This is a first in the series of posts about education toys. I buy these toys for my son who is soon turning 3-years old. My focus is on educational toys.
In this first entry of the educational toy series, I will tell you about an intuitive way to teach addition and subtraction for numbers up to 10.
A picture is worth a thousand words, so I begin with a real photo of my unit of this product:
I have removed two rows in the centre, and three squares at the bottom, in order to show you the general educational idea.
Let’s look at the open row that says “3” on the left. Sure, a child can find a bar that says 3 on it, merely by association. However, if instead you direct the child to start matching from the right of the row, then he would have to count the seven half-moons in order to understand that he must find a bar that says a “7” on it.
There is even more to this toy, than show in the above photo. The back of each bar has its length written as an English word. Here are those same rows flipped over.
Independently from grasping the mathematical principle of addition, a child associates (a) a name to a digit, and (b) a quantity with a physical length. As a result, if he has to look for a bar called “7”, he also looks for “seven”, and he is focused on longer bars.
To my surprise, my son took a great interest in the lower two rows, which I thought were superfluous and are there just to complete a square. One point he learned from playing with it is the concept of horizontal and vertical when matching the small “equal” and “minus” squares. Furthermore, he almost understood that “+” is symmetric, so it doesn’t matter how it is placed.
In addition, giving an emphasis to ones, and twos, as available in the second row, has been beneficial. These are the simplest numbers, the first and easier that a child learns. They are a safe starting point to expand into longer numbers.
After the child makes the basic associations of digit, word, and length, he begins to see how one bar complements the other to make it to a ten. At this point, an educator can get a lot of mileage out of this toy. Not only for matching up to 10, but an exercise can be made to show that “2” and “2" is the same length as the “4” bar. From there, that “2” and “1” is the same as the “3” bar. And so on.
After that one can get the child to complement lengths. Start with a “6” bar, align under it a “4” bar, and ask the child to complement by finding a “2” bar. This is the process of subtraction.
Then, explore making a 10 out of three lengths, instead of two. Instead of “6” and “4” bars, take “6", “2” and “2” bars. This would show the child that there’s a hierarchical, nesting pattern in the way that the numbers fit into each other.
This is interesting even to me, an adult, as I extrapolate these patterns to larger numbers and more complex operations of multiplication and division.
Another association this toy makes is between length and counting. Even as adults, we think of lengths and counting as two different things. You don’t count if the car can fit into the parking stall, you just estimate the situation by looking. However, you do count coins in your pocket. If there is more than 7 units of anything, a person can no longer estimate it by merely looking, he must count it.
The relationship between length and counting exists. It is the abstract concept of measurement. To measure a length, it is to count copies of a smaller length, placed along its side.
I hope that I got you, reader, to think of other good exercises to do with this toy. If you are wondering where to get it, it is on Amazon and it is called “Professor Poplar’s Astounding Arithmajig”. Here is a link:
Stay tuned to future entries in the educational toy series review. In the meantime, check out my other Medium article “Square Roots the Montessori Way” about teaching math to older kids in elementary school.