Week 1: Mathematics and the body
My reading for the week
was a couple of excerpts from Mitch Nathan’s book titled Foundations of Embodied
Learning: A Paradigm for Education. In the introduction, Nathan uses a definition
for education that I’ve never heard before, but impressed me with its conciseness.
He says “education is basically about engineering learning experiences” (Nathan,
2022). (chef’s kiss). I found that I had to check my biases before and
throughout reading the introduction, as he came off as quite critical on the
education system as a whole. I found the second excerpt that was assigned to be
less critical, and helped me look at some of the students learning experiences
with a changed perspective, a tool that was recommended through the TED talk by
Roger Antonsen (2015).
The author speaks about
how newborns are quick to walk, to understand language, etc, while computer scientists
were much slower. I wonder if the author would reconsider this statement with
the surge of Artificial Intelligence? He also says that “professionally trained
educators are, of course, equipped with a general and content-area pedagogical methods,
but the connections of
these practices to theory is often thin and insufficient to help customize
learning experiences to the suit the range of learners, topics, and teachers
(Nathan, 2022). While I almost took offense to a statement like this (*checks
bias*), I have to admit I smirked that there was a typo in the statement.
In the chapter on
grounding and embodied learning in the conscious spectrum, the author talks
about types of grounding metaphors relating to quantities and collecting (how
humans develop the notion of two by picking up one thing in each hand),
object-construction operations (combining, removing, sharing, repeating)
arithmetic operations and measurement (using concrete objects as
referents). The chapter made me realize that even in my grade 6 class,
students seem to begin to stray away from grounding methods. What happens at
this stage in their math development? Do we put too much emphasis on
memorization of formulas, while leaving the grounding approaches behind?
The questions continue. Have
you used embodied learning in math? If so, when and how? How can we stretch the
limits of grounding metaphors to higher level learning?
The introduction to the
week provides us with an exciting blueprint of where the course will take us, to
“challenge this Platonic prejudice”. It makes me excited to learn from the
modules over the next few weeks, and how to incorporate more holistic, embodied
learning into my own math class.
Video
I have saved the video to watch again. I especially liked how the presenter
tied in the Ted talk to a lesson on empathy, and how to be empathetic by
changing our perspective. I really enjoyed seeing the different perspectives of
his fraction, and am curious about what sounds and shapes other fractions can
make.
Activity
I was able to partially
do this activity with my group of grade 6 students. We will be taking it up
again, as we didn’t have time to complete the task. I grew up learning French
as a second language, and still this activity helped me realize that the French
word for inch (pouce) is the same as the french word for thumb. When I measured
the width of my thumb, sure enough it was exactly an inch. The students enjoyed
comparing their results, as well as trying to understand the difference between
inches and centimeters. This activity is an example of what Nathan calls the
“grounding” where “Measurement…is grounded in the length of tangible things
such as sticks (Nathan, 2022)”, or in this case, parts of the body.
References:
Nathan, M. J.,
& Taylor & Francis eBooks EBA. (2022). Foundations of embodied
learning: A paradigm for education. Routledge.
Roger
Antonsen (2015 TED talk 17:04) Math is the hidden secret to understanding the
world. <https://youtu.be/ZQElzjCsl9o
Hi Pat,
ReplyDeleteI appreciated reading your thoughts on the Foundations of Embodied Learning. Throughout the courses we have taken I am starting to notice connections between ideas and terms. I am noticing that there may be multiple terms that refer to a similar idea. For example, you brought forward the idea of “grounding methods”. To me, this sound like student-centred experiential learning opportunities. We have heard lots about the power of allowing students to have choice and take autonomy by learning skills and content in meaningful ways.
I notice that most of the readings this week involved integrating gestures into mathematics education. Was this brought up in the article you read?
Hi Amanda,
DeleteThey didn't discuss gestures as much as grounding metaphors, in other words, connecting physical experiences to math concepts. In our task for example, we can now use our body to help measure other items. Like Shawn's example, he can now use his hand length to estimate the length of his shed
Hi Pat,
ReplyDeleteThanks for the digestible summary of the first reading. Engineered learning experiences sound complex and time intensive, well at least at the beginning of one’s career. I too liked the representations of the fractions. I wonder what program he used to create the Spirograph looking image. It would be nice to see other fractions, like 5/3, 6/3, 7/3, … to compare.
Have you used embodied learning in math? If so, when and how? How can we stretch the limits of grounding metaphors to higher level learning?
I’m not sure I use embodied movement to the extent or as intentioned as the researchers did in the readings. However, I’ve taught grades 2 to 12 over the past 14 years and I can loosely recall using gestures and body movement to some extent in each grade. The strongest connection I can remember is angles in grade 6. Where your head is the angle center and your arms move to make various angles. I paired the movement with the names. For example a straight angle is your arms straight out. I think my strongest connections were always from the geometry and measurement units. Whereas, other gestures were me pointing and hand circling parts of an equation while solving,with no intent other than showing students where I was looking.
Maybe one topic that could be embodied in high level math is linear functions and equations. If there was a big mat that had a cartesian plane then students could physically act out the slope and y intercept. Perhaps, in an ideal classroom for this type of learning style, teachers and students would explore how to make math concepts more embodied. Students and teachers would be used to thinking this way, trying new perspectives, and with some success finding great new ways to embody mathematics.
Thanks, Pat, for this thoughtful and interesting summary, observations and questions about the Nathan excerpts -- and thanks Amanda and Shawn for your great responses! I am also struck at Nathan's quite extreme writing about the (US) education system and his seeming lack of regard for teachers. He has taken a very oppositional stance here -- although I think he would be more respectful in person! Pat, thanks for being patient with the part that was so difficult and keeping going to the really interesting parts about grounding methods (and yes, Amanda, I think this is something very close to student-centred experiential learning, but with a focus on grounding abstract mathematical concepts in embodied work).
ReplyDeleteI'm glad you had the chance to try some of the activities with your students, and to see that a 'pouce'/ inch is pretty close to a thumb width! Shawn, I like your idea about doing linear equations in embodied ways. I've played around with this as well, using both old-fashioned Etch-a-Sketch toys, and with marking out axes on the floor and using a wheely chair... (In case you're interested, I've written about it in the CMESG Proceedings for 2006, pp. 56-75, available at https://www.cmesg.org/wp-content/uploads/2015/01/CMESG2006.pdf)