Common Core Math

Common Core Math might actually be a good idea…
… but I doubt those that support it have any clue as to why.

Before I get into my thinking of this topic, I need to write about some basic concepts in mathematics, and a mini review of some history. It’s not because I think my readers don’t know these things, it’s because these concepts are so basic or commonly known,  we simply do not think about them consciously. So please bare with me for a few here while I try to set the base line of translation  of what I am trying to communicate.

When my generation was in kinder-garden we were taught how to count from zero to ten. This was the start of giving us a basic understanding of a number line like the image below.

commoncore1We then learned how we just carried over the next digit to the next column, and we were off the the races counting from zero to  twenty, then onto a hundred … ad infinitum…

As we progressed in school, and Math class in particular, we even learned about negatives on the number line…

commoncore3

This understanding of the number line was then used to teach us basic addition and subtraction …

commoncore2
Which was the basics for multiplication and division, and trigonometry, algebra etc. Up to the late 1990’s this was a good idea. But then something happened, the paradigm of the information age exploded.

During my classical education I was taught what can be referred to as classical mathematics, and imperial measurements. Half way through my basic education Canada changed from imperial measurements to the metric system. Metric was a different way of thinking about distance, volume and mass. Although in many ways Canada’s industries still use imperial, a 2 by 4 beam of wood is still a 2 by 4, we have metric in many areas now where it wasn’t before. The British use metric, the Americans use imperial, and  Canada tends to use both because of our relationships with the other two countries.

There have been both advantages to metric in Canada, and some draw-backs, but over all Canada has benefited from metric because we still really speak both languages of metric and imperial.

Now what I want you the reader to do, is to stop thinking about math as a logic problem solving skill set, this is key to understanding the advantage of Common Core. Math is the universal language, metric is only one dialect of it, imperial is another.  Or…. better and more accurately portrayed … base-10 is one dialect and base-12 is another. (Yeah, I know, other geeks will see that as an error, ignore it.)

Today, because I’m a total geek, and I love figuring out ways to hack different forms of encryption, I was trying to solve a road  block. I could not get out of my own way of looking at the problem, it wasn’t just being target fixated, it was that my basic  understanding of the problem was limited. So I began searching the net to see if others had tried to solve the same, or similar problem, and found an answer.

But the answer to my problem, wasn’t what really caught my attention, it was HOW it was solved. As I looked at the solution, which was written in long form, I kept thinking to myself, this looks a lot like common core math. So I looked around for a better description of what Common Core was really all about. Bottom line, Common Core is a different way of thinking about number-lines. Common Core does not replace the basic or classical mathematics my generation was taught, it’s an add-on to the skill set.

So to get to the point, I’ll give you a simple number such as Three Hundred and Twenty One.

321 = 300 + 20 + 1

This is what we adults sorta see when we look at Common Core. Not the best example, but I’m writing this to make it easy to follow along. But the correct way to represent the number 321 is to write it like this…  (syntax for non-geek)

321 = (3 x 10^2) + (2 x 10^1) + (1 x 10^0)

Translated into English this means: Three Hundred and Twenty One is equal to three multiplied by ten raised to the power of two, plus, two multiplied by ten raised to the power of one, plus, one raised to the power of zero. The reason for the the “ten” is because we use base-10. Think about that for a moment.

If the number I was trying to translate was in base-7, say421, to my dialect of math (base-10), I can now do this easy as follows:  (syntax for the geeks)

421(base-7) = 4*72 + 2*71 + 1*70 = 211(base-10)

Translation: Four Hundred and Twenty One in Base Seven is equal to four multiplied by seven raised to the power of two, plus, two multiplied by seven raised to the power of one, plus, one multiplied by seven raised to the power of zero, which equals Two Hundred and Eleven in base ten.

Being able to do this, and understand it, is fundamental to cracking some basic cryptography. But it is also used in binary computer models, and hexadecimal programs. And those are just the examples related to my field of work. Chemistry, Physics, Astronomy, Engineering, and a host of others also use different base systems for different problem solving.

The whole purpose of Common Core is to get children at a young age to develop, a different way of thinking, about numbers. Because without the ability to understand the different dialects, or at least recognize them, there are a host of careers that are out of reach.

– wolfe

Recommended Reading: You’re wrong about Common Core math

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