When I started homeschooling my son, I assumed that helping him to learn math was going to be my hardest job. It was never my strongest subject, and I never loved it. Nevertheless, math has proven to be one of the easiest subjects for my son to learn, and one of the areas where he has excelled.
At age five, he can add up to five two-digit numbers in his head, without paper, accurately and, in some cases, faster than I can. With paper and pencil, he can add or subtract any series of whole numbers, and he can multiply and divide not only with ease, but also with a clear grasp of what the numbers he is working with represent. He knows the relationships between fractions and percentages and decimals. He can read and create graphs. He understands the rudiments of algebra; for instance, he can solve for x in problems such as 3x = 12. And he can apply these skills to real-world problems, organizing the data visually and solving them in a straightforward manner.
According to the Common Core standards (for what they’re worth), he is currently working through problems at a fourth-grade math level, and by any reasonable standard he is quite advanced for a five-year-old.
Although my wife and I have guided him in various ways, the effort that got him to this level has been his own. But a variety of math apps have been of inestimable help. And, of all the apps our family has tried, the following dozen have proven most useful.
Intro to Math by Montessorium
One of the first math apps my son used was Montessorium’s Intro to Math, and we love it—in large part for what it does not do. It does not tell children they are good for getting an answer right—and thus does not imply that they are bad for getting an answer wrong. It also does not use silly illustrations, goofy voices, or visual explosions in a vain attempt to keep children interested.
What it does, instead, is to help children understand the numbers from zero to nine by, in traditional Montessori fashion, presenting objects in quantities that correspond to those numbers; letting children trace the numerals; showing them how even numbers are grouped differently than odd numbers; and letting them see, compare, and organize rods of differing lengths and differing segmentation. . . .
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1. See video, “Intro to Multiplication,” Khan Academy, https://www.khanacademy.org/math/arithmetic/multiplication-division/mult-div-concept/v/multiplication-intro.