What does math really take?

[OlgaLA]

I was reading the thread below, and finally decided to ask the question that is on my mind more often than not. It was said in that thread that math is really logic. A few years ago I would have totally agreed with it. Now I have my DD13. I have never had her tested for giftedness/learning disabilities, and maybe I should have.

 

Anyway, her brain definitely doesn't work "normally". She is very logical, she is strongly VSL, loves geometry, has no trouble with proofs, but only when I let her do two-columns as she hates writing. And she is terrible at algebra. Well, maybe not really terrible, but still it feels like she is missing a little something, and I can't tell what exactly that something is. It's almost like dyslexia when it comes to mathematical notations. Recently  she was doing a problem, and while I do not remember the topic, she derived whatever formula she was supposed to be using. So she does understand it. The thing is, she was supposed to know that formula since prealgebra. She is also very slow. At some point I thought it might be processing speed, but during practice with CR sections of SAT she finished with at least 7 minutes to spare. And there you have to read it, keep it all in your brain, and then analyze it to answer the questions. So it can't be processing speed, right? Her long-term memory is fine, too, at least when it comes to other things, like noticing a mistake on a map that she looked at, not really studied, weeks ago, but remembering how to deal with parentheses after two years of regular review sessions, is apparently an insurmountable task. So, what does math take that she doesn't have? And how can I help her?

[Gil]

1) I don't know what the "thread below" is that you were reading so I'm no help there.

 

2) You say that she is terrible at algebra (not really, but you know what I mean) but then the only mathematical "flaw" or short coming you mention is that she...what? Derived a formula she was supposed to have memorized a long time ago? Leaves off parenthesis?

 

I'm not sure what problem you're hinting at your daughter having but it doesn't sound crippling or anything. Being careless/sloppy can be rooted in simple immaturity. How did she do with arithmetic? Does she understand that by and large polynomial arithmetic is just arithmetic in base-X?

 

If it helps you feel better, my boys forget details when it comes to algebraic notation from time to time.I have started having them do "warm ups" where they solve/manipulate several expressions and equations but in painstaking detail and they have to use different colors for different symbols. It helps to get their brain paying attention.

 

Have you asked your child to sit down and think about why they are under-performing in math? At 13 she should be old enough to self-evaluate and relfect on her work product. If she's not able to do it alone then have you both sat down and analyzed her mistakes together?

 

If not try doing that with her so that she is tracking to see what kind of mistakes she is making. SHE has to be aware of what she's doing wrong. Her thinking process sounds pretty solid based on what you describe.

[Gil]

Also remember that the algebraic notation that we use is a man-made convention . Placement of parenthesis are no more inherent to math than they are to English.

If she's having problems with the conventions than that is separate from having a problem with the concepts and ideas of math.

 

I could be misunderstanding you, but based on your comment about it being like a dyslexia where math notation is concerned that is what I gather. Don't mesh the two issues if they have nothing to do with each other. Being sloppy is being sloppy, not misunderstanding the concepts and ideas

 

Perhaps to aid in her long term memorization, you could have her do derivations of 1-3 formulas as a part of each days drill/practice work. After she's derived the formula enough you could also have her do copy work with the formulas. Give her a sheet of paper. At the top:

Derive the formula for ________.

Write and read aloud the formula for ____________ ten times.

That would (theoretically) help with speedy recall so that when she is taking a test she is more efficient.

 

 

[Kathy in Richmond]

Deriving math formulas as she needs them is great!  I'd rather see that any day than rote memory in math.

 

Sounds like your daughter is 2E to me, as strongly VSL big-picture learners often are.

 

I have an extremely VSL daughter, and some things that worked here:

-using a big picture curriculum like AoPS

-whiteboard use to ease writing fatigue (my dh installed a large wall board; we took photos of any work she wanted to save)

-colored pencils for note-taking, problem solving, ...anything really (the colors seemed to help her brain track details, esp. in algebra)

-annotate, annotate...even in math (underline or circle what you want to remember as you read to help it stick)

-learn to type and use Latex for math writing

-keep working on speed drills

 

For the last item, I had her work on speed drills well into middle school, till they finally stuck in her brain. I separated this from math class, where she was very advanced concept-wise, but worked at her own speed w/o emphasis on speed.

