Common Core: Sixth Grade Mathematical Functions

Tonight I sat down with my stepson to help with his math homework. He's in the sixth grade and they've been doing some introductory algebra at his school. What I found, in my mind, is horrifying.

Welcome to the world of Common Core.

The fourth problem we encountered read like this:


I'll admit I was confused for a moment. If I looked at this for a few seconds, I could probably come up with the answer in my head, however, I'm certain that isn't what the teacher is looking for. I'm also certain that my 12-year old stepson isn't going to come up with the answer in that manner.

Man, they're teaching advanced function solving to these kids awfully young, I thought. There has to be a trick; they didn't even give them room in the book to show their work.

This being the first time he's let me help him all year, and the chapter being about linear functions, I figured maybe my memory was off from when I learned this same stuff years ago. Graph paper in hand, we started at the beginning...

y = mx + b

"Have you ever seen this?"

"No, never."

I browsed through the entire chapter. Nope, nowhere is the equation for a line (technically the slope-intercept form) mentioned. But this chapter is titled "Functions and Equations" and the lesson is about linear functions. How could this not be...?

Sigh

Moving on...

We know X and Y from the table. In fact, we know six pairs of X and Y from the table. I solved the problem like so:


Hold on a minute, I just did the same math I learned in Algebra II from high school, this poor kid is in the sixth grade. My stepson is understandably mortified and ready to start crying.

Maybe I should read through the chapter a little and see what the book really wants. I stumbled upon this following:


What in the world?

Well, let's try it out...


This is just ridiculous. By filling in the middle number on any line, you always make the rest of the lines untrue.

We took a step back and I explained that our multiplication step in the table above is no different than the slope m in the equation mx + b = y and that perhaps if we added a fourth column for b that we might be able to solve this. The new table looked like the following:


We didn't even bother trying to solve it. The poor kid was confused enough and I knew from solving the problem earlier that m was a fraction and this was going to confuse him worse. I suggested something different -- lets flip the table and solve for x instead of y.


Now we're cooking with fire. We filled in 0 for m (the multiply number), and the first line tells us what the constant b should be. Unfortunately, using 0 for m only gets us past the first line before the equations are untrue. Let's keep going...


Same problem as before. Continue...


Hey, look at that! 

2y + 6 = x

It's the same equation (with respect to a different variable) as the algebraic solution above.

We finally got a table where all expressions evaluate as true. It only took drawing 5 damn tables and flipping the variables -- which I would never expect a 12-year old just learning algebra to know to do.

What did we actually accomplish here?

  1. Confuse the kid
  2. Teach him to derive an equation through trial and error. Honestly, how is this different from learning to add by using your fingers? What if the equation was more complex?
  3. Introduce concepts before the kids have mastered the building blocks.

I personally don't mind the kids being challenged in school. I have a serious problem with how this material is presented and the methods the kids are learning to solve problem.

Common Core is supposed to teach better and alternative methods of solving problems as each kid learns differently. Too often I find that it causes confusion and promotes bad habits (see above).

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