kitchen table math, the sequel: Taming the Math Perfectionist

Sunday, August 28, 2011

Taming the Math Perfectionist

(I was going to make this a comment on another post but it got so lengthy and unwieldy that here I am making it a full-on independent post. Pardons.)

Speaking of perfection/distraction/panic/etc, we've finally made a bit of headway with a problem we've been having at our house for some time: my daughter is a pretty bright girl, enough that, well, I really haven't had to teach her anything yet. (My son, I teach; my daughter, I expose and she just does it.)

The dark side to this behavior is that if she comes across something she doesn't just "get" immediately, she shuts down and panics.

[[Small digression for background:

We cruised through Singapore 1 with no hiccups, and I put the brakes on Singapore 2 when it was clear (starting multi-digit addition/subtraction) that she didn't have her single digit facts down cold enough yet. That didn't seem to bother her because while she didn't have immediate recall of the facts, she certainly "got" simple addition, it wasn't a conceptual issue for her. We spent a couple of months working through just Math-U-See Alpha which is nothing but hammering well-grouped math facts until she made significant progress. We're starting back to Singapore 2 tomorrow morning, in fact.

OK, enough digression.]]

A. happens to greatly enjoy computer games, so while we were hitting the math facts hard, I spent some time looking at various math practice sites for her. I ended up giving Math Whizz (based in the UK) a try and we had a bit of a break-through with it.

It started with an evaluation, in which I told her that it was (by definition!) going to ask her questions that she could not answer, because it had to know at what point she could no longer answer questions. She freaked out a little when it got to multiplication and asked me for help, I told her I couldn't help her because that would goof things up -- if it thought she knew multiplication well, then it would be giving her even harder multiplication that she definitely couldn't do. We talked about the fact that she was required to fail in order for it to work. She eventually got used to this idea.

Then, later when the assessment was all over, she was doing one of the lessons which was something she was "sure" she couldn't do and she panicked, asking me how she could get out of it. I came over and said:

"Well, let's take a look at this. You know if you get the wrong answer, it'll just give you slightly easier stuff next time, so no big deal."

"OK, let's just put in all zeroes!"

"Well, sure, we could do that, but let's see if we can get as far as we can with this, and then maybe it can see *how* we got it wrong and use that information to figure out what you need practice with."

So, I left her alone to Fail With Style ... and wouldn't you know she got most of the questions right. When freed to "get them all wrong" because the system needs her to fail if she doesn't understand it, the stress and panic went away, and she went on to figure 8 of 10 of them out. And she was excited by that, instead of freaking out that it wasn't 10 out of 10. (It was 3 digit subtraction with regrouping, which we sure haven't covered officially yet. And, now that I think about it, I'm a little mind boggled that she placed high enough for them to try that in the first place. Hmm.)

I've been worried about what was going to happen once we started hitting things that she just didn't "get" immediately because it was bound to happen at any point and, before, it would have been a disaster for her. I am currently ... cautiously optimistic.


Jo in OKC said...

Hooray! This is a huge step for a perfectionist. And, it's really important if she's good in math and likes it because everyone eventually hits problems that they can't work out immediately.

Math research is, by definition, staring at a problem no one else has ever solved and making progress on it. And, it's usually over quite the long haul.

My daughter did a math research project during the 6 week RSI program this summer and most math profs consider 6 weeks too short to do real math research.

sidheag said...

What Jo says - but I'll go further. This is a great start, but please try to make it an every day (well, at the very least, a several times a week) occurrence that she meets problems she doesn't know how to solve - including problems where she *can't* figure them out. So many people land at university or graduate school having always found maths easy up to that point, e.g., knowing that if they can't do something it must just be because they haven't been taught it yet, and as soon as they have an explanation it'll be fine. Sooner or later, anyone continuing with maths gets to something they have real, extended difficulty getting their head around. Kids who are normal at maths get that before they're 10; not getting it until your 20s can be really harmful. And the more you find things easy, the more exposure to hard things it takes to feel that that's OK.

Also, give her lots of problem solving that isn't aimed at practising any particular technique, so she doesn't know what she "should" be applying.

Things I use or have used with my mathy DS: Enrich (nrich dot maths dot org); Alcumus; the Mathematical Association Primary Maths Challenge past papers; the Scottish Mathematical Challenge; the UKMT Junior Mathematical Challenge past papers.

