 Oct 2015

newclasses.nyu.edu newclasses.nyu.edu

Although Ms. Barry was not Samantha’s 6thgrade teacher, she was aware of the curriculum Samantha had had, and had also had Samantha in her homeroom that year. Drawing on this shared history, Ms. Barry continues to hold her pointing gesture toward the Shadow Fractions photograph while looking at Samantha. Sustaining the pointing gesture while referencing the previous year’s curriculum, Ms. Barry’s multimodal utterance keeps present together yesterday’s exhibit experience with last year’s classroom treatment of slope. Nodding, Samantha confirms that she remembers covering the topic of slope in the previous year.
I think this gets very tricky when thinking about 'nodding' as a physical cue to demonstrate understanding. As a teacher, I feel like often times this is not a valid way to demonstrate understanding.

As the 5thgraders walk handsalong the edges of textbooksor thesmart board, pop off shoes to size up the teacher’s desk, and liedown on the floor to measure the room’s width in units of body length, the bodybased design of Math Moves!again mixes with and transforms the classroom space
Spatial features learned and understood through the use of body parts and related elements to measure. This is particularly relevant for students to understand the need for "standardized" measurement tools and units, as they will probably be able to experience the differences of measuring with A's feet or B's feet.

the exhibit invites visitors to use body parts to measure and compare different dimensions of its three chairs
An opportunity to understand the meaning of foot/feet in the imperial measure system

While the hand version of “Whole and Half” initially drives the students out of their assigned desksand into the classroom’s edges, it is the game’s wholebody variation that most clearly impinges on the microgeography of the classroom
The realization of space to move and limitations/features of different movements (hands vs walking) are also intertwined with the practicing of fractions and ratios

On the one hand, these moments often had an explicit quality in which exact definitions and formulas were clarified in relation to specific exhibit features. At the same time, far from being planned in advance, review of classroom definitions and formulas was almost always sparked by students’ happenstance noticing and questioning.
This seems like a struggle between trying to make it more 'school math' friendly, and trying to make it an organic experience.

I interpret her gesture as both interactional and experiential. It is interactional in the sense that it produces a depiction of the cup and saucer for and available to Ms. Barry. It is visible embodied conduct, the aspect of gesture that has historically received the greatest attention in naturalistic studies of human interaction (Streeck, 2013). And yet, alongside the semiotic valence of Samantha’s tracing gesture, there is a lived sensory dimension, a proprioceptive and kinesthetic reemergence of the feeling of drawing the cup and saucer. This felt quality is a kind of multisensory reverberation that participates, I suggest, in the experience of interrelating Sensing Ratios with school mathematics. Considering Sensing ratios in relation to school math evokes for Samantha a felt resonance with the act of drawing the cup and saucer
The author suggests that by using embodied cognition she is not only seeing the saucer and cup as having resonance to school math through her experience, but she is able to translate that experience to someone else through this physical interactions.

n a way, the chairs are much less chairs than they are, in Heideggerian language, present at hand (Heidegger, 1962/1927). Meanwhile, embodied activity and experience work fluently in the background, positioned largely in service of performing the practical work of measuring, writing, and communicating.
I'm having a hard time parsing out what this means. Is it that: the chairs are present for the students, but embodied activity (and cognition) works to make sense of what the chairs are for the students?

Together, Claire’s talk and gesture identify and bring the exhibit to quasipresence by evoking the aspects of it that involve listening as well as moving and feeling with the hands.
The combination of gesture and talk bring the exhibit into "quasipresence." Meaning, learning happened with the mind and the body together, not separated, and at this point in time, Claire is utilizing both to access that learning, to bring the exhibit into the room (quasipresence)

As Claire says “the noise one?,” she curls her righthand fingers in towards her palm and moves her hand back and forth in front of her, depicting the manipulation of the exhibit’s handles
Here, Claire's bodily motions are part of her remembering the exhibit. This shows that the involvement of her body, in manipulating the exhibits handles, was part of the engaged learning process.

At the museum, she and Tilly had developed the sense that walking faster along the tracks would produce “smoother lines” instead of curves that were “squiggly.” In other words, the two experienced a perceptuomotor blending (Nemirovsky, Kelton, & Rhodehamel, 2013; see also Section 2.4) of enacting swift movements with seeing smooth lines.
The "perceptuomotor blending" mentioned here is an example of how Kelton links body motion with learning. In this case, the students are immediately perceiving how their bodily motion changes the graph; this perception provides immediate feedback, enhancing their understanding of how the line worked; however, as this vignette indicates, we cannot assume the learning will fit directly into the boundaries of "school math learning"

n the process, settled measurement as an impersonal (i.e. reliable) mode of quantifying objectsis interrupted withimprovisatory, autobiographical acts of reimagining (“like I’m the king,” “like I’m playing with my dolls”) and remembering(“like I’m in preschool again”)selves in relation to scale. Valueneutral ordering is juxtaposedwith allusions to material (“the best”) and social hierarchies (“like I’m the king”).
Embodied measurement allows the space for a values judgement, where measuring with an objective tool is just a number on a piece of paper.
This makes me think of furniture shopping. I know that the couch might fit in my living room, but I can't decide if the size/shape is actually "right" until I see it in place.

