Last summer I wrote an essay about how feedback and the math that visual pattern problems can help students learn.
Looking back, I don’t think this essay ever worked entirely, as a piece of writing.As my initial excitement about the piece soured, I never got around to giving it the big edit that it needed. Still, there are some good ideas in there that it helped me to figure out.
Here’s the essay: On Visual Patterns and Feedback
Here’s an excerpt:
I knew what I wanted to help Toni see. She was looking for a pattern in the growth, but she was having trouble getting specific about it. I wanted to ask a question that would draw Toni’s attention to helpful features of the pattern’s growth and help her get specific about precisely how this shape is changing.
This would involve a bit of guessing on my part, though, since I didn’t really know what question would work!
My first question was a promising dud: “Can you see the previous step in the following step?”
To which Toni responded, “no.”
I tried again, this time directing her attention more directly: “Do you see the second picture in the third? Imagine that you were building the third picture from the second. Where would you put the extra bricks?”
Bingo. She grabbed her pencil and started sketching.
Why did that question work? I think it’s because it encouraged Toni to see the static picture on the page as a changing thing. Toni had lots of experience playing with blocks and adding on parts to existing doodles. By asking her to think of one picture in the next, I helped direct her thinking to this analogy, and she was able to see the pattern’s growth in a useful way that related to things she had lots of experience with.
Like I said, an interesting failure. Enjoy! Let me know if you find parts of this useful.