TerriW said...

Thank you for the advice! I knew this was an issue, but i go back and forth on how to tackle it. I also have to deal with the fact, for instance, that she placed super high in fractions ... which we've never covered. (Though I suspect is due to the copy of Life of Fred we have sitting in the shelf that she likes to pull down and read. And the iPad Motion Math game that she loves.)

So, then, we'll have to get to fractions naturally at some point and she'll be all, "Oh, Mom, this is easy, I know this.". But she has no idea (let alone me yet) where her gaps are! Thank God for theIntensive Practice series -- because even when she thinks she has something nailed, it can help me ferret out where the are gaps.

TerriW said...

Ugh, pardon the goofballs formatting, the iPad leaves much to be desired on that front.

Anywho, with her I sometimes have trouble balancing the keeping her challenged enough with the forcing her to do something she's "got" but not mastered when she's chomping at the bit to conquer new things, if that makes sense. The addition facts were like that.

She would roll her eyes at the fact that she had to work on mastering her facts for months when in her free time she was reading all this stuff that was so far beyond that. And then I'd explain to her that moving on to the "fun stuff" without having a solid foundation would be like the pig who built his house out of straw instead of bricks. And that in math, you need a brick house.

That's an analogy she can wrap her head around (there's only so much forward-thinking wisdom a 7 year old can grok!), and she's been able to accept it. And she can also relate it to the idea of "Well, how much fun was it to learn to ride a bike vs. how much fun is it to ride your bike? You gotta put in the time to master the basics so you can have the fun."

TerriW said...

Oh, and I don't want to make it sound like we did *nothing* but drill facts all that time. I'm not quite that cruel, heh. She got to work through Critical Thinking Company's Mathematical Reasoning book, too, so she could do something laterally while waiting for move forward with Singapore.

sidheag said...

FWIW, I never did drill basic number facts into my DS; I just trusted that they'd end up learned because he used them so much in working out more complicated sums, and so it proved. He did learn his tables, using Timez Attack, which I recommend [though a little while ago I downloaded an updated version and we had trouble making that run - prob. just our antique computer though] but although it was my decision to download it it was his to go to mastery right then; I'd have been happy to leave that a few years too. (Mangahigh's game Sigma Prime is good too, btw.)

I wouldn't really worry about gaps too much; they're mostly very easy to plug as and when you discover them. The only kind I'd worry about is a conceptual gap which means that something higher seems like black magic - if she's solving a problem using a memorised algorithm but not understanding why it works, that's a problem. If it's just that there's something most people who know the other things she knows would know, but she doesn't yet, NBD.

Crimson Wife said...

In our house, we work math at multiple levels. There's exposure to high-level stuff through things like Life of Fred, the Danica McKellar books, Edward Zaccaro's Challenge Math and so on. I even allow calculator use if calculation is the only thing stopping the child from working through a challenging problem.

Then there's working systematically through the regular math curriculum (Singapore Primary Math 5A for my oldest, Right Start Level B for my 5 y.o.) No calculator use permitted in these. I have, from time to time, re-ordered lessons so that the child can continue to work on different concepts while facts are being learned by heart.

At the lowest level is fact practice, which I do separately from the main lesson. My understanding is that this is how Asian countries do it.

lgm said...

Problem of the Day for Elementary School Arithmetic Students. As always, be selective. These are meant to be used by challenging the students, then discussing the solutions and incorportating Polya's problem solving techniques.

Rivka said...

Have you read Carol Dweck's book Mindset? It's been helpful for me in dealing with my young perfectionist, who also panics if she doesn't know something immediately. Because of Dweck, we have a lot of explicit conversations about the value of struggling: "The only thing that makes you smarter is doing hard things."

I learned the hard way never to introduce a math concept or a new format with "this is easy." It seemed to paralyze her with fear that it wouldn't be easy for her, and then she'd be a failure. She responds much better to statements like "okay, this next one is tricky, but I bet we can figure it out."

One thing was surprisingly helpful for us: one day our curriculum (MEP Primary) introduced a new concept by having me put several completed problems on the whiteboard, some of which were wrong, for my child to review and correct. Something about the idea that I had already "made mistakes" freed her up to not worry about doing the same, even though she knew I had just copied the items out of the teacher's book.

Glen said...

lgm, thank you for that.