**So what’s really going on in this image?**

One way to solve thirty-two minus twenty-two is to count up from 12 on your fingers, “13, 14, 15, 16, 17…” all the way up to 32. If you keep track of the count correctly, you will get an answer of 20. Let's call this the counting up by ones method.

The “new method” shows counting up by groups. Starting at 12, first you count up by ones“13, 14, 15” and write down 3. Now you can count up by fives, starting at 15, and arrive at “20.” Write down a 5. Now you can count up by tens, starting at 20 and ending at a new current value of “30.” Write down a 10 for this step. At this point, we have to go back to counting by ones, so we think “31, 32” and write down 2. Now, add up the numbers you wrote down 3 + 5 + 10 + 2 and you get 20.

The method described above could be used to check you answer after you solved the problem via the traditional vertical column subtraction method we all know so well.

We don’t have any context on the photo, so we don’t know if the student and teacher were, in fact, checking their work when they made these notes.

Everyone solves math problems in their own way. I personally think counting up by ones (counting up from 12 to 32 on your fingers) is a lot quicker than counting up by the groups 3, 5, 10, 2. My brain works that way. But if you prefer to count by groups, go for it!

What if I asked you to solve $5,000 - $4,995? You can probably do this in your head and get 5. If we wrote out how you solved the problem, it would look like 4995 + 5 = 5000. That’s the so-called “new method.” If we tried to solve this by subtracting in columns (or the “old fashioned” method), we would be required to borrow in the ones, tens, and hundreds places. For some people, that’s no problem, but many people prefer not to do subtraction with borrowing. Counting by groups makes solving this second example problem a breeze.

**What does this image have to do with Common Core?**

Common Core suggest students master certain skills (say, subtraction) by certain grade levels. It does not force math teachers to use any specific form of math instruction.

This is one of many ways of explaining subtraction to elementary school students who have just learned addition. Just go with it!

A talented tutor will adapt to the method that the student prefers to use.

The assertion that teachers have more freedom to use different forms of math instruction with CCSS is patently false. Teachers are told which curriculum to use by their districts, all of which teach math in a specific way. Even if a particular method doesn't make sense to a teacher and s/he decides to use the old/new/green/blue way, the CCSS-aligned tests now demand that students explain their mathematical thinking- often solving problems in several different ways- and some methods are 'approved' while others are not. Take, for instance, my own 5th grader, who can often look at a multi-step problem or a 'word' problem and tell me the correct answer while I'm still getting out my pencil and deciding which operation I should use or what the common denominator will be. After I spend a minute or two solving the problem and arrive at the same answer she retrieved from her brain in 3 seconds, I ask her how she got it, and she can maybe explain it, more or less- but really she just 'got it from her brain' because that is her way. But 'I got it from my brain' is not a CCSS approved method of problem-solving, and her correct answer to the problem would be marked wrong. I fear for her test-taking future (I'm opting her out this year), even though her natural mathematical talent is sometimes incredible to behold. My rather lengthy point is that even though, in theory, teachers should have more freedom under CCSS, the reality of the high stakes tests obliterates that wonderful theory in one fell swoop.

ReplyDeleteAs a math teacher, I have a lot to say. Basically, I will say this: mental math strategies are something that should be taught but are often not taught or taught poorly. Throwing this stuff at elementary teachers without giving them the proper tools to teach it is disastrous. Expecting parents to figure it out is also equally disastrous. We want to "catch up" to our Asian counterparts in math but we are doing it all wrong. They spend all year on a few broad concepts, even Common Core continues the mile wide and an inch deep methods of failure in the past. It doesn't matter how they advertise it, it is the same and actually even worse.

ReplyDeleteAlso, while Common Core is merely a set of standards and do not say anything about using specific methods, it is very clear from the materials that have been published thus far in conjunction with those who designed Common Core that these methods ARE a part of Common Core. They can distance themselves as much as they like from these methods but when 100% of published materials have nearly the same methods in them, it is clear that the intention of those who wrote Common Core has been shared with someone other than teachers and parents.

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