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Discussion Starter · #1 ·
DD is 10. She is homeschooled.

We have been working on fractions for the last month or so - for the most part she enjoys it.

Where we have issues in when I ask her to show her work.

She was adding mixed numerals, and doing it in her head, and getting the answer right (example: 2 &1/2 plus 4 &3/4). I, however, was worried that once the numbers became more complicated she wouldn't be able to "do them" in her head. I tried to show her how to do them on paper, and honestly, it went over like a lead balloon.

a) she does not like to do paper works. She fidgets and does not focus and....well, you get the picture

b) she struggles when asked to do stuff on paper. She is brilliant at the mental math - but paper stuff -


Please note I am not asking for busy work or for her to write out the answer in complete sentences - merely that she keeps track of stuff on paper as opposed to in her head.

She scored quite high (hit the ceiling, actually, on the part of the WISC associated with visual spatial gifts) and I think I am more audio-sequential. Oh, I am a little visual spatial - but the way I learned to do math was quite orderly and step by step.

So, I am a bit at a loss. How the heck do I help someone do math who seems to learn it differently ?- and how do I reconcile my desire for her to show her work with her lack of desire/inability to do so?

Kathy
 

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Hey Kathy,

I think I am headed in the same direction with my son. He is only 6 (this month he'll be, that is) and he adds and subtracts in his head. He's right when he does it, but I have no idea how it plays out in his head.

IME as a former elementary school teacher, the number one reason I asked students to show work was because I could not sit with each child to hear them give answers. The second reason, of course, is to "show proof" that the student understood *my* method (whichever was the focus of the lesson).

So, I am wondering if, as homeschoolers, you really need the "proof" when you can be there with her? Can she explain how she gets her answer?

We are unschooling, so soon I will probably be more apt to want to see what my son knows on paper (just to reassure myself, probably). But, I am prepared for the hemming and hawing that will probably occur.

I know that's not really helpful...wish I had better advice.
 

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I was your daughter.
And beyond gifted in math and HATED writing it out--it was "a waste of time" blah, blah, blah.

My son will be writing it out. Doing things in my head became a habit and when things got complicated and I NEEDED to write it out--I struggled with getting all of it down because I'd write out part of it (thinking that was the only part I needed to write) and then it was piecemeal. It wasn't even remotely natural OR learned to write it out.

And this carried over into other stuff, too. When I was in high school, I didn't take notes and to this day, I really don't have a clue HOW to take notes. The reality was: I NEVER needed it until it was too late. When I went to teach high school, I actually sat in on a co-worker's lesson on taking notes to help ME finish grad school. Blech. I had no idea how to study, either. Any argument my teachers made was met with my parents telling them to make it part of my grade. "How can I reprimand her when she's getting As and knows the content?". Fair enough--right? I also changed schools almost annually until high school--so they were always learning these things the year before or after I was there (same for grammar-which I still don't know well).

We are also homeschoolers and I totally get what the pp said. But my personal experience (which may or may not be anything like your daughters) lends me to feeling like I DO need to push mine to at least learn HOW to do it even if he doesn't do it all the time... kwim? Just enough that I know he CAN do it (without the process itself being laborious) in case he needs to. Same with taking notes and studying.

I'm 37yo and still a voracious learner. But it was a lot harder than it needed to be if someone would've forced me to come out of my head once in a while.
 

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I was one of those kids who refused to show work on her math homework and exams, and my teachers often marked off for it. I still harbor deep resentment for the time I failed a math test for failing to show my work despite getting EVERY problem right.
My teachers accused me multiple times of cheating (somehow) because there was "no way" I was able to do it in my head. Honestly, I think showing work when it does not help one to get the answer right is a total waste of time and I will NOT be asking DD to do that if I end up homeschooling her. (Unless, of course, it helps her to get the work right.)

I do think there is value in being able to explain how to do something (which is basically what writing the work out is), but I don't see why doing that over & over again is necessary once understanding has been demonstrated. And I think if a kid can explain it orally there is really no need to write it down. JMHO.
 

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Math is a language, really several symbolic languages. We use it to communicate ideas about quantities, changes, trends, physics, chemistry, probability, logic and lots of other things. The reason you have to 'show your work', at least a bare minimum, is because the person looking at it isn't telepathic. If you're trying to prove something using an argument with words you have no problem with showing the words. Basic arithmetic can be done in your head, but showing the process with fractions means you can use the process when doing things like rational equations that have things like 3x(2x+4) and 6x+9x for denominators and numerators. If you have access to an Algebra II book you could show your DD examples of complex problems that are in the form of fractions and use the same rules as fractions do to solve.

