The staff at our school is working on making kids better mathematicians by teaching them to reflect on their processes.
In one Grade 1 class, the teacher gave the children a simple exercise: you have 8 goldfish to distribute into 3 bowls. Draw them in the bowls. The children had to say how they knew they had eight, i.e. how do you know your answer is right? The teacher shared them in the staffroom, because the answers (which she scribed onto their pages) were fascinating.
- Some children, even being given eight actual goldfish crackers to use, ended up drawing far more than eight fish in their bowls.
- One child had the right answer, but when asked, “How do you know your answer is right?” wanted to change it to something incorrect. Poor guy.
- Some said, “Because I counted them.” Good answer.
- Someone said, “Because I know 3 + 3 + 3 equals 9, so 3 + 3 + 2 must equal 8.” Wow!
- Another child said, “Because I made a pattern: 3, 2, 3.” Creative.
- Another child said, “Because I was thinking in the imagination station today that we can’t go up the hill.” (???)
- Another child said, “Because I looked at Melissa’s and that’s how she did it. I think it’s right.” Ah, honesty.