 

She started taking a couple of online classes around your dd's age: Write@Home and AoPS helped with output for essays and paragraph math proofs. It was a lot more fun pleasing others then mom at that age. :rolleyes:

 

Besides geometry, I've noticed over the years that these VSL kids often excel at counting & probability; you might want to try the AoPS intro book.  Later on, she might also be interested in exploring topology, knot theory, or graph theory (all highly visual).

 

Your dd's high CR ability combined with everything else you wrote suggests stealth dyslexia to me. You might want to read up on that (we believe my dd has it). Here's one article on the Davidson site. These kids have sequencing issues, & that might be what you're seeing with the parentheses?

 

 

[OlgaLA]

Thank you  for your comments!

Kathy, your post especially hit home. I recently started suspecting 2E, just couldn't place that second E. When she was a kid, I thought she was just bright, but in the normal range. She did have a small trouble starting to read. She learned Russian alphabet around 3, but wouldn't blend sounds. I didn't push, and she started reading sometime after English K. So pretty normal. Math was fine. She had and still has executive skills troubles. But the way she talked... I have a son who is ahead of her in many areas, but I feel that she is more gifted, just has to compensate for something. Stealth dyslexia plus dysgraphia symptoms sound eerily familiar although she compensates for many things they mention, such as spelling. I am pretty sure that if I ask her to spell a word she doesn't know/hasn't seen it written, it will be a disaster, but she never had to study for spelling tests. And dysgraphia is almost 100%. She always had aversion to writing anything down. If there is any hope of skipping a word, she will. For a long time she would try to do everything in her head. Now we are at the point when she writes scribbles consistently, and I started requiring her physics problems written out neatly all the way from given to answer. She doesn't like colored pencils, but the glittery gel pens are a total hit. Nothing like a page of physics problems in sparkly pink :) Still, she often has trouble writing down a word on the first try, so her writing is often messy because of all the corrected mistakes, but she knows her spelling.

 

AOPS is working here. I started pre-algebra with her the summer after her disastrous 6th grade. It really helped with her ITBS scores (her school tested during the first few weeks of the year, just before I took her out in 7th grade), and she does fine with it, although I do sometimes  have to explain thing to her in another way. We did have an episode of total wipe out of anything algebra-related from her brain this fall, so I sent her to master Alcumus. She did, and pretty fast, sometimes a few tasks a day. In general, her math has improved a lot since her 6 grade test when she was in 24 percentile for calculations, and from an outside perspective, she is doing fine, It's just I see that she struggles more than she should, given the rest of her abilities. It's kind of like she struggles in the wrong place.

 

And thank you for the recommendation of CP book. She does pretty well with that and it might be just the morale boost she needs to break that "I am bad at math" mindset. I am a bit apprehensive about AOPS class, since it will require both algebra and writing, but I may start with a writing class next year.

 

So, thank you once again. I feel much better now that I see that there might be more to it than just lack of attention.

 

[oscilatorium]

I was reading the thread below, and finally decided to ask the question that is on my mind more often than not. It was said in that thread that math is really logic. A few years ago I would have totally agreed with it. Now I have my DD13. I have never had her tested for giftedness/learning disabilities, and maybe I should have.