The above reasons worked when I was teaching gifted 7th grade math. You can also explain that people use higher maths (number theory, group theory, linear algebra, etc.) to prove ideas. And then other people use the maths developed in those proofs to invent new technologies.

Maybe you could compromise and have her show her work in at least one of each type of problem.
 

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I really appreciate the insights. My DD is also gifted at math - she freaks us all out with how she can do figures in her head. She says she's guessing, but her answers are correct 99% of the time - I can't imagine how she's getting the figures.

My biggest concern is that her school's math curriculum is obviously different from how she does math in her head. So she makes mistakes on simple things, like 7-4, that she's *known* forever. Then she gets discouraged and decides she's "bad at math."
I haven't talked to her teacher about it, because if I told the teacher the sums/percentages she pulls out of her butt at home, no one would believe me.

But I tend to agree with heatherdeg - that kids need to at least understand how they're getting the correct answer, although I wouldn't force them to do it over and over as mindless busywork. My SIL works at an engineering university, where these crazy-smart gifted kids come in, never having had to crack a book. Then they fail out, because they don't know how to study or take notes. The lost potential makes me
: .

I also tend to believe that people who are naturally gifted at something, whether math, music, baseball, or whatever, need to understand technique. Otherwise, when they run into a snag, they won't know how to get themselves out of it.
 

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Discussion Starter · #7 ·
Quote:

Originally Posted by dillonandmarasmom View Post
Hey Kathy,

So, I am wondering if, as homeschoolers, you really need the "proof" when you can be there with her? Can she explain how she gets her answer?
.
It is not proof so much - I am more concerned that when the numbers or operations become more complicated she will be in trouble. I know people can learn skills (like writing out work) later - but sometimes it is good to start out on the right foot rather than break habits later, yk?

There are two issues I am seeking guidance on:

1. Is it necessary for all kids to write stuff out in math and why? If it is not necessary for some kids - who are they?

2. If it is necessary to write stuff out, how do I encourage it without having a math session dissolve into fidgetting or unpleasntness - which is counter-productive to learning anyways?
 

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What kind of conversations have you had with her about it.

If you haven't already done so I'd start with a conversation about WHY people show work. What is the point? What problems might it cause if she doesn't show work? Why is it important to be able to communicate mathematically? And, then try together to come up with a compromise solution. One idea might be to work WITH her to write it out together at least once for each kind of problem (just to make sure she really gets what "writing it out" means - often kids don't get this and it is easy to assume they get more than they do). And, then don't aim for repetition than she really needs to get it - most curriculum have way more problems than some gifted kids will need.

In other words, I'm suggesting to appeal to the fact that she is bright by giving hear a real understanding of why this is important and involving her in creating a solution. That is really different than just telling a kid you'll be in trouble later if you don't get it.
 

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Visual spatial learners have a very hard time with "Show your work" type of assignments. The reason being they don't conciously go step by step. They see the whole thing and know the answer. It's good to encourage writing out steps in math because it can help, but making it a nessicary part of the work will likely backfire. It can make the work much more difficult.

Annecdote: A girl I went to school with was much like that, she could do math but when it came to writing tests she would go step by step and almost always get the wrong answer. But the step by step was required and so she ended up having to sit tests with making a choice between the right answer or the right method. She was willing to give up a few points for the greater good so to speak and would get back tests with almost every question being 4/5 because the steps taken where right, but the final answer was wrong. And yeah, she still has some level of belief that she can't do math even when the evidence says otherwise.
 

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Quote:

Originally Posted by MusicianDad View Post
Visual spatial learners have a very hard time with "Show your work" type of assignments. The reason being they don't conciously go step by step. They see the whole thing and know the answer.
I'm a highly VS person and I agree with this -- I know I tend to make leaps without necessarily working out all the pieces in between. And that was fine when I was doing simpler things, but really came back to bite me when I got older because I was in the habit of going with my leaps and didn't have any way to check and make sure I hadn't missed something. I think it's important to be able to write out all the steps both so you can communicate your work, and so you can check yourself when the work becomes more complicated.

And for what it's worth -- you might look up some of the breakthrough math solutions by top mathematicians -- you have to assume those people are true math geniuses, but they certainly have to write out the steps to their answers just like anybody else! Otherwise they couldn't communicate or prove the solution to everyone else, right.
 

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Quote:

Originally Posted by Aufilia View Post
I'm a highly VS person and I agree with this -- I know I tend to make leaps without necessarily working out all the pieces in between. And that was fine when I was doing simpler things, but really came back to bite me when I got older because I was in the habit of going with my leaps and didn't have any way to check and make sure I hadn't missed something. I think it's important to be able to write out all the steps both so you can communicate your work, and so you can check yourself when the work becomes more complicated.

