Parent Guide to Math

How Children Learn Math

When faced with a real-world math problem, a well-trained student will be able to analyze the problem, decide the best method to use to solve it, and apply mathematical rules in order to get the answer.

To do well in math, one must be proficient in these three key areas:

concepts - an understanding of the number line and the place value system, what it means to add, multiply, break into fractions, or measure
algorithms - mathematical rules such as counting on (to solve 7 + 2, start with 7 then count twice: 8, 9), how to divide fractions, or when multiplying by 10, add a zero
problem solving - comprehending what a math question means and deciding which concepts and algorithms apply

Mathematical learning starts with concepts. To learn how numbers and shapes work, students must have many experiences with actual materials to count or to measure. When they have learned a particular concept, they will be ready for algorithms, equations, pencil and paper work, and basic fact memorization. Throughout the process, they must encounter real-world problems so that they will know which tools to use in any given situation.

Here is a third grade example. "A farmer wants a rectangular pigpen with an area of 72 square feet. One edge of the pigpen is 8 feet long. What is the perimeter of the pigpen?

Using problem solving, a well-trained student will recognize that this is a two-step problem in which she needs to find the missing side length first. She will first draw and label a rectangle. Then using the algorithm for area, A = L x W, she will use 72 = 8 x ? to find the missing side length of 9. She will use the algorithm for perimeter P = 2L + 2W to calculate P = (2 x 9) + (2 x 8) to get the answer of 34 feet.

Helping Your Child With Math

If your child doesn’t know how to approach a problem:

Ask them to read and explain the math problem or activity to you.
Make sure they understand the meaning of the problem.
Brainstorm some ways that they could solve the problem.
Ask them to make a drawing to represent the problem.

If the child needs help with addition, subtraction, multiplication, or division facts:

At beginning levels, give them pennies or counters to simulate the problem. There are 5 rows of 3 pennies, let’s count by 3s: 3, 6, 9, 12, 15, so five times three is 15.”
At intermediate levels, ask them to use an equation that they know to help them solve the problem: "You know what 6 x 6 is, so to get 7 x 6, all you do is add another 6, right?"
At advanced levels, ask them to generalize and discover rules about the basic facts: "Look at the square numbers: 1, 4, 9, 16, 25, 36, 49. What do you notice about the differences between the successive square numbers?"

Typical Third-Grade Math Sequence

August - introduction to multiplication
September - multiplication, division
October - time, measurement, rounding
November - multiple-digit addition, subtraction
December - multiplication and area
January - area
February - fractions
March - fractions, graphing
April - geometry, perimeter
May - perimeter and area

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