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I hope someone has encountered this issue and can provide guidance.  My 12 y.o. DS is highly mathematically gifted, but has "detested" math since First Grade because of the slow pace of teaching in a classroom.  We removed him from a well-respected private school because the pace was making him miserable and put him in a school designed for gifted children, where he still found the pace incredibly frustrating.  Largely because of this, I began homeschooling him last year.  Because I am not at all good at math, I did a lot of research (including on these boards), and thought the Stanford/GiftedandTalented on-line program might be a good fit.  He aced the course but, because of the way the program is structured, we did not realize until the end that, while he can complete algebraic problems in his head, he does not know the mechanics of writing out the steps (and, more problematic, gets the answers wrong if he tries to write out the problem).  He basically "sees" the correct answer, but can't work through a problem to get there.  He was finally starting to feel good about math, and I am loathe to have him repeat an entire year of Algebra with, which will almost certainly cause him to hate math again.  Has anyone encountered this issue in his/her child?  If so, what did you do?  We are contemplating letting him move on to Algebra II (which does have a lot of Algebra I review) and just making him write out the problems from here on out, but I'm concerned that if he can't write out problems at this stage, he may still not be able to.  Eventually, he's not going to be able to hold all the numbers in his head!  I'm sorry for the length of this post - just thought a lot of background would help in the analysis.  I would be so grateful for any guidance.

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At some point, he will need to write out the problems in order to be successful - and he will be more motivated to do so at that point - though he may need to be taught how to do that properly.  I would definitely have him write them out properly in Alg 2 as I imagine that is such a point.

As an aside, look at AoPS if you haven't already, as it was written for gifted math students.

Edited by wapiti
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This is a definite challenge to overcome.  I don't have a specific recommendation, but around the age of 12 my kid started to be willing to write out steps.  I don't know what exactly changed.  By 13 I enrolled him in math courses at the CC.  He just finished Calc 1.  I took Calc 1 too (long story short he has always been homeschooled and I got him as far as I could go, but wanted to continue myself).  So we'd sit down and study together and he'd correct me on steps!  He did a 360 in this department!  It's rather funny.

 

Only tiny suggestion I have is since he learns quickly, he doesn't have to do a ton of problems.  Look for a math program/book that doesn't have tons and tons of practice or that lets him move through at a pace that suits him.  AoPS (that maize recommended) might fit the bill. 

 

AoPS does on-line courses too. 

 

 

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At some point, he will need to write out the problems in order to be successful - and he will be more motivated to do so at that point - though he may need to be taught how to do that properly. I would definitely have him write them out properly in Alg 2 as I imagine that is such a point.

As an aside, look at AoPS if you haven't already, as it was written for gifted math students.

This is the right idea. Don't sweat the detailed steps until he can't progress without them. It should be desirable to write down steps in order to free his brain to think. For now, it's inconvenient for the teacher, not the student.

 

If he can do advanced problems without writing, he IS doing the steps - in his head. Don't worry - it will get harder.

 

I wouldn't even assume algebra 2 is that point. Our boys (both) needed AoPS challengers and tougher physics problems to get them to write. They do write.

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One last point: making a child write down all steps actually punishes them for using working memory. It's good they can solve complex problems in their heads.

 

What is difficult - for the teacher - is understanding where they need help when they do. If you know they aren't cheating, work on this issue, instead of the mental math non-issue. You can even write down steps as they state them. It well help demonstrate the value of putting pen to paper. (BTW, yes, we make the kids use pen, not pencil - a good mathematician should not destroy his/her work, even if it hits a dead end).

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A lot of our kids have been through this phase, so there are a number of threads discussing it. Here is one:

 

http://forums.welltrainedmind.com/topic/565942-ease-doing-math-mentally-but-struggling-with-writing-it-all-down/?fromsearch=1

 

In our case, I usually had my child write out a couple of problems from each section rather than only writing the answer that just appeared in their head: "Demonstrate to me how that kind of problem works, and then you can move on."

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One last point: making a child write down all steps actually punishes them for using working memory. It's good they can solve complex problems in their heads.

 

What is difficult - for the teacher - is understanding where they need help when they do. If you know they aren't cheating, work on this issue, instead of the mental math non-issue. You can even write down steps as they state them. It well help demonstrate the value of putting pen to paper. (BTW, yes, we make the kids use pen, not pencil - a good mathematician should not destroy his/her work, even if it hits a dead end).

