The left half of the video above shows a multiplication problem being done using the Common Core method. The right half of the video show a person solving the same problem using the traditional method, followed by that person making a cup of coffee and taking their dogs outside to play. The actions on the right side of the video take exactly as long as the actions on the left side of the video. The obvious point of this video is to ridicule Common Core math. Judging from 95% of the comments of this Facebook post, most people seem to agree that Common Core math should be ridiculed.
I don't comment very often on public Facebook posts, but in order to inject some sanity into the discussion, I made the following comment.
I was heartened to see at that at least 14 people and a teacher agreed with me, but for those of you who still don't agree, allow me to expand my argument a little bit.
Common Core math teaches kids to consider multiple ways to solve the same problem. It may seem odd to solve a problem in an indirect way when the direct way works just fine, but the ability to solve math problems in several different indirect ways is an important mathematical skill to develop, because in higher orders of math, the direct method almost never works.
In just about every important mathematical proof, terms of equations need to be re-arranged in what can sometimes seem to be counter-intuitive ways. Take the quadratic formula, for instance. Many basic calculations in science and engineering rely on it. I'd be shocked if the systems that run you car or your phone do not use the quadratic formula to calculate something. If you take a look at how the quadratic formula is derived, you'll find that the derivation cannot be done without rearranging the terms of the equation multiple times.
The need to rearrange terms in mathematics equations only increases as one progresses through higher levels of math. By the time one gets to advanced calculus, a high percentage of equations cannot be solved without dealing with imaginary numbers. *
* A quick lesson in "imaginary" numbers for the uninitiated.
An example of an imaginary number is the square root of -1, which is referred to in mathematics as the letter "i". "i" is defined such that i multiplied by i equals -1. Expressed as an equation ...
i x i = -1
A basic mathematical principal is that a positive number multiplied by a positive number yields a positive number and that a negative number multiplied by a negative number also yields a positive number. For example ...
1 x 1 = 1
(-1) x (-1) = 1
So, with that in mind, it seems impossible that a number "i" could be multiplied by itself and yield a negative number, because ...
If "i" is a positive number ...
i x i = a positive number
and if "i" is negative number ...
i x i = a positive number.
So, whether the number "i" is negative or positive, "i" multiplied by "i" will be a positive number. So, how could it ever be possible that "i x i" could be a negative number? The answer is that the number "i" is defined to be neither a positive number or a negative number. "i" is considered to be an imaginary number.
If you've never heard of imaginary numbers before, this may sound a lot crazier to you than the concept of Common Core math. However, believe me when I tell you that imaginary numbers are vitally important, not only to mathematics, but to lots of the modern technology we enjoy today.
In advanced calculus, it is quite common that imaginary numbers are an intermediate step in solving equations that start with real numbers. For example, you could start with a real equation, with real numbers that needs to be solved for a real world application. It often turns out that the only way to solve the real equation is to convert it into the imaginary realm ( look up "complex numbers" if you want to learn more about this "imaginary realm" ), do additional calculations and transformations in the imaginary realm, and then convert the equation back into the "real" realm to get the final real solution.
It's been more than a quarter century since I've taken any courses in advanced calculus, or physics or engineering courses, so I'd be talking out of my ass if I told you I knew exactly what current real world applications rely on the advanced Calculus that uses imaginary numbers. However based on this and other things you can find online, I'd be shocked if your smart phone or GPS would work without the mathematics of imaginary numbers.
So, to get back to how this blog post started, my larger point is that the kind of thinking being taught in Common Core math is the kind of thinking is required to understands ( and develop ) the kinds of technology that makes our modern way of life possible. In the coming decades all this new technology is going to replace a lot of traditional jobs. There may not be any human cab drivers. There may not be any human truck drivers. Cashiers in retail stores may be as uncommon as non-automated tellers in banks today. AI has already replaced a lot of jobs that used to be handled by receptionists, secretaries, and customer support, and these jobs will only become more scarce as AI improves.
So, if you're a parent you've got to ask yourself if you want your child's education to train them for jobs that are disappearing, or if you want your child's education to train them to work in the technological fields that are going to make so many of these traditional jobs obsolete.
I believe that Common Core math is a great first step in training children for the jobs of the future. If you can't see that, your going to be doomed to stay stuck in the past.
Rich
