Friday, November 25, 2011

New Math vs. Old Math

Last summer, I put together a 10 week math workshop for 5-6 year old kids entering first grade the following fall. My approach was math boot camp during the sessions, and to have the kids plod along with a math workbook during the week. I selected Every Day Math (University of Chicago) because it is used in school and I like the approach.

As I was walking around the neighborhood presenting this idea to parents, I stumbled across a sensitive issue. Those parents with older kids found that the new math fails in one respect - the kids forget how to add and subtract. The new math emphasizes problem solving, math applications, conceptual maturity - and drops altogether repetitive practice of the basics - unless the parent sticks to a regimen of 2 workbook pages per night with no skipping of problems. No teacher assigns 2 pages of math workbook per night to first, second, and third graders.

So we've got math for geniuses turning out dummies.

Of course, the problem with the old math which I grew up with is that the child doesn't develop a mastery of the concepts by exercising these under different circumstances. A child can multiple 5 x 3 but doesn't really know what it means, and sees a word problem begging for 5 x 3 and get can't solve it.

The new math is highly qualitative, and you're left to fend for yourself on the quantitative mastery. The old math was primarily quantitative.

The answer is of course you need both. If you use new math in a homeschooling setting, or your child does it at school, plan to supplement it.

I like the new math because it is consistent with gifted and talented programs and with my working theory about the super secret GAT test. If you are in a program that uses the new math, or you are teaching your braniac yourself using the new math, look for supplemental material to reinforce quantitative skills. There are plenty of workbooks that cover math operations without the confusion provided in the new math book.


  1. I know this post is rather old (though trust me I have read many, many of your more recent posts). I'm wondering if you have any suggestions for "new math" workbooks. And I'm talking about for what you referred to recently as Mode #1 for math practice. I don't know "new math" very well, though my second grader is learning it at school (for which I'm happy). But when we're working a couple of grade levels ahead on computational stuff, I am reverting to "old math" because I'm not 100% confident on how to do it with new methods. For example, how do you subtract two three-digit numbers using "new math"? I don't know, so I end up doing the "carrying" business with my son (though I tried to relate it to what he's learned about in terms of thinking in tens). Anyway, I'm a big proponent of the new math, but can't find workbooks that use it for instruction/examples so that I can be confident I'm teaching him the methods he'll eventually use in school.

    Also, I've ordered your Teaching Math Concepts book and am looking forward to using that for Modes #2 and #3 of math instruction.

    And finally, thanks for this amazing, amazing resource. It's level-headed, funny, sane, and research-based when basically everything else written by parents about education is precisely the opposite. (But I do wish it had a search function. I'd love to find the definitive post on "how to" do the Word Board, but I can't find it. I'm digging, though! I'm digging!)

    1. First of all, here's the search feature. Go to google and type in "word board" and it's the first hit.

      New Math depends on the grade level. There are very good books for grades 5-8, but before that, the curriculum is closer to common core, so that's why I wrote the Test Prep Math series.

      Carrying and long division are a disaster for thinking. We subtract or do division, we subtract or divide a little at a time until there's nothing left. Carrying = no thinking, Problem Decomposition = the making of a genius.

      I've been studying all of the math I didn't get in 4 years of graduate school, which is about 84% of it. I see no correlation between success in high school and beyond and the way math is taught today. If you approach solving problems the right way, both today's math and really complicated problems future become easy. I'll have to write an article to elaborate.

    2. Yes, I would like an article on this. BTW, we started doing Test Prep Math yesterday. It is already a hit, to the extent that a workbook can be a hit. I would love to show you a picture of my kid's work on the first page: a weird equation that made no sense to me and generated the wrong answer. Then, as he tried to walk me through that weird equation/wrong answer, he discovered the right way to think of it and knocked that out on paper. It was great. The hats one he did in his head while rolling around on the floor. Then we argued about the hat colors. Wonderful.

      One small comment to think about for future editions. It strikes me that real "checking one's work" is like "reverse engineering." Easy "checking one's work" is telling a child that addition is the opposite of subtraction and have them do the opposite function to make sure their arithmetic is right. But the kind of "checking one's work" that your problems require (what I would call "reverse engineering") is not so simple. I think it's also a skill that needs to be taught. In other words, how do you know that you approached the problem the right way? How do you go backwards to figure that out? That's not so easy.

      The struggle I've had with all of this is that I don't want to be invested in my kid getting the right answer. But he was totally convinced after the first question that he had it right. I knew he didn't. I forced him into explaining his thinking to me, but it makes him very angry and frustrated. From his perspective the problem is done, and what I am asking of him is unfair and pedantic.

      Anyway, so if you go back to that first question in the first section, it would be interesting if the book itself prompted reverse engineering, rather than putting that onus on the parent in such a way that the parent seems to be needlessly putting the child through boring, insulting extra work. With that question, it would have been great if there were two pictures of two cakes: "Draw the candles after the brother got done with it" and "Draw the right number of candles." Then -> "Go back to you answer. Were you right?" In other words, it would be so helpful as a parent if the book sought to help teach reverse engineering as a distinct skill set. Convincing my kid he might be wrong shows him that I care too much about his answers OR that I'm a nag. Neither are what I'm going for.

      These are just quibbles or better just ideas to think about since I find all of this so fascinating. I'm already thrilled with the book, and he seems really engaged with it too. I have yet to crush him with Section 2. I'll keep you posted.

  2. Oh, and I know carrying and long division are awful for thinking. I have enough friends with math PhDs to know that I don't know jack about how math works. At the same time when I'm sitting there with one of those workbooks, I literally don't know how to show it to him the way I know he should be thinking of it (and the way he already does).

    It's so easy for him to break numbers into their disparate parts in his head, and I'm struggling to do it on paper. What I definitely don't want to do is disrupt or help him unlearn his good habits with my garbage ones. That's why it would be nice if I could see this stuff written down in the workbooks themselves. I grasp it conceptually, but struggle turning that into a method/structure for solving an actual problem.

    I love this blog so much. Thank you for it.