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Math: Is there really a difference in thinking styles?...And what do I do?.


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My 10th grade ds is using Saxon Algebra II this year, and he *gets* it. At least, when he does his homework. He gets the right answers when I show him just the test and say, "Look at this problem fresh." But invariably he is getting C's on his tests. (sometimes A's, sometimes D's - oh, yeah, guess which one it was today - LOL - :glare:) And most of the errors are negative signs, addition errors - stupid things, kwim?

 

The problem is I *know* he could do better, and he feels rotten about himself because he knows that he knows the material (but he doesn't know why he makes these "dumb" mistakes). I have begged him (for years) to show his work. But, frankly, he doesn't *think* like I think. He can really do all the work in his head. And when I finally do get him to explain to me how he's thinking about math - it's like a foreign language to me! I don't know how to even begin explaining how differently we approach the same problem.

 

I asked my brother about it (he has a degree in Elec Engineering from Ga Tech), and he said it sounded to him that my ds thinks "like a guy" - and that he often made the same kind of errors in college. Not helpful, really. I don't know what to *do* about this - or if I should do anything.

 

DS has the Art Reed videos, and has been doing his work pretty independently. I don't know why, but it seems whenever I try "independent" with my boys, it is a recipe for disaster.

 

At any rate, I am open to suggestions. I have even considered putting my DD (5yo) into public school so I can maybe squeeze in an extra hour or two to work with him one-on-one. (Not that I will be much help!)

 

Thanks!

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I completely believe that he may "think differently". I have observed this with students, and I have also observed it with my children: DD is very good at math but has to work it out - DS just magically "sees" it.

 

This said, even if he sees it, I would MAKE him write it out. Not beg - force. This is a valuable preparation for college. It is not sufficient to arrive at a brilliant solution - part of the learning goal is to be able to explain it to somebody else, using diagrams, formulas and logic accessible to other people. (Chances are that he will stop making his mistakes as soon as he is forced to put things on paper or even to explain it to another person.)

 

I have students every semester who are extremely smart, probably smarter than me, and for whom the biggest hurdle is to learn how to write things down. For some, that is the most important skill they acquire during the semester - because I am quite relentless in enforcing it.

So, aside from being able to comprehend his oral explanations or not, make him write down every single step and do not award credit until he can show his work. Maybe have him think of it like a geometry proof: there, too, it is not sufficient to "see" that the diagonals in a parallelogram have the same length - you have to go through logical steps and prove it. You can promise him that he will eventually hit math so challenging that he must write it down to figure it out - he might as well develop these skills now.

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The problem is I *know* he could do better, and he feels rotten about himself because he knows that he knows the material (but he doesn't know why he makes these "dumb" mistakes). I have begged him (for years) to show his work. But, frankly, he doesn't *think* like I think. He can really do all the work in his head.

 

But the thing is, he *can't* do all the work in his head, because if he could, he wouldn't be doing C work.

 

I finally put my foot down with my 14yo son a few months ago. I wrote up a thing that I put on the wall above his desk that outlines exactly what I mean by showing work. And if he doesn't show his work to my satisfaction, then he does the work over. And amazingly, he doesn't make as many dumb mistakes. Not only that, but when he does make a dumb mistake, I can tell that it is a dumb mistake and not a fundamental misunderstanding of a concept.

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Sounds like my son. He can go several lessons getting an A and then have several pages of C's and D's. :( I don't count homework grades so I'll let it pass if I know he does understand. If he does poorly on a test then a review page will become an alternate test.

 

With Saxon you could take the next lesson and use it as an alternate test. Don't count the "new" material in the test grade. But DO count all the questions/problems that are review.

 

After several times of taking extra tests my son is now more careful and makes fewer mistakes.

 

Just an idea.

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With Saxon you could take the next lesson and use it as an alternate test. Don't count the "new" material in the test grade. But DO count all the questions/problems that are review.

 

After several times of taking extra tests my son is now more careful and makes fewer mistakes.

 

Just an idea.

 

That sounds like a great idea. Thanks!

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Rhonda,

Its very easy to get them to write the work down..... offer partial credit if it is set up correctly, has the correct steps, then a careless error doesn't cost the whole entire problem.

 

I started making dd show her work in prealgebra. I told her that it was teaching her how to set up her problems for when they got harder. No problems since. She actually writes more than the solutions manual does, LOL. My graduated son did the same thing in math, messing up negatives was the number one reason he would miss about 1/3 of his problems.... I made him write steps, went over it with him so he could see (in his steps) where he messed up. The funny thing is that he got the hard stuff right, and messed up the easy things!

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Rhonda,

Its very easy to get them to write the work down..... offer partial credit if it is set up correctly, has the correct steps, then a careless error doesn't cost the whole entire problem.

 

 

 

I have wondered about partial credit (because he does write down his work for about 1/2 of the problems). Art Reed says not to, and it has frankly just been too many years since I took a math class. I *thought* we received partial credit, but honestly don't remember.

 

That would definitely raise his grades a long way. ;)

 

Thanks!

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I have wondered about partial credit (because he does write down his work for about 1/2 of the problems). Art Reed says not to, and it has frankly just been too many years since I took a math class. I *thought* we received partial credit, but honestly don't remember.

 

That would definitely raise his grades a long way. ;)

 

Thanks!

