Wednesday, December 21, 2011

Learning From Your Mistakes

Recently, Younger Daughter's teacher has sent home YD's workbooks from their math program, Investigations in Number, Data, and Space.  Looking through these books, the first thing that strikes me is the (large) number of uncorrected errors.  Does the teacher correct these workbooks at all?  If not, what's the point?

Older Daughter told me that in her experience, this is one of the main differences between public and private school.  She was amazed to find that in her private school, they go over the homework the next day, in class, with the goal that everyone should understand all the problems.  Back in public school, homework might be graded, but there was no attempt to fix mistakes.

I don't get it.  What good does it do Younger Daughter to write wrong answers, if she's never corrected?  It's actually worse than not doing math at all -- she's confirming wrong ideas.  On this page, she's made a consistent mistake, thinking that "doubling" is the same as "putting a 1 in front of".  (Hence, "4 doubled is 14", "7 doubled is 17", "9 doubled is 19", and "8 doubled is 18".)

I can see why YD thinks that schoolwork is mostly a question of filling things out.

When I work on Singapore Math with YD, I check her answers immediately after she writes them, and if the answer is wrong, I erase it and we go back over the problem.  Every page is filled out correctly by the time we're done.  Isn't that how it's supposed to work?

While we're at it, I can't believe the amount of wasted paper in the Investigations workbooks.  They use an entire page for one simple addition problem.  This also results in worse handwriting -- YD's handwriting is neater in the Singapore Math workbook, which gives smaller spaces.


  1. Suburban Chicken FarmerDecember 21, 2011 at 10:21 AM

    I think the mistake was a language (possibly auditory processing) rather than number sense here.
    Take the first problem as your example or template, without other instructions. 10+?=20
    Plugging 10 in the rest makes sense to me. (I don't think she was just putting a '1' in front)
    I bet your little girl can "double" no prob when she understands that's what the problems are.

    Her teacher should have done a better job, really.
    This kind of stuff drives me batty.

  2. Thanks, SCF! I see your point. I'm planning to go over this with YD after she gets home today -- I'll see if that's what the problem was.

    It doesn't help that her reading skills are not wonderful -- I'll try getting her to read the text while I'm at it. It's entirely possible that she couldn't read "Doubles" at the top of the page.

  3. It doesn't help that the worksheet doesn't explicitly say to double the numbers. You just have to infer that by the fact that the pot is called "the doubles pot." If your daughter is already having trouble reading then having to make inferences at the same time just makes things worse.

  4. Update: I went over the page with YD. The good news is that she was able to read "Doubles", and she understood that she was supposed to double the numbers, which means adding a number to itself.

    The bad news is that she didn't want to do the page because "it isn't homework!" (it doesn't have a backpack logo at the top of the page) and "the teacher said it was OK!" (Me: "the answers are wrong and we're redoing it.")

    With some prodding, she eventually got the page filled in correctly. Did she originally think it was just about adding 10? Who knows? I didn't want to ask her directly for fear of confusing her.

  5. In defense of the paper-wasting...I remember my workbooks in school never seemed to have enough space. I'd end up writing on top of what I'd already written, or starting off in normal handwriting and then trying to write really tiny, or erasing and ripping the paper or getting big smudges all over it. An otherwise quick and painless assignment would become frustrating, and my paper was a mess.

  6. Megan, I guess it's hard to get the exact right amount of white space. In your case, you should have been allowed to use extra paper.