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How to teach Math to children
- Start early and move as fast as can be absorbed.
- At least 15 minutes every weekday. Make up on weekends for days missed. No stocking up. The goal is regular exposure. Bursts and spurts are not good.
- They work on problems I assign or make up for 15 minutes. Then I check and help them solve with understanding.
Counting, Addition, Subtraction
- Count by ones to 120 or larger - first visually then from memory. Use the digits zero, one, ..., nine only. Say 'one zero' instead of ten, 'one one' instead of eleven. Distinguish between Math and English. Emphasize the generality of the number system, without exceptions all the way to infinity. You can English words for numbers when the child has confidence building up the number system.
- Introduce negative numbers as debt or loss or opposite.
- Introduce addition in everyday conversation. Use counting of fingers or sticks to solve.
- On paper do problems on big grid paper. Introduce column values in grid. Teach how to carry and how it is the same for any size number. Once the mechanics is understood add humongous numbers to give confidence.
- Introduce subtraction in every day conversation at the same time as addition. Explain the different uses of '-': subtraction vs negativeness. Use grid paper and reinforce column values.
- Introduce borrowing using grid paper. Once the mechanics is understood subtract humongous numbers to give confidence.
Multiplication
- Start counting by twos. Show how that is related to addition and times or multiplication. On grid paper, do sums vertically starting with zero and adding two again and again down the page. To the side of each sum show the multiplication associated with it.
- Repeat with threes, then fours, etc.
- At 10 and above, introduce long multiplication using grid paper. Write the product of a pair of digits on a new line in the appropriate column.
- Continue repeated adding with the same number for ever increasing number. When fluent, start the adding with a large negative number and adding the same number repeatedly until reaching a large positive result. The goal is to get familiar with sums on both sides of zero. Use multiplication and subtraction to check the final result.
Division
- Introduce division as fair sharing. Have the child distribute some item one by one around the table, making sure that everyone has a fair share and also seeing the remainder.
- As the numbers become bigger, teach long division using grid paper. Do not teach shortcuts. Show the general process repeatedly. Let the child recognize shortcuts on his/her own.
- Later introduce division for chunking. How many chunks of a certain size can I get from a big lump?
Prime Numbers and Prime Factorization
- Once division is understood. Teach prime numbers. Prime Factorization should follow naturally.
- Practice factorizing 1, 2, 3, 4 and so on until in the hundreds.
Fractions
- Fractions are for fair sharing. Emphasize the equivalence of fractions. Two apples fair shared by four people is the same as one apple fair shared by two people. And so on. Hence common factors in numerator and denominator can cancel.
- Teach addition and subtraction of fractions. Emphasize the need to make all denominators the same number. Hence show derivation of lowest common denominator for the prime factorization of all the denominators.
Workbooks
For grade 1-6, I use the Singapore Math workbooks and the problems for Mathcounts. For grade 7-8, I use the problems for Mathcounts, New Mexico Math Contest and USAMTS.
