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Common Core Math is Not the Enemy ~ Brett Berry

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Brett Berry is a math teacher and blogger at Math Memoirs. This blog has been republished in part from it’s original post with the author’s permission.
We are not computers. We are not machines. We do not think procedurally.

That’s why the “old way” of teaching math is not the best way.

The traditional way involves rote memorization and algorithms performed on paper. They require little to no understanding of why the algorithm works. It simply works.

In some situations this is great. If I were to program a computer, I would use algorithms and procedural instructions because that is how a computer thinks.

It’s not how humans think though.

We have an advantage that computers don’t. We think strategically. We optimize for the easiest solution. We’re adaptive. We can think about a problem forwards, backwards, in chunks, from the middle out. We can rearrange terms, regroup, combine and split it apart. We can round up and down, and back again. We find patterns and draw connections.

Even in mathematics, we are creative beings.

If Algorithms Work, Why Shouldn’t We Primarily Teach Them?

Reason 1
We forget. All the time. Especially when we don’t understand why the algorithm works or if it has been a long time since we last used it.

I can guarantee if I took a survey at Starbucks right now, and asked people how to perform long division, convert a mixed number to a fraction, recite the quadratic formula, factor a binomial, and complete the square — most would fail.

Not because math is too hard or people are bad at it, but because memorization and algorithms are not the best ways to retain information.
We remember through contextunderstanding and application.

Reason 2
The #1 complaint about math is: When will I use this in REAL LIFE?

There are plenty of opportunities to perform basic math everyday, yet most people resort to a calculator or simply give up.

Why?

Algorithms are not convenient for real life, even if you remember them. They are difficult to do mentally. They aren’t intuitive. And often we don’t have a pencil, paper and the time necessary to do long-hand math.

This Isn’t New Math, It’s Number Sense

We call this new math, but it isn’t new at all.

In fact, it has been around for a very long time. It’s called number sense. And it’s the way mathematicians have been thinking about numbers for centuries.

For example, take this story about the famous mathematician Friedrich Gauss.

In elementary school, little Friedrich was very good at math, and he often finished his assignments quickly. As a result, he’d get bored and disrupt the other students. So one day to keep him busy, his teacher asked him to sum all the whole numbers from 1 to 100.

If he were doing this the traditional way, as the teacher expected, he would add each number to the previous making a running total.

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As you realize, this process is tedious and time consuming.

But Gauss didn’t think about numbers algorithmically. Instead he thought about them as components of a system.
To his teacher’s dismay, he solved the problem mentally in a few minutes!

How did he do it?

He began by imagining all the numbers in front of him in a long line.

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As he thought about the numbers he discovered a useful grouping technique. If he paired the very first number with the very last and continued this process inward, he noticed every pair summed to 101.
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In total, he had 50 pairs of 101. So the answer is 50 times 101.
Note: We can complete this multiplication mentally by splitting 101 into 100 + 1 and multiplying the 50 through to obtain 5050.
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This beautiful display of numeric intuition, creativity and ingenuity is taught as the following formula in second year algebra classes, often without a mention of little Friedrich Gauss.
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But I never forget this formula.

Not because I memorized it, but because I remember the story of it’s origins.

You see (a-1 + a-n) represent the sum of the first and last terms of the sequence, 1 + 100 in our story. And n represents the number of terms in the sequence, which we divide by 2 to obtain the number of pairs. Finally, we multiply them together to yield the total.

The point is we need stories, illustrations, and context to give the formulas and algorithms meaning. We desperately need to understand the foundations of our knowledge. Otherwise math becomes meaningless and forgettable.

What Now?
Befriend math! Be open to new perspectives and ask questions!

Common Core is attempting to expose your child to this flexible way of thinking. It may not be perfect, but it is in the right direction.