Reading: Berezovski, Cheng & Damiano (2016). Spinning Arms in Motion: Exploring Mathematics within the Art of Figure Skating.
Summary:
This reading emphasizes mathematical modeling as a key goal in mathematics education, in which students apply their knowledge to real-world scenarios and phenomena. The authors highlight the importance of incorporating contexts that may be meaningful and engaging for students, such as art and sport; in this paper they focus specifically on singles figure skating spins. Two workshops are introduced: one designed for elementary and middle school pre-service teachers, and another for high school pre-service teachers. In both workshops, students analyze a diagram of a figure skater during a spin that includes relevant angles and lengths.
The authors note that this represents a simplified version of a complex real-world system, as the model focuses primarily on one arm motion rather than full-body movement, demonstrating best practices in mathematical modeling instruction. Using both the diagram and dynamic geometry software that depicts the changing positions of the upper and lower arms during the spin, students are asked to respond to a series of mathematical questions. This approach allows students to engage with a more accurate, dynamic representation of motion, rather than relying solely on a static two-dimensional model that fails to capture movement over time. Overall, the paper illustrates how teachers can design meaningful models and contexts that draw on students’ interests and experiences, while integrating mathematics with artistic forms such as figure skating.
Stops
1) “Mathematical modeling is recognized as an important content area to be learned in school mathematics. Students are expected to apply their knowledge of mathematics to different real-life situations and solve real-life phenomena” (p. 625).
This quotation really stood out to me in this paper (even though it’s the first sentence!!) because I strongly believe it captures the foundation of meaningful mathematical and scientific learning. Modelling helps students visualize processes while also recognizing the importance behind what they are learning, shifting schooling away from rote memorization and toward understanding real-world phenomena. Through the incorporation of modelling, embodied or multimodal approaches can also be integrated into classroom practices as well, allowing instruction to become more accessible for students may not thrive under traditional methods. By using modelling regularly, we can move away from viewing it as a form of enrichment and instead recognize it as a necessary component of authentic learning.
2) “Usiskin [4] has advocated simplifying complex real-life problems for the purposes of mathematical modeling in the school curriculum. Consistent with this suggestion, we focus on the motion of one particular body part, the arms. Also for simplicity, we ignore the additional distance traveled by the rotation of the skater’s body” (p. 625).
This quote stood out to me because it directly addresses one of the reasons teachers may be hesitant to incorporate modelling into their practice. I have heard other educators suggest that using real-world contexts would be “too complicated”, and I recognize that I have likely been guilty of this thinking myself. By giving ourselves permission to simplify complex scenarios or focus on only certain components of them, we are still able to integrate students’ contexts and experiences with meaningful mathematical representations, standards, and competencies. This reframing helps make modelling more manageable and realistic within typical classroom constraints.
Questions:
1) What are some potential limitations or hesitations teachers may have to incorporating modelling into classroom practices?
2) How might teachers design modelling activities in ways that are accessible and intelligible to all students with different personal contexts and lived experiences?
Hi Sarah, thank you for your thoughtful response and questions. I agree that mathematical modelling should ideally be foundational rather than treated as enrichment. At the same time, drawing on my own teaching experience, I’ve noticed that many students struggle to grasp underlying concepts before being asked to apply them to real-world contexts. I remember my head teacher emphasizing that modelling should be reserved for students who were already confident with the mathematics, which reflects a common concern in secondary classrooms, even though I don’t fully agree with this approach. While some students readily extend their understanding through modelling, others can feel overwhelmed by the added complexity. That said, your response made me reflect on the possibility that modelling itself can be a way into understanding concepts rather than something that must come after, which connects directly to your second question.
ReplyDeleteHow this is done would depend on the specific concept being taught, but in general, I think teachers can make modelling more accessible by focusing on sense-making rather than producing a single “correct” model. One way to do this is by offering multiple entry points through different representations, such as visual, physical, graphical, or verbal approaches, so that students are not excluded simply because they struggle with one particular mode of representation. In this way, students may feel less afraid to explore, to be wrong, or to be playful with mathematics (which connects to my reflection from this week’s reading), and begin to see modelling as legitimate mathematical work rather than an added burden.
Hi Sarah, thank you for sharing these reflections, especially how you described the concern regarding connecting real-world contexts to learning in a way that's not simply enrichment. This also connects to Amy's comment, and I found it quite relevant how she talked about offering multiple entry points through different representations or languages - visual, physical, graphical, verbal, and so on.
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