 

Where were you when I was sweating bullets over this?

 

I worried my way through wondering what would happen because I could not get my kid to write down steps and the common opinion seems to be it's absolutely direly necessary for success.

 

It turned out fine. 

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Where were you when I was sweating bullets over this?

 

I worried my way through wondering what would happen because I could not get my kid to write down steps and the common opinion seems to be it's absolutely direly necessary for success.

 

It turned out fine.

For classroom settings, it is essential because one teacher cannot simultaneously observe 30 individuals. That limitation is lifted for home schoolers and tutored sessions.

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My kids were willing to write out working for the one or two questions in their AoPS online classes. They did most of the online homework in their heads even for calculus.

 

I worried my way through wondering what would happen because I could not get my kid to write down steps and the common opinion seems to be it's absolutely direly necessary for success.

My DS12 reverse engineer working to get credit for free response questions type of exams. When he looked at how credit is given for the AP Calculus exam, he wrote out working after he wrote the answer down. This kid will write for credit but not a letter more. He will try to be as concise as possible.

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My DS12 reverse engineer working to get credit for free response questions type of exams. When he looked at how credit is given for the AP Calculus exam, he wrote out working after he wrote the answer down. This kid will write for credit but not a letter more. He will try to be as concise as possible.

 

I see my kid doing stuff like this!

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It's also necessary, frankly, because for every 10 students who think they can do the work in their head about 1 actually can and the rest can do a few steps in their head and then get the wrong answer about 50% of the time. But they want to do their work in their head because "the smart kids do". So it's still a good thing for a classroom teacher to enforce.

 

For my college classes, the rule is that: Short problem, no work, correct answer, full credit. Short problem, no work, incorrect answer, no partial credit. Long problem (and I'm pretty generous here, but if I as the instructor would write down work to get the correct answer I consider it long), no work, no credit, regardless of correctness of answer.

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Well, and I know in a one on one situation this is less of an issue, HOWEVER, I never knew if I would be able to homeschool always.  KWIM?  So I tried to at least keep one toe into the idea of maybe my kid would have to go to school for some reason and I didn't want to set him up for difficulties.

 

 

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If you plan to use the AoPS algebra book, you might consider skipping directly to the Review and/or Challenge Problems at the end of each chapter.  If he he has trouble with the Review Problems, then go back and reread and do the relevant exercises.  If the Review Problems are too easy, do the Challenge Problems, which might be fun for him, if they aren't too easy.  

 

For inspiration, you can watch some of the best math students in the country compete in the Countdown Round.  (Save time and skip to about minute 22.)  In particular, watch Luke Robataille from Texas (starting at minute 45)...what he can accomplish using only his working memory is simply amazing. 

 

PS, Luke is homeschooled.  

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My tremendous thanks for all of these responses!  (And thank you Slackermom for pointing me to a prior link - I'm not sure how I missed it).  I feel slightly less in the wilderness on this, and appreciate the recommendations.

 

We started with AoPS at the beginning of the year and I switched to Stanford/G&T because 1) I was pretty sure I would be out of my depth with AoPS pretty quickly and Stanford/G&T offered a standby tutor (who we never wound up using because he pre-tested out of most of the units - although I did have him complete the units for completeness); and 2) AoPS seemed like a hard grind, and my goal this year was to get him excited about math (the books were a grind - but the videos are fabulous, as if Dr. R wrote the videos directly for my son).  Now I'm wishing we stuck AoPS out.  For those who used AoPS, but may not be "mathy" people, were your kids able to proceed through the books on their own (perhaps with the aid of the AoPS videos), or do they really need someone who knows Alegebra II well to run questions by?

 

Again, I can't thank you all for taking the time to respond.  I am so grateful! 

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Switching between algebra I & algebra II might be tricky.  Much of the traditional algebra II is in the "Introduction to Algebra" text.  The "Intermediate Algebra" text has the balance of algebra II plus a whole lot more.  If you are thinking about it, you might need to have him work through some examples and challengers in the early chapters of the first text...

 

After that, it can be self-taught, but a tutor should be at the ready.  Most kids need some support, because they aren't used to fighting through challenging math problems.

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Can he explain it and teach it to someone else? That has been my acid test as to whether DD really understands the steps she's skipping. If she can explain it to someone else and teach it, she knows it. Even AoPS doesn't necessarily require writing it out for her benefit-only for whoever is grading the work.

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