Gifted Issues Discussion homepage Forums Learning Environments Woe is DD

I like Primary Grade Challenge Math by Edward Zaccaro and then the next one is Challenge Math.

This one looks good too...Becoming a Problem Solving Genius: A Handbook of Math Strategies by Edward Zaccaro

While I was out of town, I left DD a division problem to convert to words, and she was not successful - every word problem she wrote was a multiplication problem.

When I got back, I gave her a sheet of paper with "Write the equation you need to solve the problem. A full set of blocks has 100 pieces. How many blocks does Alex have if she has" across the top, and a list in the form "x sets" down the side. She filled it in in no time at all. When x was a whole number or decimal, she correctly wrote a multiplication problem. When x was a fraction or percent, she wrote a division problem. Oh, dear, not good. And completely consistent with our observation that she was almost always fine with whole numbers and almost always wrong with fractions.

So I talked at her for a long time, while she sat with her fingers in her ears. "I'm bored!" "Nope, you're frustrated. Bored is when you already know the answer, not when you don't know it and really wish you did."

Finally, I said, "If this were a multiplication problem, do you have the two factors, or one factor and the product?" And she could answer that question for every problem I threw at her. And knowing the answer to that question, she could correctly identify whether the word problem called for multiplication or division, and could set the division problem up in the right order. Every single time, without hesitation.

OMG. That is not a gap that would have been remediated in the classroom. Time might have resolved it, but I don't think time alone would have been sufficient. I had a similar mental block years ago in my professional life, where I always arrived at the right answer in my workpapers, but wrote up the entry that changed the official records backwards. And I did that for years (like 10 years - long past the time my work was being reviewed routinely), making the change, checking the results, and reversing everything because it was backwards. Then one day I suddenly realized how the workpapers related to the change entries, and I never made that mistake again.

Kid-who-learns-by-epiphany is hard to teach. (And as an adult who learns by epiphany, I can attest that it is a frustrating way to learn, too, when the epiphany does not come quickly.)

Alexsmom, you have just described both dd and myself exactly. I took me until my 30s to understand this because I just thought (and I think teachers did too) that when this happened I was reaching the limits of my capabilities. It was extremely limiting. Once I realised it opened up a whole new world.

I see the same in dd. She has a FSIQ of >145 and if sit with her while she's stuck I can usually figure out the block eventually. But it's very time intensive and I only get there in the time I do because I know her well. It makes it extremely difficult in advocacy - she's skipped and in all the top groups in class, but because she gets blocked her teachers think she's reached her limit and seem to have the approach "skipped, top of the class - this is her limit and it's very much good enough". But once she's passed the block she can understand an entire concept without further instruction and it's there, locked in - but of course it'll be repeated at increasing levels of difficulty for years (elementary school). And her teachers only see that she was blocked so therefore she might know it now, but she didn't and so needs the repetition It's happened again and again. Sorry - OT - just excited to hear the 'learns by epiphany thing described by someone else!!

Yep, and then you look like the pushy parent of the kid who's very smart - but not quite as smart as mom thinks.

DD's other parent is a much better teacher of math than I am, and generally a better teacher of DD (because DD and I are similar enough we butt heads). But when it comes to a block, I'm the one who needs to identify and resolve it, because DD goes wrong in such unusual ways that the similarity between us becomes a help, rather than a hindrance.

I've heard of classrooms with "fraction means divide!" as a mantra - wonder whether that might be the root of this mistake? Glad it's sorted, anyway!

Learning by epiphany, blocks - does this indicate too great a tolerance for not understanding the first time a mistake is made?

I have too low a tolerance for not understanding, which (used to) get(s) me into trouble in situations where a lot of information is dumped on me at once too fast to understand it. I had trouble with my first hard university maths lectures, because I'd get stuck at the first line I didn't understand and get nothing from the rest of the lecture. These days, I have a special mode I go into in seminars after the point of nonunderstanding, that lets me still get something, but it was hard to develop. But on the plus side, it means I rarely make the same mistake twice in technical matters, so your workpapers/change entries example is strange to me: I can't quite imagine having let the first instance go before having understood what was going on enough to never make that mistake again.