the multisensory, interactive, and materialsrich design of the exhibits tacitly proposes a more material ontology of mathematical objects and a fleshier epistemology of mathematical knowledge. Math Moves!tells the visitor a story in which mathematics inheres in tangible objects and events while mathematical knowing happens in hands and feet just as much as in the head.
This makes total sense in the embodied world of this exhibit (and of science centers/children's museums in general), but I wonder if "presenting a more material ontology" of other subjects also creates a "fleshier epistemology"?
Do students who visit living history museums to "cook like the colonists" come away with a similar feeling of history being alive in their life (or at least relevant)? What about humansized prairie dog colonies that are common at zoos  are the kids who play in them more concerned about conservation because of this experience?
I would (unscientifically) argue that these kind of exhibits do work to engender these kinds of feelings (dare I say identification?) in the participants  but what are the conditions where a simulation can become reality?

Ms. Collins has urgedthem to forgo standard measurement toolsin favor of using their bodies alone to hunt downtheobjects. She has explained that they may not have these kinds of tools when they are at the science museum, saying, “I want you to be able to use what you have with you, and that would be your body.”
I think this idea of using the body as a tool is really fascinating. I think this method of teaching and use of the body is to help students realize they can do math without traditional toolstoo many people think they can't do math without a calculator, etc. Ms. Collins is teaching her students they can do math with what they've gottheir bodies.

“Same thingwith math strategies you know. So many different ways to get to the mountaintop.
For me this is one of the key arguments in favor of incorporating kinesthetic teaching methods, as well as other varying methods. There are many different styles of learners and traditional notetaking and worksheet teaching methods only caters to one, very specific (and not even that common) type of learner. A good lesson should cater to as many different types of learning styles as possible.

the very embodied modalities (e.g. spinning wheels and walking) and materialities (e.g. shadows and stuff) of Math Moves! wereunexpected contexts for the mathematical objects of fractions and ratios
Here we can see how math is perceived as only existing in a certain way, and that there is no room for variation. Math Moves! show that math can exist in everyday, natural ways.

It asks,and prompts its visitors to ask,“What counts as mathematics?”
Really appreciating that this is where the "desettling" argument ended up. That is not just another way to teach or to learn the same old mathematics that we've been doing, but that it shakes math to its core and asks what else is math? How might we know? How might we interact with it? And these are all questions about learning that might be best answered with our bodies, our experiences, etc. Awesome

I have increasingly come to view Math Moves! as a practice of desettling tacit mindbody dualist assumptions that narrowly delimit mathematical sensemaking
I see Kelton's argument about bodies and learning to be two fold, first that embodied learning is a valid and important activity for the math classroom  and tied to that is that examples of embodied learning push on what she considers out of date and incorrect ideas about mathematics being something without culture and "bodiless"

Motivated by the conjecture that even the most apparently abstract mathematical concepts are ultimately understood in terms of concrete bodybased experience
This is an important point, that it isn't just the things that are obviously appropriate for the body (E.g., measuring) that count for learning with embodied experience, but that even the seemingly most abstract ideas boil down to "bodybased" experiences. (And Kelton says a little later on that not only can they be embodied, but they should be  to challenge the traditional disembodied notion of math).

Math Moves!is not so muchan alternative way to the mountaintopas it is a proposal to reenvisionthe landscape itself. Through itsbodybased and materialsrich design,the exhibition stages a confrontation withlongstanding disembodied and immaterial philosophies of mathematics
Math Moves! and embodied learning not as "just another path to the same destination" but a reenvisioning of the destination itself. It supports seeing learning math, and learning in general, as affected by the body if engaged.

mapping each of these to a specific exhibit in Math Moves!.
I think this points to one of Kelton's ideas about the connection of bodies and learning, that you can call on past shared experiences of bodily movement and exploration in meaningful ways after the experience is over and the students' physical location is different.

Ms. Collins has urgedthem to forgo standard measurement toolsin favor of using their bodies alone to hunt downtheobjects.
I really like this idea of putting aside "standard" tools and using bodies instead. Using what they have naturally supports reasoning about the space around them in a new way and it validates their embodied experiences as legitimate tools for understanding and reasoning.

The exhibition’s emphasis on somatic experience and wholebody movement layers incongruously over the classroomenvironment,built for quite a different suite of activities.
The teacher's effort to bring the museum into the classroom highlights ways in which the classroom is not designed for embodied learning.

Players can vary the game by alternating whether Whole or Half takes the lead, or experimenting with different fractions. Another version of the game played during the North Lake preparation activities involves wholebody ambulation; as Whole walks some trajectory through the classroom, Half responds by walking that same path at half the speed. Again, this version of the game can be modifiedto include different speed relationships and variations in leadership
The "whole half" game makes the students' bodies part of the effort of understanding ratio relationships. Not only are their bodies involved, but the coordination of more than one body is necessary to correctly exhibit what the whole and what the half is. Learning is happening with whole bodies, actions by bodies, and coordination of bodies.
