I'm especially interested to hear from HN readers about good methods for teaching math to children.
My son is 3, so at the moment we're just counting everything and making little groups to add them together.
My son is 3, so at the moment we're just counting everything and making little groups to add them together.
* Good questions for math teaching (http://amzn.com/0941355519)
* Young Mathematicians at Work (http://amzn.com/032500353X)
* Number Sense Routines (http://amzn.com/1571107908)
* Dr Wright's Kitchen Table Math book (there are three) - http://amzn.com/0982921128
I haven't finished these next two, but they look promising:
* Fostering Geometric Thinking (http://amzn.com/0325011486)
* Fostering Algebraic Thinking (http://amzn.com/0325001545)
I also like the approach of the Art of Problem Solving curriculum, though it doesn't currently have elementary school material. I haven't used it on my own kids yet because they're still too young, but I did buy the set and I think it looks good. If you read "Good Questions for Math Teaching" you will probably modify the way the problems are presented to make them more open-ended, but I like that topics are introduced with a problem that is later explained, instead of explaining then drilling.
http://www.artofproblemsolving.com/Store/curriculum.php
Finally, I thought that this online course was a nice introduction to the approach. It's a pretty short course, but I just put the audio on an mp3 player so I could listen while working on other things and there were only a couple of places where I couldn't tell what was happening in the video.
* https://class.stanford.edu/courses/Education/EDUC115N/How_to...
For a more general book about early childhood education, I really liked
* "Engaging Children's Minds - the Project Approach" (http://amzn.com/1567505015)
* Making Thinking Visible (http://amzn.com/047091551X)
* Learning Intelligence: Cognitive acceleration...(http://amzn.com/0335211364)
Sadly, most of these books are pretty pricey for the page count, but the material I thought was quite good. If you were to get only two, I'd say go with "Young Mathematicians at Work" and "Good Questions for Math Teaching" because they will probably give you the quickest jump start, especially if you can get the "How to Learn Math" course.
If you're interested in where my evidence for the approach outlined here comes from, my main sources are the following books:
* Effectiveness In Learning (cognitive load theory) http://amzn.com/0787977284
* Visible Learning (synthesis of 800 meta-analyses) - http://amzn.com/0415476186
Edited because I put some of them in the wrong spots and forgot links...
The only goal is to familiarize them with doing stuff with numbers. The 6yo's kindergarten class has heavy emphasis on math, so I try not to get in the way of what they are doing. I avoid confusion by just staying away from the same stuff (at first, I thought I'd reinforce, but that turned out to be a bad idea. The 6yo needs a disconnect from what's happening in school, not a reminder. It's tiring).
The one thing I can confidently say is that what works changes as they pick up more concepts, and have more influences on learning (ie, other parent, school, other kids). My kids are not especially smart or gifted. The trick is that we stay just at the border of what they can do. We try new things, which fuels their confidence when they get it. We practice old things, which fuels their confidence with little cost. We stay focused and brief.
I try to get as many information and pedagogical tricks as I can. But they only work, if they work, for brief points in time. Kid thinking changes much faster than adult thinking.
A concrete way of demonstrating this would be to point out that several same size groups of objects have something in common.