Categories

## Children and Teachers on Feedback

How do you predict that a group of students (9th Graders, Geometry, nearly all are comfortable with scaling) would respond to this prompt? Do you think they’ll disagree? Converge on one option? What reasons do you think they will bring to support their answers? Do you think that their responses will differ significantly from the responses that a group of teachers would give? If so, how?

Sheesh, that’s a lot of prompts. Let’s condense that:

1. What do you predict students will respond?
2. How do you predict that a group of teachers will respond?
3. How would you respond?
Categories

## Making up a relationship

In the library today, I tried to run a little experiment on a friend.

I told him that there was a relationship between the numbers in the circle and the numbers to the right, and I asked him to try and guess what the relationship was between the numbers at the bottom.

The catch was that I didn’t have any relationship in mind when I made this “puzzle.” Really, I wanted to see if I could get him to say, with confidence, that the answer to the puzzle was “21”.

Here was the “experiment design”:

• I used sets of three numbers, so as to not literally resemble any multiplication facts.
• In the first set, I gave three numbers whose product was easily recognizable as 16. I expect that my friend would make that connection.
• Then, I give him numbers that explicitly contradict the pattern in the first bubble.
• Finally, I made up some numbers that had very little to do with the others.
• Then, I asked him a question that was really similar to the first bubble. (Though I shifted the numbers around so that it didn’t literally match the first one.)

My friend said some really interesting things, most of which I didn’t expect.

The first thing he told me was that there was a pattern with the first and third bubbles, but not the second. He said the relationship was “multiply the top number by the bottom, and then multiply that by the number on the side.”  In other words, he was telling me that 12 times 9 was 78.  But he knew that didn’t work for the second one, so he was puzzled. After that, I pushed him to guess, and he told me that it would be 27 for the bottom set, which he quickly corrected to 21.