Parents say: ‘Just add the numbers’

In a New Orleans suburb, Common Core homework is confusing parents, notes a Hechinger Report story.

When Mike and Camille Chudzinski tried to help their son with his homework earlier this fall, they were bewildered. The fourth-grader brought home no spelling lists, few textbooks, and a whole new approach to solving math problems. When he tackled multi-digit addition, for instance, Patrick did not just line up the two numbers and then add the columns, as his parents had been taught to do. Instead, he sketched out a graph with a series of arrows and marks that appeared at first to his parents as indecipherable as hieroglyphics.

“The first few weeks of homework … there was a lot of us asking, ‘Why are you doing that? You are wasting time. Just add the numbers,’ ” said Camille Chudzinski.

When their son, Patrick, got to multi-digit multiplication, “a single equation could consume an entire page.”

Faced with the problem 452 x 4, for instance, he started with the “break apart” method, which entails multiplying 4 by 2, 4 by 50, and 4 by 400, and then adding up the results. He depicted a similar problem graphically using the “area model.” He also tried “repeated addition” (adding 452 four times) and what’s referred to as the “standard algorithm” (lining up the problem vertically, as his parents were taught to do).

Teachers hope “children will come to understand the meaning behind math problems—and not just learn how to follow rules.”

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Comments

  1. Deirdre Mundy says:

    My daughter actually uses the “Break apart” method to multiply numbers in her head. It’s really not bad… though I don’t get all the drawing and whatnot…

  2. Personally, I’d go for double double and add eight. It’s nice to know the traditional lining up method, but so often it’s just easier and faster to to do it in your head. I suspect that all that drawing is done to help students understand that they can actually break apart this problem to get the answer in a wide variety of ways.

  3. It’s important to me that my homeschooled children learn what’s really happening when they, say, do multiplication by lining up numbers by place value. So I show them how to solve large number multiplication by breaking them down. But then they drill primarily using the quicker algorithm. I actually use the long, tedious breaking down method as an unspoken threat if they fail to keep in mind how to solve using the shorter method.

  4. Sounds screwy to me. Seems like you want to teach them a simple, workable method (such as the standard algorithm) and practice them until they’re good at it. THEN teach them alternate methods and algorithms for doing it in your head and all of that.

    Until they’ve mastered the basics, I think all of this other stuff just confuses the kids and teaches them that math is some sort of arbitrary punishment.

    You know, it would be pretty easy for some researcher to try the “standard algorithm” next to all of this other crazy stuff and see which taught kids better… I’m always suspicious of “innovation” when it comes to teaching the three R’s. After all, we’ve been doing it for hundreds of years and it seems to me you would only make a change if you had something that was really, clearly better.

    • Crimson Wife says:

      I disagree. I think teaching the “break apart” method is useful prior to introducing the standard algorithm because then the student knows why to put 0 or 00 etc. That was never explained to me and while I learned how to calculate the correct answer, I never really understood why the algorithm worked until I started using Singapore Math with my kids in our family’s homeschool.

    • This has all the appearances that “showing multiple methods” will become the primary goal of the exercises, not learning how to do the arithmetic and move on to the higher skills which depends on it.

      Learning method, or crippling method?  Time will tell.

  5. Time to find the local Kumon affiliate.

  6. …But the “break apart” is exactly what the standard algorithm does, only vertically instead of horizontally.

    • Crimson Wife says:

      Bingo. It just makes explicit what is going on in the standard algorithm.

      • and adds a little practice in being conscious of place value, a concept that many 4th graders don’t quite understand.

  7. Mike in Texas says:

    The “break apart” method has been around for awhile, but its usually called the partial products method

  8. Ze'ev Wurman says:

    Sorry guys, this is plain stupid.

    First teach everyone to do it fluently and efficiently. There is a good reason why it’s called the standard algorithm.

    When using numbers extensively, some will pick up mental tricks over time. Nothing wrong with spending a lesson or two once in a while — long after they have mastered the standard algorithms — to explicitly show such “tricks” and the special situations when they are helpful to use. But routinely expecting fourth graders to use those inefficient and specialized tricks for mentally handling large numbers? Pure stupidity.

    It’s one thing to try and develop mental fluency with 1-2 digit numbers — they’re a helpful building blocks for almost any math. Developing mental tricks for large numbers? Have we gone mad? What is it needed for?

  9. Roger Sweeny says:

    I see two arguments here. One says that doing it this way to start makes sure that children develop an actual understanding of what happens when you do addition or subtraction. They can then proceed to the standard algorithm. Because of their understanding, they will make better progress in later math.

    Another argues that too much time and effort will be taken up by this method, and lots of kids won’t actually get a permanent understanding. The class will be behind and crippled in its ability to proceed. Better to have them do the standard algorithm first and once they’ve mastered that (and maybe developed some confidence in their mathematical skill) try to get them to develop deeper understanding.

    These are two empirical hypotheses. As far as I know, we don’t have the data to choose between them AND HAVE NO PLANS TO GENERATE THAT DATA. Which is symbolic of much of what is wrong with education.

    • two empirical hypotheses…

      Roger, your approach would be reasonable if the main goal was maximum efficiency of instruction or some such metric. Personally, I don’t believe that this is the point of most educational theory and practice these days. We’ve got social justice, self-esteem and what not that seem (to me) to have a much higher priority. Heck, we aren’t even really serious about “safe” schools in some cases.

      The data could probably be generated, it’d take a while because we’d need some longitudinal tracking; but, I suspect, the results would likely conflict with other priorities. Oh, and we can’t usually pay attention to an idea long enough to see the fruit it bears; we’d switch to another fad long before the answer was obtained.

      • Roger Sweeny says:

        The people who run schools and school systems certainly have multiple goals, but I think they honestly want good instruction. However, they don’t have the data to decide what is good instruction.

        It bothers me that this doesn’t seem to bother them.

        • Singapore math produces the highest achieving students in the world. I would say that data is pretty convincing. Beyond that Korea, Japan, and Finland also use the break apart method and they also have sky high results on international tests. Is that enough data for you?

          • Roger Sweeny says:

            No, not at all. It’s like saying that people who speak English are, on average, the richest people in the world. Therefore, speaking English made them rich.

            What kind of data would convince me? If half of Finland’s and Korea’s students were randomly assigned to Singapore math and half to something different and the Singapore math group had consistently higher results. And I’d want to be sure that any dropouts weren’t lost track of. For example, if students dropped out of the Singapore math group because they thought it was “too hard,” the students left in the Singapore math group would be those who had better math abilities and would do better anyway. (This kind of problem is common in drug studies.)

  10. As Kiana said, the ‘break apart’ method is the standard algorithm, written sideways. Singapore teaches this method, and it helped my son (who is now great at doing math in his head). First, it teaches you to do it ‘break apart’, and then it shows that the standard algorithm is the same thing, only vertically. I’m not sure that it even adds an extra lesson compared to a standard book. I don’t really understand using a bunch of drawing techniques, though, once students understand what multiplication represents.

    One problem in evaluating complaints about common core is that many parents can’t do math. One mom I know has complained a lot about her kid needing to draw and explain 2 digit addition, which he understands and can do. While manipulatives and drawings can be a great teaching tool, the point is to move on, so I don’t understand why kids who can do math should continue to draw it for years. However, the same mom complained about them having to put fractions on a number line, saying it was too vague. While she or her kid may not remember that 8/2 is 4, it is as specific as a math problem can be and isn’t new – I did it as a kid, and my kid does it with Singapore Math. So, while some common core things are just craziness, it’s hard to tell from parent complaints what is overkill and what is parents who never really understood math.