “envision interactions with students on a mathematical issue.” As the authors suggest, this creative envisioning can lead to follow-up instruction that addresses a need to narrow the gap between undergraduate and school mathematics and “strengthen the link” between them.
A different pathway into the human realm leads to understanding how sensory-motor experience can inform mathematics thinking and learning. Dr. Nathalie Sinclair and co-authors of “The Sensory Politics of Mathematics: Aestheticizing Multiplication” (2024) acknowledge growing interest in this topic and propose expanding our understanding of sensory experience. To this end, they extensively survey Western and non-Western conceptions of the senses to draw our attention to how an “entangled and expanded complexity of sensing” can play a role in mathematical learning.
It might be possible, the authors suggest, “to ponder whether the fingers think, organize, and solve when they are employed in multiplication via a mathematical tool.” With that in mind, this study focuses on how digital technology—particularly exploring students’ reenactments of their experiences with the iPad multiplication application TouchTimes designed to aestheticize mathematics—makes math learning “available to the senses through visual, gestural, and tactile interactions.” As a self-described political project, this approach not only challenges conventional notions of the senses but enables learners to “register or be affected by mathematics and for their sensing to become a knowing—a making sense—of mathematics.”
References:
Chorney, S., Evans, K. R., & Staples, M. (2024). Conceptualizing reasoning practices in the context of sociomathematical issues. Journal of Mathematical Behavior 73, 101124. https://www.sciencedirect.com/science/article/abs/pii/S0732312324000014
Güneş, C., Paton, K., & Sinclair, N. (2024). The sensory politics of mathematics: aestheticizing multiplication. Educational Studies in Mathematics 117, 239–261. https://doi.org/10.1007/s10649-024-10326-4
Kercher, A., & Zazkis, R. Scriptwriting as a catalyst for linking undergraduate and school mathematics. Recherches en Didactique des Mathematiques. In press. hal-04733152. https://hal.science/hal-04733152v1
Shure, V., & Liljedahl, P. (2024). The use of a scriptwriting task as a window into how prospective teachers envision teacher moves for supporting student reasoning. Journal of Mathematics Teacher Education 27, 411–440. https://doi.org/10.1007/s10857-023-09570-x
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