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.
For example, in one exercise the whole screen is white except for one red rod. The narrator says, “This is one.” Then, as a dot of light shows up on the rod, she counts it, “One.” Next, a rod segmented with two colors, red and blue, appears. The narrator says, “This is two.” And, as the dot shows up on the red part, she counts it, “one,” followed by “two,” as the dot transfers over to the blue part. This continues once more. A rod segmented with a red, blue, and red part is displayed. And the narrator counts each part of it, “one,” “two,” “three,” as the dot follows. Finally, all three rods are shown. The teacher says, “Tap on one.” After doing so, the teacher repeats, “One.” Then she says, “Tap on two.” Then she says, “Tap on three.” Each time she repeats the number after it is chosen. The program then progresses to the next section, which builds on what was learned in the previous sections.
My son finished the programs in this app with a strong, though obviously limited, grasp of numbers. And he enjoyed the learning process. I heartily recommend it.
Maths 3–5 and Maths 4–6 by One Billion Apps
For young children still learning the basics of mathematics, One Billion’s math apps for children three to five and four to six are the gold standard.
The first of these helps a child learn how to count from one to ten and how to add or subtract within that same range. It shows different shapes, provides their names, and gives children practice identifying each. In similar manner, it also teaches basic concepts regarding size, number, weight, and length.
The second app builds upon the concepts introduced and knowledge gained in the first. It helps children learn to count up to one hundred, and again how to add or subtract within that range. It shows how to count by twos, fives, and tens. It presents additional shapes, including 3-D shapes, provides their names, and gives children practice identifying each. It similarly introduces children to concepts of direction, time, and position.
All of the concepts are conveyed visually and verbally, using exercises and games, in ways that are easily understandable, engaging, and enjoyable for children. And, at the end of each section, the app includes a quiz in which children have to get every question right to pass. The result is some dramatic fun, and, when the child passes, a certificate and a well-earned sense of pride.
My son finished these two apps a mentally different child. He had a greater understanding of mathematical concepts and a greater appreciation for the kind of focused thinking that mathematics requires and develops. He has also returned to these apps many times since, often commenting on how formerly hard parts are now much easier.
Montessori Math: Add & Subtract Large Numbers, Montessori Math City, and Montessori Math Multiplication by Edoki Apps
After a child has gained a basic understanding of mathematical concepts and operations, he can deepen and solidify that knowledge using these three apps: Montessori Math: Add & Subtract Large Numbers, Montessori Math City, and Montessori Math Multiplication.
Montessori Math: Add & Subtract Large Numbers uses two staples of the Montessori method, the stamp game and the bead frame, to make crystal clear what is happening when we add or subtract numbers and what the numbers refer to in reality.
For example, the stamp game shows how to represent (i.e., specify), add, or subtract numbers with stamps. . . .