The “Common Core” Subtraction Technique Caleb Bonham Criticizes is Actually Useful

I’m a fan of Caleb Bonham’s work. However, in his recent video on Common Core, he gets a little off-track. The subject is a technique for subtracting one number from another. Bonham claims the technique in question was imposed by a Common Core curriculum and that it is overly complicated. In fact, the technique is very old and very useful. The fact that a Common Core program happens to use it is no cause to damn it.

As Bonham explains, the traditional solution to the problem, thirty-two minus twelve, is to first subtract “two minus two” in the “ones” column, then subtract “three minus one” in the “tens” column, for the correct answer of twenty.

The approach used by Common Core, by contrast, asks a student to see the following:

32 – 12 = ?
12 + 3 = 15
15 + 5 = 20
20 + 10 = 30
30 + 2 = 32
The sum of the 3, 5, 10, and 2 is 20.

Bonham thinks this approach is overly complicated, and, in some situations, he’s right. But the approach indicated is, in fact, how I often do subtraction problems in my head (except that in this case I’d jump straight from twelve to twenty, and so get eight plus ten plus two), and it’s a perfectly legitimate approach. It is also an approach that helps students reach a conceptual-level understanding of addition and subtraction, rather than merely learn rules of subtraction by rote.

Of course, in this case, because we’re dealing with two, two-digit numbers that end in the same digit, adults and more-advanced students can easily see that the difference between the numbers is some increment of ten (in this case twenty). But what to do in other cases?

To illustrate the advantage of the approach given, consider the problem thirty-one minus twelve. In this case, the rule-based approach requires that a student “borrow” from the three. It’s much easier to solve the problem in your head by saying, “eight plus ten plus one equals nineteen.”

Or consider the problem seventy-three minus twenty-eight. A good way to do this problem in your head is to think, “To go from twenty-eight to thirty I need to add two; to go from thirty to seventy I need to add forty; to go from seventy to seventy-three I need to add three. The total is forty-five.” There are other good ways to find the answer, of course, but, for me, the way I described is the easiest way to do it in your head.

The broader lesson here is that, just because something is associated with Common Core, doesn’t mean its bad.

Update: I’ve also written about a vague, nonsensical problem from a Common Core-approved test.

10 thoughts on “The “Common Core” Subtraction Technique Caleb Bonham Criticizes is Actually Useful

  1. Kazriko Redclaw

    The question is, is it merely presenting this as a potential solution, or are they requiring kids to actually use this method in homework and on tests? The former has some value, the latter actually does harm.

    It’s like allowing them to use the scaffolding division method if they need to. Once they can remember the division table in their head, they shouldn’t need scaffolding anymore, but it can help them until they learn the table, and forcing them to use it if they don’t need it causes them to learn that they must use an inefficient method to arrive at the solution when they could have used a more efficient one.

  2. John Kranz

    It concerns me that the discussion changes from “who decides?” to “which curricula is better?” I agree that the method may help develop greater numeracy. But the more important question is whether this should be centralized in Washington.

  3. ariarmstrong

    I agree that’s the important political question, but I have no obligation to always discuss politics. This is simply about how to subtract numbers.

  4. ariarmstrong

    A good technique can be taught poorly, no doubt. I agree it’s ridiculous to require students to show “work” that’s not actually useful for solving the problem at hand. My point is a very simple and limited one: The technique in question can be a useful way to subtract numbers.

  5. Kazriko Redclaw

    I think the point I’ve seen on Common Core is that the homework actually requires them to do it in a slow and inefficient way and show the work. Not really complaining about teaching this method, complaining about requiring them to use it. Some might complain about teaching the method, but that’s not the point that really causes me to dislike the concept of Common Core.

  6. ariarmstrong

    What you’re discussing is a real problem, but it’s not one unique to Common Core. My math instruction in school was largely horrible, and that was long before the Common Core fad. Much of my school career consisted of doing irrelevant “busy work.” There’s no good learning method that a bad teacher or a bad textbook can’t misuse.

  7. John Kranz

    What? Something not politics? Huh?
    Agreed. I was just at an anti-Common Core presentation last week and thought the people, though bright and passionate, were less than effective because they get into the minutia — like subtraction and failed to present a bigger picture against it.

  8. Mel_M

    In 50 years, Objectivists have gained little or no ground toward replacing public education with a private educational system; I really doubt the next 50 years will be any better. The only major group interested in dropping public education are the Religious Right who believe that education will fall into their hands; they may be correct: the R.R. can come up with train loads of money and plenty of organizational skills to make sure they dominate. They’re already doing a pretty good job of infiltrating the public schools (see The Good News Club for a chilling look at what’s going on with “child evangelism”).

    But, Objectivists can legally write textbooks, design curricula, provide teacher training (including books), start schools and school franchising, or even online education.

    I recall that ARI was going to undertake an initiative this year that seemed to be in support of such a move. However, I don’t see anything about it at the ARI site. Part of the initiative was also to be support for the writing of a book about education.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>