Reasoning about Rotations


I got some Sqairs to try out. Four of them. My kid wanted to play, and I wanted to figure out how these things work.

Part 1: “A circle is 100 degrees?”

In this first video, my kid put the mats together based on the design in the center when all four mats made a larger mat. Her initial exploration seems to be guided by direction of the hands on the mat.  I should say that she has had very little exposure to rotations but that her responses were still surprising to me given she seems to have good idea of what a 90 degree turn looks and feels like.

Part 2: “You said  back-to-front was half way…”

In which things get confusing and she starts making sense of it but continues to think of “the whole” as 100.

Part 3: “90 degrees is half-way of half…

…so how do we go half-way of the whole, which is 360?”

Part 4: In which understanding of rotations appears to be integrated into the body…

…but only after time, practice, and the presence of visual cues on the mats.

Normally, when I work with kids we explore rotations in the center of our Math in Your Feet square. A rotation can happen around any point, however, so each jump/turn she is doing in this final video is actually two transformations, a translation and a rotation.

In the end, this whole exploration points to the foundational need for understanding parts and wholes and units. The moving body is well positioned to explore the idea of rotations and, as she did so, we were able to clarify the necessary part/whole relationships which then seemed to lead to a big jump (literally and figuratively) in her understanding of the concept.

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