丁香园AV

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 鈥溾�� (2024), mathematical reasoning should consider social and political aspects that shape our world. By extending socioscienti铿乧 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鈥� deliberations and judgements as they work with a pressing social problem: fairness in elections. To conceptualize how 鈥渟ociomathematical reasoning鈥� informs mathematical education, Dr. Chorney and his team examined undergraduate students鈥� 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 鈥渋nterwoven with students鈥� own opinions and stances as well as mixing with contextual factors that led to an overall comprehensive awareness,鈥� including empathy and ethical concerns. In this case, the students鈥� reasoning 鈥渨as not separate from their own personal feelings or sense of fairness.鈥�

Another pathway toward teaching and learning mathematical reasoning is scriptwriting. , 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 丁香园AV Faculty of Education professor Dr. Rina Zazkis, building on initial collaboration with Dr. Nathalie Sinclair and Dr. Peter Liljedahl, serves 鈥渢he dual function. . . of helping prospective teachers prepare for instruction as well as serving as a diagnostic tool in teacher education.鈥�

This study explores how the 鈥渕oves鈥� prospective teachers employ in their scriptwriting tasks provide a deeper understanding of how and why these teachers plan to support students鈥� 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 鈥渃onceptual understanding.鈥� 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 鈥溾�� (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鈥� concept of the lesson play鈥攐riginally 鈥渁 more robust鈥� form of preparing for instruction where teachers anticipated when they would need to respond to students鈥攊nto creating a 鈥渉ypothetical mathematical dialogue that is already underway.鈥�

Surveying a number of studies using scripting tasks for teaching mathematics, this article shows how scriptwriting can help teachers 鈥渆nvision interactions with students on a mathematical issue.鈥� 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 鈥渟trengthen the link鈥� 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 鈥溾�� (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 鈥渆ntangled and expanded complexity of sensing鈥� can play a role in mathematical learning.

It might be possible, the authors suggest, 鈥渢o ponder whether the fingers think, organize, and solve when they are employed in multiplication via a mathematical tool.鈥� With that in mind, this study focuses on how digital technology鈥攑articularly exploring students鈥� reenactments of their experiences with the iPad multiplication application designed to aestheticize mathematics鈥攎akes math learning 鈥渁vailable to the senses through visual, gestural, and tactile interactions.鈥� As a self-described political project, this approach not only challenges conventional notions of the senses but enables learners to 鈥渞egister or be affected by mathematics and for their sensing to become a knowing鈥攁 making sense鈥攐f mathematics.鈥�

References:

Chorney, S., Evans, K. R., & Staples, M. (2024). Conceptualizing reasoning practices in the context of sociomathematical issues. Journal of Mathematical Behavior 73, 101124.

G眉ne艧, C., Paton, K., & Sinclair, N. (2024). The sensory politics of mathematics: aestheticizing multiplication. Educational Studies in Mathematics 117, 239鈥�261.

Kercher, A., & Zazkis, R. Scriptwriting as a catalyst for linking undergraduate and school mathematics. Recherches en Didactique des Mathematiques. In press. hal-04733152.

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鈥�440.