In our discussion the other day of whether the difference between van Hiele levels 0 and 1 is the use of official math vocabulary terms, or whether there is something more there, a student asked this (I am paraphrasing):
Is this like the CGI research, where children know things about addition and subtraction before they are taught in school?
Here’s what I love about this question:
- It demonstrates the power of having these students for a second semester;
- It demonstrates that students will—over time—make these ideas their own; if we keep at it, and build cases for the importance of the ideas in our courses, students will play with these ideas, and they will look for opportunities to apply and connect them; and
- It made me stop and think. I’m still not 100% sure whether it’s like that or not. I have something new to think about.