Monday, March 3, 2014

Core Math

There have been a lot of negative things published by conservatives about core math. I do agree there are some issues with how this approach to computing math is taught. That being said, there are generally several ways to solve a math problem and teaching multiple approaches is, in my opinion, favorable. I am an engineer and do not use a calculator for basic math – I can compute numbers in my head. In fact, to compute basic math in my head I use core math principles and break the problem down into sets of 5’s, 10’s, 100’s, 1000’s, and so forth. Why? It is because it is much easier to deal with 10’s than 3’s or 100’s than 31’s. I teach kids these principles when working with advanced kids. It is confusing to most people because that is not how we were taught and most of rely on calculators to compute any simple math once the numbers get higher than 100. This is why the metric system is so much easier to work with than the English system of measurement – the metric system is based on multiples of 10.

In math, to compute things there are many ways to solve a problem (not just the one we are taught). That is because with math there are patterns that can be used to solve problems. For instance, can you do 31 squared in your head (31 x 31)? This is simple math. Even if I showed people that 30 squared (30 x 30) is 900 (3 x 3 = 9 plus 2 zeros in the problem equals 900) they still could not tell me what 31 x 31 is. Any time a number is squared there is a pattern: 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 5 x 5 = 25 and so on. Can you see the pattern? The difference between 2 squared and 1 squared is 3; the difference between 3 squared and 2 squared is 5; the difference between 4 squared and 3 squared is 7, and the difference between 5 squared and 4 squared is 9. Can you guess what the difference between 6 squared and 5 squared is? I hope you can see it will be 11 since 6 squared is 36. Knowing this, it can be surmised that that 31 squared is simply 30 squared plus (30 x 2) plus 1 or 900 plus 61 or 961. Hence, I know 32 squared will just be 31 squared plus 63 more or 1024. In math terms, if n is the number we want to square and we let m = n - 1 then n squared = m squred + (m *2 +1). Similarly, to find n cubed = m cubed + (m x n x 3 +1). Obviously, I am not solving this problem using traditional procedures we were taught in the classroom. I am able to visualize patterns and solve the problem that way. Does this make what I am doing stupid, wrong, or ridiculous? Well, this is exactly what conservatives are saying.

I have been called a walking computer, I am far from that. I do not have the amazing recall of many, but I can do basic math in my head (and it includes big numbers, fractions and decimals). However, if I did not use core math principals I would not be able to solve or visualize math problems in a different way and do them in my head.

Conservative are wrong on this one, but I agree the way it is being taught is not necessarily the right way.


  1. I'm not familiar with the complaints about the Common Core math program, Patrick, so I will bow to your superior grasp of that subject. I just hope the kids can count to 20 trillion so they can understand the ominous size of our debt!

  2. Most people really do not realize how big 20 trillion dollars really is!