And for what it's worth -- you might look up some of the breakthrough math solutions by top mathematicians -- you have to assume those people are true math geniuses, but they certainly have to write out the steps to their answers just like anybody else! Otherwise they couldn't communicate or prove the solution to everyone else, right.

Yeah, but I think there is a big difference between the work that you are "supposed" to show in school and the steps real mathematicians write out. If mathematicians had to write out every single step, it'd just be silly. E.g., if I have to go from x+y=z to x+y-y=z-y every single time, I'll go nuts. It makes perfect sense to go right from x+y=z to x=z-y. YKWIM? And my understanding is that mathematicians certainly do skip the steps that are obvious to their peers.

I get that it might sometimes be important to show how one reaches the result, but I think you can do that without showing every single blasted step. And I think an overemphasis on showing steps can kill the joy math-loving kids feel at learning new things and figuring out new types of problems.
 

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Quote:

Originally Posted by no5no5 View Post
E.g., if I have to go from x+y=z to x+y-y=z-y every single time, I'll go nuts. It makes perfect sense to go right from x+y=z to x=z-y. YKWIM? And my understanding is that mathematicians certainly do skip the steps that are obvious to their peers.

I get that it might sometimes be important to show how one reaches the result, but I think you can do that without showing every single blasted step. And I think an overemphasis on showing steps can kill the joy math-loving kids feel at learning new things and figuring out new types of problems.
Very, very true. I'm no mathematician, but I am a BSc in physics and no I don't do every. single. inane. obvious. step.

Not unless I'm actually talking someone through the process for the first few times. My profs never cared much either. The obvious is the obvious. In school though, when doing algebra we actually had to write down why the next part of x+5=y-3 is x+8=y. It's so painfully obvious, but we had to actually write the 5+3=8...
 

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I would say that whether or not it is important for her to show her work deppends on why she doesn't want to.

If she doesn't want to b/c she doesn't really understand how the steps work, then it is important to show the steps. There really is a need to understand the steps, even if one doesn't need all the steps everytime, you are correct that in the future the math will be more complicated and she may need the steps.

However, if she doesn't want to write it out, simply b/c writing is hard for her, then who cares. By the time she needs to write stuff out to solve problems (I would say around when she starts algebra or geometric proofs) her writing skill will have improved, and she will have the need as motivation.

So, you need to figure out if she understands the process b4 you know whether or not writing out the work serves a purpose. Of course the easiest way to tell if she gets the process is to look at the written out work. Maybe you could mke a deal with her that if she writes it out correctly once, then she won't have to do it for that type of problem ever again.
 

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Quote:

Originally Posted by kathymuggle View Post
She scored quite high (hit the ceiling, actually, on the part of the WISC associated with visual spatial gifts) and I think I am more audio-sequential. Oh, I am a little visual spatial - but the way I learned to do math was quite orderly and step by step.
Kathy -- I'm wondering if your dd's reluctancy to write down her work is because she doesn't "see" the steps in a linear fashion and *can't* write them down. She may be processing in a totally different way. I don't know much about WISC -- but hitting the ceiling for VS definitely could be what the issue is for her.

I agree with the pp's that it is important for her to learn how to write it down in a way everyone else will be able to understand her process -- but not make her do it for every single problem. It may be very likely that this will be challenging for her -- more so than getting the right answer. She will need to learn how to translate her internal language, so to speak.
 

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Discussion Starter · #15 ·
Quote:

Originally Posted by Roar View Post
What kind of conversations have you had with her about it.
.
This is a good point. I need to do a better job communicating with her on why I think showing work is important

Quote:

Originally Posted by eepster View Post
I would say that whether or not it is important for her to show her work deppends on why she doesn't want to.

If she doesn't want to b/c she doesn't really understand how the steps work, then it is important to show the steps. There really is a need to understand the steps, even if one doesn't need all the steps everytime, you are correct that in the future the math will be more complicated and she may need the steps.

Maybe you could mke a deal with her that if she writes it out correctly once, then she won't have to do it for that type of problem ever again.
I think the reason she does not want to write out the steps is because she thinks it is unnecessary (as she often gets the right answer without doing steps) and she does not really understand how they work (she has some perfectionism issues - she is not keen to do things when she is not assured of success).

I think the advice to get her to show or even say the steps for one question in a group is spot on. It will be tricky to even get her to write one answer - she really flounders when asked to show her work. I think some of the root of it is perfectionism,though, and we will just have to work through it.