 

 

Hi Rhonda,

This was the ONLY thing that forced our DSs into showing their work: 1 point for the answer, 1 point for showing the steps (even if there was an error in one of the steps of the math). So, to get all the answers correctly but not show the work could only earn at best 50% -- an "F" or failing grade, while showing the work for every problem, even if you don't get the right answer on many of them, will probably boost you to at least a "D" at minimum.

 

Probably just me, but correct answers really mean nothing; I want DSs to understand the process and the math thinking behind it. And that means showing me the steps. And when they whine that they will never use the math again, I say, "Yep; you're probably right. But you ARE learning the skills of self-discipline, logic, and orderliness. And you'll use THOSE skills ALL your life in every aspect of your life. So, let's get on to the next problem..."

 

Still have whining, but not so much. I think they are tired of my "it builds character" answer. :tongue_smilie: BEST of luck, Hugs, Lori D.

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Hi Rhonda,

This was the ONLY thing that forced our DSs into showing their work: 1 point for the answer, 1 point for showing the steps (even if there was an error in one of the steps of the math). So, to get all the answers correctly but not show the work could only earn at best 50% -- an "F" or failing grade, while showing the work for every problem, even if you don't get the right answer on many of them, will probably boost you to at least a "D" at minimum.

 

Probably just me, but correct answers really mean nothing; I want DSs to understand the process and the math thinking behind it. And that means showing me the steps. And when they whine that they will never use the math again, I say, "Yep; you're probably right. But you ARE learning the skills of self-discipline, logic, and orderliness. And you'll use THOSE skills ALL your life in every aspect of your life. So, let's get on to the next problem..."

 

Still have whining, but not so much. I think they are tired of my "it builds character" answer. :tongue_smilie: BEST of luck, Hugs, Lori D.

 

Oh, you are a member of the Draconian Homeschoolers after all! :lol:

 

On a side-note, I let me DS read the responses and he said (during out literature discussion later) that if Sir Gawain got "partial credit" from the Green Knight, then surely he should get partial credit in math! LOL

 

Your method does sound better than my old rule, which was that for each problem that requires a formula, he had to show me the formula. (Saxon always has the monster-fractions-with-scientific-notations and a dozen variables that need to be reduced. I always cross-out things as I cancel them, but he doesn't. Your method would solve that!

 

Thanks, Lori!

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On a side-note, I let me DS read the responses and he said (during out literature discussion later) that if Sir Gawain got "partial credit" from the Green Knight, then surely he should get partial credit in math! LOL

 

:lol: That is so wonderful!

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Hi Rhonda,

This was the ONLY thing that forced our DSs into showing their work: 1 point for the answer, 1 point for showing the steps (even if there was an error in one of the steps of the math). So, to get all the answers correctly but not show the work could only earn at best 50% -- an "F" or failing grade, while showing the work for every problem, even if you don't get the right answer on many of them, will probably boost you to at least a "D" at minimum.

 

Probably just me, but correct answers really mean nothing; I want DSs to understand the process and the math thinking behind it. And that means showing me the steps. And when they whine that they will never use the math again, I say, "Yep; you're probably right. But you ARE learning the skills of self-discipline, logic, and orderliness. And you'll use THOSE skills ALL your life in every aspect of your life. So, let's get on to the next problem..."

 

Still have whining, but not so much. I think they are tired of my "it builds character" answer. :tongue_smilie: BEST of luck, Hugs, Lori D.

:iagree: Our oldest did things mostly in his head and was fairly good at transcribing it all correctly onto paper. Our next one wanted to do the problems in his head, but missed things because he was careless. We started really enforcing showing his work. He "kicked and screamed" for awhile, but even he realized he was doing siginificantly better after awhile! It really helped slow him down enough to get things organized better!
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I completely believe that he may "think differently". I have observed this with students, and I have also observed it with my children: DD is very good at math but has to work it out - DS just magically "sees" it.

 

This said, even if he sees it, I would MAKE him write it out. Not beg - force. This is a valuable preparation for college. It is not sufficient to arrive at a brilliant solution - part of the learning goal is to be able to explain it to somebody else, using diagrams, formulas and logic accessible to other people. (Chances are that he will stop making his mistakes as soon as he is forced to put things on paper or even to explain it to another person.)

 

I have students every semester who are extremely smart, probably smarter than me, and for whom the biggest hurdle is to learn how to write things down. For some, that is the most important skill they acquire during the semester - because I am quite relentless in enforcing it.

So, aside from being able to comprehend his oral explanations or not, make him write down every single step and do not award credit until he can show his work. Maybe have him think of it like a geometry proof: there, too, it is not sufficient to "see" that the diagonals in a parallelogram have the same length - you have to go through logical steps and prove it. You can promise him that he will eventually hit math so challenging that he must write it down to figure it out - he might as well develop these skills now.

 

 

:iagree:

 

My oldest has ADHD and they are *notorious* not not being able to explain how they know the answer. Ds was in ps and passed Algebra despite not writing out any problems. It was a low grade, but he would get 100s on the tests and 0s on the homework.

 

When he homeschooled we fought tooth and nail over him writing his problems out.

 

Now, in college that bad habit is coming back to haunt him.

 

Do whatever it is you have to do to get him to write those problems out, step by step.

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