Seeing the graph vs. being the graph Gesture, engagement and awareness in school mathematics
-Susan Gerofsky
This chapter discusses the gestures
employed by students in understanding mathematical graphs and the meaning
behind these gestures. The study revealed three major ways in which students
gesture graphs: seeing the graph at arm’s length, being the graph by using the
whole body, and having difficulty in identifying significant parts of the
graph. Students who used whole-body gestures demonstrated high levels of
comprehension and creativity, whereas students who used precise gestures
demonstrated high levels of accuracy but less meaning. The research suggests
that encouraging students to physically “be the graph” can improve engagement
and understanding in mathematics learning.
Stop 1
Being the graph in a fully-embodied way fosters engagement and attentiveness far more than merely seeing the graph.(p.254)
I paused on this quote, as it made me think deeply about my own experience with teaching and learning. When I began my teaching career, my attention in the classroom was mainly on teaching and covering the curriculum.The use of gestures in teaching occurred to me in terms of explaining graphs, but it never occurred to me to use gestures in teaching, let alone use them as a method in teaching. I often wonder why we do not think about or intentionally add gestures while teaching, even though they are simple and natural. This reading reminded me of the graph activity with Susan, which was very engaging and educational. That activity helped me understand how simple gestures and embodiment can make a huge difference in learning, especially for a topic like graphs, which I never thought could be taught in this way.
Stop 2
Gestures produced by mathematics teachers and learners provide a rich source of data, comparable in scope to that provided by language, which can be read in terms of bodily metaphors, object development in the formation of mathematical concepts, and the relationships among mathematical concepts.(p.245)
I paused on this quote as it
challenged me to think about how understanding is typically assessed within
mathematics. We know that understanding within mathematics is often assessed
through oral or written means, but the quote indicates that gestures can also
hold equal meaning. It challenged me to reflect on how often students understand
a concept, yet struggle with expressing it verbally, all while the gestures
have demonstrated understanding. It also led me to question what it means for
educators. If gestures have equal meaning as words, why do we as educators not
incorporate or emphasize them within our classrooms?
Discussion Question
Some students may feel
uncomfortable using large or expressive gestures due to cultural norms,
personality, or classroom climate. How can teachers create inclusive
environments where embodied learning feels safe and accessible to all students?
Hi Rosmy,
ReplyDeleteI read your summary, and your discussion question has given me a lot to think about, especially since I've been involved in research on gestures for a while. I believe that when creating an inclusive classroom, it's essential to consider the varied personalities of our students. Coming from Nigeria, a country with over 250 ethnic groups and multiple religions like Christianity, Islam, and traditional beliefs, I understand how easily misunderstandings can arise if a teacher is not discerning.
In my view, learning through gestures can take many forms—whether it’s pointing, tracing, using manipulatives, or involving the whole body. While some Christians might not attach significance to whole-body activities, others may have reservations. For example, a Muslim girl who wears a hijab is expected to cover her body as a sign of respect to her husband and Allah, which is a principle taught from an early age.
I believe that while we strive to make mathematics engaging through scaffolding, we must also respect our students' boundaries and encourage them to participate at their comfort level. Additionally, we have students who may be shy or struggle with low self-esteem regarding their bodies. It’s essential to create a safe environment where they can express themselves freely. Setting classroom rules that prevent body shaming and discouraging side comments that could hurt others is crucial.
Moreover, we should encourage those who are less expressive to step out of their comfort zones. You never know—while teaching mathematics, you might reach a child in need of attention, contributing to their healing process. As teachers, our roles are indeed multifaceted, and it’s vital to support each of our students even if it means directing them to areas where they can get help if they feel safe to share in fostering an inclusive and nurturing classroom.
Hi Rosmy,
ReplyDeleteThank you for the summary of the article, and your thoughtful discussion question. As a student, I was very shy and awkward and would have been incredibly uncomfortable at the idea of any activity that required large movements. I also recognize that some students in classrooms may feel uncomfortable with this for religious or cultural reasons, among others.
I think there are a few strategies teachers can employ to apply gestures and movements into lessons, while also ensuring students feel safe and comfortable in the classroom:
Firstly, I think having students work in groups could be beneficial, so that the pressure students feel of "everyone looking at them" would be diminished. Additionally, if there was at least one student in each group that was comfortable with the gestures or movements, then the others in the group could benefit from watching, listening, and asking questions.
As a teacher, I also think modelling the activity can be beneficial - I find if I act a little silly in front of my students, they are more comfortable doing the same. This could also help students who are shy or socially anxious to potentially want to participate more as they feel comfortable in the classroom environment.
Finally, I think starting off with smaller gestures that students can do independently at their desks could help students begin to see the benefits of this type of learning, before moving on to incorporating larger-scale gestures or movements as well.