This is well worthwhile but few recall that the teaching of arithmetic was rote and used time honored recipes actually disconnected with the underlying mathematics or the natural methods used by the mind to solve the problem at hand.

 

If you are good at numbers, guess what? you develop your own protocols that do not waste your time.  You even get good at it.  You only use the school book system when you are tackling large numbers and the risk of losing your place is real.

 

What this suggest is that common core problems are derived from the break between the parent's training and their children's which is fair enough and natural. 

 

The real problem is the lack of  mathematical training for way too many senior school students.  It is my position that all students entering University need to have Grade 12 calculus or to take an extra year to pass that course. . 

This is How You Do “Common Core” Subtraction

By Hemant Mehta
 

October 1, 2014 

Erick Erickson, the editor of the conservative website RedState, is furious because of the way his third grade daughter is being taught math. I mean, just look at how her “Common Core” textbook teaches subtraction: 



Yes, that’s confusing when you look at it. I’ll admit that. 

Erickson, who (I’m guessing) mechanically learned subtraction by putting the big number on top, the smaller number on bottom, and doing a little bit of “carrying,” is annoyed that his daughter isn’t learning math the same way he did:

The traditional method of subtracting, borrowing and carrying numbers, is derisively called the “Granny Method.” The new method makes no freaking sense to either my third grader or my wife.

We send our child to a Christian private school. We thought our child could escape this madness. But standardized tests, the SAT, and the ACT are all moving over to Common Core. So our child has to learn this insanity. But we cannot help her. The book offers only one example.
…
This is maddening and angering and frustrating. This is why so many parents are so upset. They cannot help their children. The math makes no sense and seems to offer no practical purpose other than it is new. The teachers privately concede the uselessness of it.

I empathize with the frustration. I really do. But as someone who taught high school math for several years, this “new” method is soooooo much better.

The problem isn’t the method. It’s the way this textbook (and maybe even the teacher) explains it.
The question boils down to: How do you do 325-38? 

There is an algorithm we can use (the “granny” method). Erickson learned the algorithm. I did, too. But the problem with the algorithm is that many kids don’t really know, intuitively, what they’re doing. They can solve the simple problem — but when the math gets harder, they’re not sure how to transfer those skills because they never really understood what was going on in the first place.
The “new” method is basically teaching them how to do the subtraction in their heads.

Let me translate the textbook for you:

If you want to subtract 38 from 325, the easiest way to do it mentally is to count up. So go from 38 to a higher number that’s easier to work with… like 40. (You’ve gone up 2.) From 40, you can jump to 100. (You’ve gone up another 60, for a total of 62 so far.) From 100, you can jump to 300. (You’ve gone up another 200, for a total of 262 so far.) From 300, you can jump to 325. (You’ve gone up another 25, for a total of 287. Boom. There’s our answer.)

If that’s still confusing, let me use an example I’ve used before: 

Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)

You sure as hell aren’t going to get out a sheet of paper and do this:

   

 But that’s ridiculous. You don’t need pen and paper to figure this one out. We all know it’s easier to just count up the single penny, and you’re done! (10 – 9.99 = 0.01)

That’s it. That’s the sort of math most of us do on a regular basis and it’s exactly the sort of thinking Erickson’s daughter’s textbook is attempting to explain. (It just does a really horrible job of it, especially if that’s the only example.) Again, if students can get a handle on thinking this way instead of just plugging numbers into a formula, the logic goes, it’ll make other math skills much easier to comprehend. 

I should also point out that Common Core doesn’t say the “new” way is the only way to subtract, nor does it dictate that the “new” way is the way kids have to do it. Erickson is welcome to teach his daughter the “granny” method. He mentions that his daughter has to learn four different ways to subtract — and I suspect that’s because the more ways she learns to manipulate numbers, the better her math skills are going to be. That’s the ultimate goal of the Common Core math curriculum — to make sure students attain this “number sense.” If it’s politicized, it’s usually out of ignorance, even though there are some legitimate reasons to dislike it (such as the reliance on standardized testing).

I’ll add (ha!) that in my years of teaching math, I ran into many, many students who could do the basic skills on paper. But when I needed them to think more abstractly, they got completely lost. The students who could tackle basic problems in different ways had a much easier time learning algebra than those who couldn’t. And on a broader level, students should learn several ways to tackle what looks to be a simple problem, because the math you learn in school isn’t just about finding the right answer; it’s about teaching you how to think. 

Back to Erickson, who’s still mad because of his misguided perception of Common Core:

This is why Jeb Bush will not be President. It is also going to end very, very badly for many other politicians. The only champions of common core I know are paid to like it and most of them have no kids. These people want worker bees in their cogs. They want automatons. They do not want productive, independent citizens.

I’m hardly a champion of Common Core, but I’m telling you, kids who are able to figure out this “new” math will be better off in the long run. This isn’t a liberal conspiracy. It’s just a more effective way to teach the subject.



Jason Watt I have been teaching math to adults for 14 years now (25 if you count having to teach magnetic declination in the Army) and I will say that adults who learned math the old way are generally not good at math. The exceptions are people who likely would have been good at numbers no matter what

Michael Western As someone who teaches grade 7 math, I can tell you that we generally teach multiple approaches to different problems. The intention is that if a kid doesn't get it one way, they will conceptually understand it by doing it another way. Often this is effective, however, at times, this can cause confusion amongst students who initially understand it but then struggle with other methods.