Summary: In Seeing the Graph vs. Being the Graph, Susan Gerofsky begins from the observation that students’ gestures vary noticeably when they are asked to describe mathematical graphs. This variation led her to pose two guiding questions: first, whether elicited gestures representing graphs of mathematical functions can be meaningfully categorized in ways that reflect different cognitive approaches to graphs; and second, whether these gesture categories can be qualitatively linked to students’ attentiveness to and engagement with mathematically salient features of graphs. To investigate this, students were shown graph cards one at a time and asked to describe each graph using gestures, vocal sounds, and words, while avoiding technical mathematical language. Analysis of the gestures revealed three main patterns: students who used small, precise, arm’s-length gestures—placing the graph where they could see it—tended to focus on accuracy and correctness and were identified by teachers as average students; students who used large, whole-body, metaphor-rich gestures and appeared to “be in” the graph demonstrated a more flexible approach, bringing imagination into their mathematical thinking, and were consistently identified as high-achieving students; and students whose gestures were inconsistent and failed to capture important mathematical features were identified as struggling students. Based on this alignment, Gerofsky argues that embodied, kinesthetic engagement with graphs supports deeper mathematical noticing and understanding, and therefore that traditional methods of teaching graphs should be supplemented with elicited large, close-up gestures, especially in the early stages of learning mathematical functions.
Stop 1:
I was struck by how accurately the gesture categories predicted teachers’ year-long assessments of students. That such brief, non-verbal data could reveal students’ patterns of noticing and engagement highlights gesture as a powerful diagnostic tool. This finding made me reflect on my own teaching practice, where accuracy has typically played an important role in assessment, including in the rubrics I used when marking tests. While accuracy is clearly important, Gerofsky’s work helped me see how prioritizing correctness alone may limit students’ opportunities to engage more deeply with mathematics. It also underscored the importance of teacher education, as many mathematics teachers, including myself, have been trained to value accuracy over imagination, flexibility, and embodied ways of knowing.
Stop 2:
Another moment that made me pause was Gerofsky’s observation that most mathematics teachers, including herself, use many gestures when explaining functions and graphs. This made me think about how teaching sometimes resembles a kind of performance, where the teacher’s body becomes a central explanatory tool. At the same time, I found myself wondering why I had rarely invited students to use their own gestures as a way of showing what they understood. If gesture plays such an important role in how teachers communicate mathematical ideas, Gerofsky’s work raises the question of why students’ embodied explanations are not more intentionally valued as part of learning and sense-making in mathematics classrooms.
Discussion Question: After reading this article, I wonder how teacher education can support teachers in recognizing and valuing these forms of engagement. It also raises a more fundamental question: do you think embodied and imaginative engagement with mathematics can be taught, or is it mainly shaped by individual dispositions? For example, some people may feel more comfortable with correctness and control, while others are more at ease with creativity and flexibility.
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Thank you, Amy! I completely agree with your point about how solely focusing on correctness can be limiting. I reflected on this and realized that it is especially evident for younger students or those at an early stage of learning math. At this stage, students are still building their own unique ways to understand and express mathematical ideas. If teachers focus too much on correctness—such as the numeric answer, the most efficient method, or the “standard” steps expected on tests—it trains students to approach math only as a way to complete assessments. This creates a barrier that prevents them from thinking deeply and developing mathematical reasoning. Later on, students who learn math in such an environment are more likely to stick to safe approaches and remain in their comfort zone, which limits their creativity and ability to innovate.
ReplyDeleteRegarding your question, I think students’ personalities play an important role. Some students may feel uncomfortable making big gestures in front of others, while others might enjoy it. Beyond that, I don’t think gestures can be systematically trained in an efficient way. Based on the article’s findings, I personally believe that students who use big gestures do so because they already understand the math content and feel confident presenting it through large movements. In other words, they use big gestures because they are good at math, not the other way around. Gestures might help reinforce certain mathematical procedures, but they cannot be forced on the format.
Hi Amy, thanks for your summary and reflection. I had never considered how the use of gestures in our teaching might be one-directional. Embodiment has historically not been valued in traditional education, particularly in classrooms where students are confined to small desk spaces and taught to remain within their “personal bubble.” In these contexts, students’ physical movement is restricted. While I recognize that I cannot change the walls, floors, or ceilings of a traditional classroom, I find myself wondering how I might rearrange desks or alter the orientation of the space to better invite and elicit embodied learning experiences.
ReplyDeleteIn response to your question, I do think that some learners may prefer modes of learning that are less embodied. However, from my understanding, scholars in embodied learning view embodiment as an additional tool rather than a replacement for other approaches. Similar to how pre-service teachers learn pedagogical tools such as wait time or classroom management strategies, embodied pedagogy can be understood as another tool in the teaching toolkit. I do not think it should be the only tool, nor do I think that teachers who learn about embodied pedagogy must adopt it as their own preferred learning style. Rather, recent work in this field raises awareness that some students learn more effectively through movement, and that teachers should be aware of and equipped with strategies to support diverse learners.
Even Gardner’s theory of multiple intelligences (which is a conversation in itself) leans toward this idea, with bodily–kinesthetic intelligence offering another way to name learners who benefit from embodied engagement. In many ways, bodily movement has already been part of pedagogy—we have just been talking about it under a different name.