Math as a Foundation

Jul 27, 2020 | Apex

Math as a Foundation

Parents often hear one of two claims by their children. “I hate Math,” or “I hate reading.” I used to tell my students that even if they hate reading, it is the foundation for so many things that they will do that they need to learn as early as possible. Most jobs cannot be completed without some ability to read. The same is true of math, but it is a bit unique. Many basic tasks can be done with a cursory ability to read, but math continually builds upon itself. Even the most rudimentary levels of math build upon one another. When parents are home with their children during the current pandemic, they are often at a loss for how to explain mathematics to their children. Often, they said to their parents that they hated math too. Once you understand how it builds upon itself, you may find that it is not so hard, after all. Let’s take a quick look at the base levels of math and how they build upon one another.

Number Sense and Counting

If a child has no concept of number sense, he or she cannot move forward. A child must learn to count and recognize the numerical representations. While much of the Western world teaches Arabic numbers, it does not matter what number system one uses. Ancient Native American numbers can represent the counting sequence, but a learner needs to know the concept of a single item vs. many and how to classify each addition of one. We count using numerals 0-9, but they are merely written representations. Once we understand those representations, we can build to the next step.

Addition and Subtraction

I use these together because they are the inverse of one another. Students who learn “fact families” will often understand the inverse operations a bit better. Once students learn to count, they can determine how adding or subtracting amounts changes the final amount. 4+3=7 and 7-3=4. In the beginning, the student may need physical representation through classroom manipulatives or things that are used to represent numbers. This can be done with toothpicks if necessary.

Multiplication and Division

Like addition and subtraction, multiplication and division are inverse operations of each other and are simply “faster” methods of the previous brick in our foundation. Multiplication is simply a more efficient way to add large numbers. 4x5 is simply the number four added five times. If we have not built that foundation of addition, multiplication cannot make sense. Division is simply how to subtract efficiently. 20/5=4 because twenty is five sets of four. We can subtract five four times.


Additionally, fractions are simply an extension of multiplication or division. They tell us how to group things. They portion stuff for us. Fractions are just division equations that we don’t quite finish. Rather than writing 1/5 as 0.20, we write 1 divided by five. If we break one down and subtract it into five equal parts, each is 0.20 of a part. Without learning number sense, though, none of this is possible.

Final Thoughts

We could continue through advanced statistics and explain how each math concept builds upon another, but that would likely be overwhelming. Math is fundamental to success in and out of the classroom. Building the foundation for math with complete bricks will make it stronger. Take your time and build each cornerstone before moving onto the next.