When do kids understand math?

My daughter who is almost three has very little idea what numbers mean, though she is quite verbal. She can't really distinguish between one and two objects, though she can count. What are the normal developmental stages in learning math?

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I'm so glad you asked this question! Most children can count to ten or twenty by the time they are three -- it's what educators call the "song of numbers." But the basic understanding of how numbers work comes later. It doesn't even begin until a child is between three and four years of age. In my three to four's classroom, we work on the same mathematical principles all year. They are: one-to-one correspondence; the concept of amount; and the identification of the names of numbers with their symbols (8=eight, for example).

These are very simple principles, I know, but they are the first ones needed before a child can go further. One of the most important is that every number has a name and a shape. It's not something that all kids understand right away. Even when they can use numbers to count, they can't always identify numbers by name. Next, the fact that one number stands for one thing (one- to-one correspondence) is a concept which takes time to sink in. I often count the children out loud as we move from an outdoor activity to an indoor one. I tell them that there is one number for every child, and then I slowly count heads. Sometimes it takes all year for my students to grasp this idea. But they get it eventually!

Finally, they are exposed to the concept of amount. Numbers, which look pretty much alike if you think about it, stand for different amounts. A 2 stands for very few things and a 5 (which is basically an upside-down 2) stands for more things. This is difficult, but some of the children will understand it.

Since kids learn better when they're not under pressure, we have lots of counting experiences as a group, so that the listeners can learn from the counters. But the best way for kids to learn these principles is to play individually with manipulative toys and do the counting and grouping by themselves, with a teacher or parent watching and guiding when necessary. If you have no counting toys, big buttons or shells, or even Cheerios will do. This kind of experience is the best teacher.

Remember, though, that your child will only learn what she is ready to learn. Exposure at too early an age doesn't help. The best time to begin is when your child shows an interest in counting.

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