Reading:
Kelton & Ma (2018). Reconfiguring math settings
with whole-body, multi-party collaborations.
Summary:
This paper
uses two mathematics activities to "illustrate how whole-body
collaboration can transform how learners experience learning environments and
make sense of important mathematical ideas" (p.177). The first activity
focuses on developing number sense by inviting middle school students to be
part of a "series of walking number line activities. The second activity
called "whole and half" is about ratio and proportion and was developed
with elementary students.
Stop 1: naturalistic video recordings and microethinography
My first
stop was in the methodology used by the authors. I got curious about naturalistic
video recordings and microethinography:
“Microethnography
is concerned with the local and situated ecology obtaining among participants
in face-to-face interactional engagements constituting societal and historical
experience. Ethnographic microanalysis of interaction, as microethnography
is also known, aims at descriptions of how interaction is socially and
culturally organized in particular situational settings. Microethnographers
typically work with audiovisual machine recordings of naturally occurring
social encounters to investigate in minute detail what interactants do in real
time as they co-construct talk-in-interaction in everyday life” (Garcez, 1997,
p.187).
In this
sense, I was wondering if this could be an interesting methodology to analyze
how teachers make decisions while they are interacting with students and all
other events in their classrooms. I started to think if these teachers would physically
show their decisions in their body and how it these signs would look like.
Garcez,
P.M. (1997). Microethnography. In: Hornberger, N.H., Corson, D. (eds)
Encyclopedia of Language and Education. Encyclopedia of Language and Education,
vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4535-0_18
Stop 2:
My second
stop was related to the following passage:
[...] while, ontologically and epistemologically, we regard all mathematical activity to be inherently embodied and social, not all activity designs leverage the inherently embodied and social nature of mathematical thinking and learning in the same ways. The case analyses here show how deliberate designs to recruit bodies more holistically and in different modes of mutual interdependence in tum reshape the material makeup of relevant mathematical objects and operations and attendant spatial resources for and constraints on shared sense-making.
In this
sense, I re-read the whole paper trying to identify these “deliberate designs”
and how they develop the idea of “recruit bodies more holistically and in
different modes of mutual interdependence in tum reshape the material makeup of
relevant mathematical objects and operations”.
I believe the passage below (special the bold parts) may help to answer my question about what the features of this “deliberate design” are:
In both cases, the designed incorporation of learners' bodies into the activities physically and conceptually positioned learners as mathematical objects and learners' physical movements as mathematically significant operations or events. Because of this, students' repertoires of bodily movement - their possibilities for, constraints on, and histories of physical action – became resources for mathematical invention. And, as the mathematics shifted and emerged, participants differentially selected from these embodied repertoires (e.g., standing up on tip-toes to produce larger wholes or linking arms with a partner and spinning around to walk to one's opposite) to author and negotiate new mathematical practices.
In this
sense, I believe the “deliberate design” is to understand participants' “embodied
repertoires” and support them to select the embodied practices that will better
help them to understand the math concept aimed at. That led me to pose the
following questions:
Question:
1)
How do teachers identify kid’s embodied repertoires
able to support mathematics learning? and
2)
How do teachers design lessons that support kids
to make these choices about their embodied repertoire and connect to math
concepts?
I read about movement-based mathematics by authors Riley and others, which shows how physical activities led to enjoyment and learning mathematics concepts together. Similarly, I see here that the author discusses learning mathematical concepts through whole-body collaboration.
ReplyDeleteIt is true that as educators, we must keenly observe students' physical actions during mathematical tasks, recognizing the significance of their varied responses and levels of engagement. Additionally, by motivating students to reflect on their tasks, we empower them to make meaningful connections between their physical movements and mathematical ideas.
Truly incorporating hands-on activities, movement-based tasks, and various opportunities for kinesthetic learning nurtures students' ability to select and utilize embodied practices effectively. Educators can guide them to make connections between their physical actions and mathematical ideas by encouraging them to articulate their reasoning and strategies.
I remember my childhood physical activities like playing with drawing rectangular boxes on the ground and sliding a piece of stone with single leg jumps and jumping ropes. These all play and physical activities used to include mathematical concepts and provide a lot of satisfaction to the child. Astonishingly, it's the requirement of the present time that we need to include those kinds of embodied activities in today's learning experiences.
Excellent post! The consideration of teachers physically embodying their decisions raises intriguing possibilities for understanding instructional choices. Teachers identify their students' embodied repertoires by observing their movements and responses during mathematics activities. They can recognize patterns in their students' interactions during these games/activities. Teachers can create a dynamic and inclusive learning environment to support kids to make choices about their embodied repertoires and connect to mathematical concepts. A learning environment of this kind would include tasks that allow students to express their knowledge through movements and work collaboratively with each other.
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