Teach Your Kid Basic Math
Teaching your kid basic math is a little more complicated than it seems. Here I go over some important learning goals and what I've tried with my own son to try to achieve them.
0:00 So... you want to teach your kid math?
0:15 Four categories of learning goals
1:35 Some important conceptual learning goals
3:14 Some important procedural learning goals
4:36 What does your kid associate math with?
5:09 Becoming a problem solver
5:48 Setting up the time and the environment
6:25 How to use examples and abstractions
7:13 Developing more sophisticated strategies
8:28 Letting them solve the problem
9:07 Developing a skeptical and thorough problem solver
9:42 Flip the asking script
10:32 Modeling how to respond to mistakes
11:41 "Secrets"
12:18 Interesting ways of incorporating number lines
12:55 Scaffolding estimation skills
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REFERENCES:
For readable summaries of the research in these areas, check out these two excellent posts by Gwen Dewar: https://parentingscience.com/preschoo... (preschool math games) and https://parentingscience.com/preschoo... (general advice). Parenting Science is just an excellent resource, generally.
On concreteness fading and the power of using both concrete and abstract representations together, see the two references below:
Fyfe, E. R., & Nathan, M. J. (2019). Making “concreteness fading” more concrete as a theory of instruction for promoting transfer. Educational Review, 71(4), 403–422. https://doi.org/10.1080/00131911.2018...
Moreno, R., Ozogul, G., & Reisslein, M. (2011). Teaching with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions. Journal of educational psychology, 103(1), 32.
On the relationship between conceptual and procedural knowledge and the role that different kinds of examples can play in developing both, see: Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529. https://dash.harvard.edu/bitstream/ha...
On the use of number lines for learning: Lin, C. H. (2022). Developing mental number line games to improve young children’s number knowledge and basic arithmetic skills. Journal of Experimental Child Psychology, 222, 105479. https://www.sciencedirect.com/science...
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