While reading the discussion posts of my classmates, I was struck by two key points. The first was a diversity of opinion over the purpose of embodied learning in the classroom. I noticed three different proposals for why embodied learning might be important. The first proposal was that embodied learning situates mathematics in a real world context, demonstrating its usefulness and relevance to students. Personally, this argument has never been convincing to me, if only because application to the "real world" has always been the least interesting part of the discipline to me personally. I do respect that it might be valuable for a subset of students, though.
Second, some groups considered the possibility that learning math in an embodied way could lead to greater comprehension and retention of the material. While I don't have citations at my fingertips, I believe that this is something demonstrably true and think it is definitely worth keeping in mind when making decisions about where embodied learning fits in the classroom.
Finally, some groups pointed out that the act of doing these crafts and movements builds skills like noticing patterns and breaking tasks down into steps. I think the act of writing proofs is also an excellent example of a mathematical activity that is less useful for the sake of its end product and more for the mental work and training that it requires to complete.
The second key point that I mentioned, beyond assessing the purpose of embodied learning, is the critical step of reflection within an embodied mathematics process. My own group (as well as a number of others) talked at length about the possibility for exercises (embodied or otherwise) to fall flat and be non-meaningful without student reflection. I think this is especially true when the connection to mathematics is nonobvious, such as the case might be when making rope.
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