There must be a happy medium somewhere. Maybe a chat about a mistake being a sign of a learning opportunity, which should be taken full advantage of, is in order?

Related, come to think of it: DS was getting frustrated early in the AoPS geometry course with repeatedly not being able to see immediately what to do. I encouraged him to make a list of useful techniques (assign variables to things of interest; angle chase; find similar triangles; drop a perpendicular, etc.). Now he (mentally or actually) consults the list as needed, and after each problem that he finds hard I encourage him to consider why it was hard; does something need to be added to the list, or were the right techniques there but hard to pick out?

Oh, this is SO my DD and I... and sometimes, my DH.

Unfortunately (or is it fortunate?); she is a blend of both parents, but has my "learn by epiphany" thing in spades.

It's so aggravating. You reach a point where you aren't even sure that instruction and instructional materials ARE effective. At all.

It's frequently nothing-nothing-nothing-nothing- BANG... mastery.

It's been a real challenge to teach her things like "the writing process" and note-taking skills. They just aren't in her native lexicon as a learner, if that makes sense.

(I mention this in case you were wanting a preview into middle school and beyond.)

I suspect it did arise either in "fraction means divide" or in "to divide by a fraction, you multiply by the reciprocal." I originally thought the entire issue was that she was doing too much of the setup in her head, and confusing the original fraction with the reciprocal.

I think it's not a tolerance for not understanding. Erroneous belief that you are understanding, maybe, followed by a complete lack of insight into why that understanding was not producing the desired results.

DD as a preschooler was desperate to read, and begged me to use the "teach your child to read in 100 easy lessons" book. She got stuck on blending (an early step that the authors saw as so easy that they had no suggestions for what to do when your kid could not do it, which suggestions they did have for common sticking points), and no amount of effort on either of our parts would unstick her. So we gave up, and a few months later, with no effort at all, she could suddenly read anything.

She was the same way with walking - there was no incremental improvement, just bang, one day she stood up and walked without ever falling. Same with talking - she talked so little that she looked way behind, then suddenly she was way ahead.

From my own perspective, I completely thought I understood. I could have repeated back verbatim the usual explanation given in school for how to set the entries up. I'd carefully review it before I created an entry, look at each aspect and compare it to the rules, set up the entry, double-check against the rules. Everything looked right to me. And it was wrong every single time. I even thought about just reversing the entries I thought were right up front, rather than confirming they were wrong first, but I was reluctant to do that because I was sure I was right this time! (In my case, I think I was thrown off by the classroom mantra that "credit doesn't mean negative." As it happens, in my workpapers negatives are always credits, which makes setting up the entries trivial.)

OMG, "the writing process." We had that last year, with the fifth grade writing test. DD was staring at a blank piece of paper while everyone else happily wrote, during practice sessions in school. When I was studying for licensing exams, I tried doing practice essays, and not only did I spend most of my time starting blankly, but the auto-grader was giving me falling scores on the ones I was able to write. And I had no issues on the actual test, and got a high score. DD represented that she had no trouble writing on the actual test, but we won't have her scores until September or so.

I'm holding out hope that she won't have AP classes where notes are turned in for a grade. I've still never mastered the at of taking lecture notes. I tried for a while in college, because that was what you were supposed to do, but never managed to capture anything that was worth reviewing. If I could write something meaningful down, I already understood it, and if I didn't understand it, whatever I wrote down was worthless. As an adult, my notes from continuing education lectures are limited to "affects Client X," "this is incorrect," and "look this up." I'll take notes on reading if the concepts are too complex, or too fragmented, for me to understand by slow and diligent reading. But for straightforward material, it's already all right there - why waste time producing a less-useful version of it?

Alexsmom you have exactly described my relationship to note taking. Except that I now have a health problem that effects my memory, so it's no longer necessarily true that I will remember what I understand - but I still can't take notes....

How did it go, do you think?