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.
Overthinking my teaching 
I like what you say about students having an opportunity to apply and connect the ideas they are struggling to understand – especially the connection aspect – the best classroom days I have are the ones where the students connect a new idea to one they have thought or learned about in the past – that’s real learning and real mathematical conversation!
Christopher
Not really a reply to this post but more of a request for help. My school has a STEM initiative in its infant stages and our STEM director has the idea of conducting some Saturday activities to raise interest and awareness. She has asked me to help find ideas for a Saturday ‘math fun’ day for our elementary and middle school families. All of my experience is with high school and community college. Do you have some ideas or a place to steer me to find some?
Many thanks in advance!
Jim Doherty
Happy to serve. Email sent.
When I finally stumbled on the VH Levels, I remember thinking “why the hell hasn’t anyone been shoving this stuff down my throat?!” I was kind of ashamed that my math profs actually let me out the door to teach middle school and never bothered talking about the van Hieles! I don’t often drag the levels directly into conversations outside of geometry teaching, but I am constantly thinking about how brilliantly they nailed subject ignorance and growth in geometry and wish I could drag the levels around to areas outside of geometry. I don’t care how damn smart you are: when you walk through the door of a course you don’t know anything about, you’re at level zero and that’s perfectly fine. In fact, that’s good. But the teacher better be okay with that and be prepared to work with that. I bow to your student who is light years ahead of me when I was in college.