Math for Young Kids
I have been accumulating a few stories and expressing some opinions about teaching Mathematics to young kids. I will catalog these here to keep a record of our progress.
The theme evolves as I’ve been learning more, but here are my main points in brief
- Explore what the student is interested in, not what they are “supposed to know”.
- Get interested yourself. How can you interest them if you find it boring?
- Look for the idea behind student “mistakes” and try to build those ideas up into a new kind of Mathematics. They will learn that why it was a “mistake” for the problem they were solving while feeling proud of their new creation.
- Don’t do drills unless the student wants them. At some point, they will want to master a skill, or they will just think a new idea is fun and want to play with it.
- Listen, talk, and make sure they know what you find interesting and why.
And take it all with a grain of salt. I’m learning as I go along, and you should know what free advice is worth…
Opinions About Teaching Math
Dialogs with Gunnar
These posts describe some of the more interesting conversations I’ve had with my oldest son, Gunnar.
- 4-year-old Math: discovering even and odd numbers, learning how drills can stop learning.
- Rainbow Arithmetic: doing Math with colors, not numbers to put teacher and student on a level playing field.
- Primes in Pre-K: exploring the distribution of primes before learning to multiply
- A Place Value Detour: a “mistake” in using place value leads us to discover a new number system
- This Morning’s Learning: Adding arithmetic progressions (and more).
- Spacetime Walks: Teaching I would never do intentionally — using a spacetime diagram of our walk to the library to understand fractions.
Thanks, these are great ideas. Can you give an example of the third one — building up student ideas into a new kind of math?
E.
November 30, 2008 at 7:01 pm
Never mind, I just saw the “A Place Value Detour” link above… thanks!
E.
November 30, 2008 at 7:02 pm
Glad you found it and I’m glad you found some of this interesting. I haven’t looked at this page in a long time and realize I could probably spruce it up a bit and add some more links.
I have a few other posts places where I try to to build on “mistakes” or “unusual” ideas. One of them is Rainbow Arithmetic, where I talk about my oldest boy’s idea about “adding colors” and how we built on it.
For older kids, there are some common mistakes that lead to good opportunities. When someone thinks a negative number times a negative number should be negative, you can say “OK, let’s see what happens if that’s true.” It turns out to be interesting (to me, anyway).
I guess, usually when someone thinks something they have a good reason to think it, even when they are wrong. The challenge is to try to figure out why they think what they do, and what is right about it.
Rolfe Schmidt
December 2, 2008 at 9:12 am
[...] both me and the boys. The Mathematics posts are still my favorites, especially the ones collected here and the little series about the Riemann zeta function (which I really should [...]
Changes « Rolfe Schmidt
April 7, 2009 at 11:34 am