"I'm no good at math"-- "I never understood math"--- "I don't blame my kids for hating math, I never liked it either". These all-too-common plaints are to be heard among both children and adults in the United States, and they are a great worry to educators who realize that a lack of mathematical skills handicaps this country in its efforts to produce scientific leaders.
What can we do about this problem? It's not just a matter of giving more school time to math, or assigning more homework. Part of the difficulty occurs before the schools even have an opportunity to get to work. Children enter school with varying levels of ability to work with numbers. Some can't even count very well, while others know many number facts and are skilled at simple problem-solving. Some have realistic self-confidence about arithmetic, while others are convinced that they are "no good" in this area. Unfortunately, those who start behind in math do not usually catch up very effectively.
Are the early differences genetic, or do they come from experience and learning? Well, maybe there is a genetic factor, but it seems more likely that much of the individual variation comes from experiences the children had as preschoolers--- during a period of life when nobody paid much attention to instructing most children about mathematics. This suggests that shaping children's preschool experiences could help bring them to kindergarten with good number skills, and get them off to a good start for further learning about math.
Would we need elaborate, expensive, high-tech methods to improve preschoolers understanding of number? Robert Siegler, in his article "Improving the Numerical Understanding of Children from Low-Income Families" (Child Development Perspectives, 2009, Vol. 3(2), pp. 118-124), reports on the effectiveness of a cheap, old-fashioned method which is fun for everybody: the board game. Siegler reported that an hour of playing a simple board game produced gains in 4- and 5-year-olds' abilities to compare the size of numbers, to estimate where on a number line a point should be placed, to count, and to identify numerals.
How could all these benefits come from a board game like Candyland or Chutes and Ladders, when such games don't make a child practice any of them except counting? For that matter, why is it important for children to compare or estimate? Isn't it enough to be able to count and to recognize numerals?
When children learn to count-just to repeat numbers in order-they don't simultaneously learn that each successive number means a larger quantity than each of the ones before. Reciting an orderly sequence doesn't necessarily teach that lesson, even though it's a fact about our number system. (For instance, we teach the alphabet in an ordered sequence, but K doesn't mean anything larger or later than G does.) Children learn about differences in quantity in ways that are separate from learning to count, and if they have no specific experiences with quantities, they may not make this connection until much later in their lives. Middle-class children in the United States usually receive a lot of lessons in dealing with quantities, at home and in preschool settings. These lessons may be as simple as being measured regularly and having their increasing heights marked on the kitchen door frame, or as complicated as accompanying a parent to the grocery store and watching as fruits and vegetables are weighed out, or as deliberate as instruction in measuring with a ruler or tape. Children from impoverished families, like those in Siegler's study, are likely to have fewer such experiences, as their caregivers are overworked or exhausted from dealing with their many obligations.
Experience with everyday use of quantities helps children understand that 10 is not only "later" than 5 in the counting sequence, it is also "more", and more in a completely predictable way that is related to the understanding of number facts. A child who does not understand this could slowly memorize number fact after number fact, but would have little ability to do the self-checking that comes with the connection of number with quantity. For instance, if I had to add 2 + 2, and forgetfully tried the answer "3" (I'm imagining myself as a very young preschooler), I might question this if I thought about the amount of increase in quantity from adding 2, as compared to that from adding 1. But I could make that comparison only if I had some idea that numbers that are farther away from 1 also mean larger quantities.
Could it be that Siegler's preschoolers improved in ability simply because they got a lot of attention and had fun playing with a friendly adult? Those factors probably had a small effect, but Siegler made sure he could look at the results of the experience with quantity by having half the children play a board game that used colors rather than numbers. That group improved a small amount, but much less than the children who played the game with numbers.
It seems that child's play-- of some kinds-- makes for better math skills, especially for children who don't have many experiences with quantities before they start school.