How Unschooled Children Learn Mathematics


Like literacy, children are able to learn basic math just by living.

Mathematics is everywhere we turn. Not just numbers, but shapes and colors too. Patterns. Measurements. Music.

Children learn to count, and even divide, organically. If there are two preschoolers playing together and two toys between them, they understand that it makes sense to each have one toy. When my kids help me with snacks, they automatically divide apple slices evenly between everybody.  We also talk about how many strawberries, for instance, we would need if each person in our family had 4. This has led to a better understanding not only of multiplication, but of division and fractions as well. 

We figure out how many pieces of pineapple we each get if we cut it into equal parts, and they understand that the smaller the pieces are, the more there are of them. We do a lot of baking and often I double or even triple the recipe if we bring baking to groups or play dates, and they are able to figure out how much of everything we need if we are multiplying by two or three.  

My children receive pocket money every week, and they each have a jar for spending, one for savings, and one for charity, which so far has been used at the end of each year to purchase a gift to put under the Salvation Army Christmas, for a less-privileged child. The kids get to decide how much goes into each jar, and this allows him to learn about percentages, as well as learning how to manage money. When they want to buy something, they can count their money and see if they have enough for it, or figure out how much more they need, if not.

When my younger son was almost six, I wrote in his homeschooling application that he currently had a very good understanding of numbers and patterns. He could count into the hundreds, and he knew that 1,000 is the same as ten hundred, so if he had the patience to count all the way to there, he could. He knew how to count by 2s (odd and even numbers), 5s, 10s, 20s, 100s and 1000s. 

Not long afterwards, he was able to tell time on both digital and analogue clocks. My children have a wall calendar that allows them to change the day, month, year, day of the week, and season, which helps them with numbers and patterns. My four-year-old knows her shapes and enjoys using small shapes to build a large shape, which she does with Legos and tangrams and sometimes when she draws.  

When my oldest son was five or six, he had a multiplication chart that I figured was a bit advanced for him but I put it up anyway along with the wall calendar and other educational charts and maps. One day he told me he pointed to it and said he wanted to “do that” so we sat down with his Lego pieces and made groupings so he could see that five groups of five Legos, for example, equals 25 Legos. We went through the chart, starting with 1×1 so he could see that one group of one Lego equals one Lego, then went on to one group of two Legos, and we didn’t stop until he wanted to, which was at 7×11. By that time, he understood how multiplication related to groups of items, rather than single items, so he could understand why four TIIMES four equals sixteen, when four PLUS four only equals eight.  He could also see that three groups of four Legos is the same as four groups of three Legos, so the order does not matter.

Another time, he wanted to know exactly how many stickers were in his sticker book that boasted, “More than 1,000 stickers inside!” So, we either counted the stickers on each page (sometimes as few as 12 stickers), or, on pages that had over 100, because they were lined up nicely in rows, my son counted how many were across and multiplied that number by how many rows there were. We wrote down the number of stickers on each page, and then he added them all up, coming up with 1,056. My younger son, who was about six at the time, was curious too, and he watched with interest as we did the equations and explained each step to him, and why we were doing what we were doing. Some of it was a little advanced for him, but he understood why we multiplied the columns by the rows, because he would often count the bumps on a large Lego rectangle and then count only the top row by the side column, and then tell me that six times eight is 48. The addition of stacked numbers was a new concept that we introduced to him, but he was able to become familiar with it in context to what we were trying to accomplish, even if he wasn’t quite ready to start doing it himself. This is one thing I love about having my children of all ages learning at home – all of the kids have the opportunity to be exposed to the things that their siblings are interested in and are learning about. 

We also play a lot of games. Sorry, Monopoly, Chess, Yahtzee, Rumikub, Canasta, and Farkle Party are some of our favorites. These games allow my kids to further their understanding of numbers, probability, counting, patterns, color-matching, money management, strategy and tactics, risk versus reward, etc. Games are a fantastic teaching resource, and a great way to have lots of fun while learning. I am always on the lookout for fun and educational games to add to our collection.  

Other opportunities for children to become competent in mathematics include playing with Cuisenaire Rods, dice, dominoes, and tangrams; doing puzzles, mazes, and number games such as Sudoku; using scales, calculators, and tape measures; playing an instrument and learning how to read music; doing carpentry projects; using a pattern to sew, knit, or crochet; reading math books (such as Apple Fractions, 100 Hungry Ants, a book about division and fractions; Sir Cumference books; and, as they get older, the Math Murder Mystery books); using math workbooks; building things with Legos, through using the manuals, their imagination, and/or replicating structures that they can see but do not have the instructions for; and using a subscription for Mathletics or similar program.