Thanks, everyone!

Kathy
 

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Discussion Starter · #16 ·
Quote:

Originally Posted by LauraLoo View Post
Kathy -- I'm wondering if your dd's reluctancy to write down her work is because she doesn't "see" the steps in a linear fashion and *can't* write them down. She may be processing in a totally different way. I don't know much about WISC -- but hitting the ceiling for VS definitely could be what the issue is for her.

I agree with the pp's that it is important for her to learn how to write it down in a way everyone else will be able to understand her process -- but not make her do it for every single problem. It may be very likely that this will be challenging for her -- more so than getting the right answer. She will need to learn how to translate her internal language, so to speak.

Very true. This is what I was attempting to say earlier with my references to VS. She does not come to answers the same way as I do - and it makes me wonder how much to push in this area. Am I just pushing my audio-sequential upbringing on her? Or is knowing how to write down steps important for anyone who is mathy - and how do you facilitate that in someone who is highly VS?

PS. I think I talk too much, lol! I need to ask her how she comes to her conclusions instead of showing her how I came to mine - and expecting her to apply my steps to problems she is doing.
 

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I'm in the same boat - both my children dislike showing their work. One, because he has written expression issues, and I think the other may be a more VS learner.

I'm very sympathetic to the view that gifties shouldn't have to do unnecessary, rote and repetitive work. I know it can be difficult to show the process when they have simply leapt to the answer. However, I've encouraged them to show their work especially in math and science problems. I agree that math is a language, and "showing their work" is part of communicating.

One of the posts above demonstrates another good reason for showing your work:

Not unless I'm actually talking someone through the process for the first few times. My profs never cared much either. The obvious is the obvious. In school though, when doing algebra we actually had to write down why the next part of x+5=y-3 is x+7=y. It's so painfully obvious, but we had to actually write the 5+3=7...

It's very easy to make a small error, early in a long math proof or complicated scientific calculation, and have to go back and figure out where it all went wrong. If there is some work shown, it's a little easier to work out where the problems are.
 

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Quote:

Originally Posted by kathymuggle View Post
Am I just pushing my audio-sequential upbringing on her? Or is knowing how to write down steps important for anyone who is mathy - and how do you facilitate that in someone who is highly VS?
Nope -- I wouldn't say that you are being pushy, but she does need to understand that eventually she will need to communicate her process. I remember reading something about Einstein saying that after he figured out *something* it was an arduous process to figure out how to get it down on paper. He did know that it was important to *prove* whatever it was that he was trying to prove. Just coming up with the answer wasn't going to cut it with his peers.

And I have no idea how to help you facilitate this. I'm recognizing this potential problem with my ds. The other day he was working on some math and was mumbling under his breath, "dial to 7, now dial to 3, ok....(incomprehsible blah, blah) - yup. There it is." He *rarely* speaks while doing math, and I probably had a quick glimpse into his thought processes. It was on the surreal side *for me.* Perfectly normal, I suppose, for him.

Thought of something - You can try to see if it's possible that once she comes up with the answer if she's able to work backwards or start in the middle since her process probably isn't a start to finish kind of thing.
 

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Quote:

Originally Posted by LauraLoo View Post
Thought of something - You can try to see if it's possible that once she comes up with the answer if she's able to work backwards or start in the middle since her process probably isn't a start to finish kind of thing.
I think this is a really excellent point. It might even be what Silverman suggests in Upside Down Brilliance - I vaguely recall that someplace she has a suggestion on this but I can't remember what it is at the moment.

I also think it takes into account the fact that it's hard to show steps if you literally didn't take any steps. Or took very few. Or figured it out in a manner that wasn't really a step by step way. In such case, showing work would require a "translation" of sorts into a step by step process- which would be time consuming and might require lots more mental effort than it took to solve the problem in the first place (making right brain talk to the left brain).

(by the way, I think some practice in having both halves of the brain talk to each other is a good thing, I think, especially at a younger age - I finally forced myself to do it as an adult and it was hard!).
 

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Quote:

Originally Posted by Ms Apricot View Post

Not unless I'm actually talking someone through the process for the first few times. My profs never cared much either. The obvious is the obvious. In school though, when doing algebra we actually had to write down why the next part of x+5=y-3 is x+7=y. It's so painfully obvious, but we had to actually write the 5+3=7...

It's very easy to make a small error, early in a long math proof or complicated scientific calculation, and have to go back and figure out where it all went wrong. If there is some work shown, it's a little easier to work out where the problems are.
Except that was a purely visual error.
 
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