 

Anyway, her brain definitely doesn't work "normally". She is very logical, she is strongly VSL, loves geometry, has no trouble with proofs, but only when I let her do two-columns as she hates writing. And she is terrible at algebra. Well, maybe not really terrible, but still it feels like she is missing a little something, and I can't tell what exactly that something is. It's almost like dyslexia when it comes to mathematical notations. Recently  she was doing a problem, and while I do not remember the topic, she derived whatever formula she was supposed to be using. So she does understand it. The thing is, she was supposed to know that formula since prealgebra. She is also very slow. At some point I thought it might be processing speed, but during practice with CR sections of SAT she finished with at least 7 minutes to spare. And there you have to read it, keep it all in your brain, and then analyze it to answer the questions. So it can't be processing speed, right? Her long-term memory is fine, too, at least when it comes to other things, like noticing a mistake on a map that she looked at, not really studied, weeks ago, but remembering how to deal with parentheses after two years of regular review sessions, is apparently an insurmountable task. So, what does math take that she doesn't have? And how can I help her?

 

When you say she has no trouble with proofs, does that mean she can understand it and explain it well? Can she also write down the logical steps of the proof in a paragraph? If so, is it only the 2-column format that's troubling her? Many bright kids are averse to the 2-column format of proofs taught in geometry and prefer the more natural paragraph form used everywhere else outside of geometry class because it's more expressive and less constraining.

 

You say she is bad at algebra, but what about her arithmetic/calculation skills? Can she quickly multiply small numbers and do small computations pretty easily? If she is visual she might be able to see/manipulate some of the smaller steps in her head without having to write down every intermediate step, as is normally stressed in school. Additionally, is she comfortable with negative numbers and fractions and can think about them visually/intuitively (i.e. on the number line)? 

 

Assuming she has no weak spots with arithmetic and doesn't make a lot of computation errors, I don't see why she should have much trouble with algebra. Unless she doesn't really have the intuition in place for how to solve/manipulate simple equations (e.g. one variable linear equations), and is just blindly applying rules learned in school. Given her good logic and VSL ability, she should be able to learn how to solve simple equations intuitively (i.e. think of them visually as balance scales, and visually understand how operations would impact them). For most kids all that is too much; it's easier just to remember and apply the rules, but for her it might be a lot more beneficial to "see" certain steps in her head since she can more easily do that than others.

 

I don't think memory is an issue, it's possible that unless she understands something really well conceptually, she will not remember it long term, even with practice. Her ability to derive stuff is a great thing and suggests that she is naturally using reasoning/logic. This might mean that she cannot pick up something that is partially picked up in her mind, unless she sees/gets the whole picture and how all the pieces fit in. I know I was like this when I was little. I was slow at learning new things well (I could easily pick up simple rules and blindly follow them and was quite good at arithmetic and calculation) but without practice I would forget stuff after a while and would need to re-read, re-derive how the rules worked. I always thought it was a memory thing, but later as I grew older I realized that my "forgetfulness" was not really a memory issue (I could remember all kinds of very specific stuff from the past that was memorable), my issue was that I could not remember stuff that I hadn't fully understood well. In her case it might be that she doesn't really see the reasoning/logic behind certain rules that still feel arbitrary to her, so after a while she forgets them.

 

 

 

[OlgaLA]

She actually prefers 2-column proofs, because she hates writing. We are working on that in other classes, so I allowed her to use 2-colums with AOPS geometry, which teaches paragraph style. It made a difference between geometry being her favorite and most hated subject, and since 2 column proof is an acceptable form of proofs, I didn't push. I do require all steps mentioned and explained, including those that AOPS solution guide skips as obvious.

 

Her computational skills are actually were her lowest subscores in ITBS, with whole number computations trailing far behind fractions and decimal computations. I don't understand how one can do computations with fractions without computations with whole numbers, but I have two years worth of tests to prove it. And she did fine with simpler equations that she could do in her head, although her reasoning was often not obvious to me. That is why Kathy's suggestion that there might be hidden dyslexia involved really rings a bell. Sometimes she looks at an equation and it feels like she has never seen anything like that before. She calls algebra Elvish. I ignored it before, thinking she was just being silly, but there might be more truth to it then I cared to admit. Maybe there are even moon runes involved :) I am not going to test her, as she still performs well enough not to need any accommodations for that, except maybe an advance apology for writing with excessive corrections, but at least I have a grounding point. Before it was total twilight zone for me, now it makes sense and I can deal with it.