Instinctive math students...

[Donna]

My dd(6yo) seems to "instinctively" understand math concepts. She tends to be a whole to parts kind of learner in everything. I am a very sequential kind of person so I find myself having difficulty "teaching" her because she always seems to be a step ahead of me.

 

She tends to learn math in huge chunks that don't correspond to any grade level so fitting her into a math curriculum is difficult at best. (For example...when she was 4yo, I was teaching her what 1/2 and 1/4 meant because she asked...she took off with the tiny bit of knowledge I provided and by the end of her playing and questioning understood how to write any fraction...add and subtract fractions with like denominators...and figure out equivalent. That's just one example...she's done the same with subtracting and adding large numbers with borrowing and regrouping on her own, multiplication, etc...). I loosely follow a curriculum with her more for my benefit...so I know she isn't missing anything.

 

Because she breezes through math, she tends to do a lot of the problem solving in her head without writing down the steps and it leaves me wondering if she even knows "how" she got the correct number. Sometimes, she talks through her problems aloud so I can tell if she understands more from what she says than what she is writing down. Like today, for example, she had the problem (X-456=243). Instead of rewriting the problem to solve for X, she skipped that step and just added up from the bottom erasing the X and filling in the answer. So, I know she has the correct thinking but don't know if she understands why this is the correct thinking if you kwim.

 

I am wondering if people out there with older kids who seem to instinctively know math have found that later, for higher level math skills, they have difficulty?

 

I don't want to force her to learn my way because I know that is just not her way but I want to be sure she has the skills to do higher order math when the time comes.

 

Thanks.

[C_l_e_0..Q_c]

Very quick answer.

My son at 11 is doing Algebra with Lial and not getting into any difficulties.

The main difficulty he ever encountered in math was boredom.

[dawn of ns]

I am wondering if people out there with older kids who seem to instinctively know math have found that later, for higher level math skills, they have difficulty?

 

I did. Things really fell apart for me in middle school. I had a feel for how to do certain operations and it was enough to do well but when math got to the point where I really had to reason out what to do and use a reasoning that came from a good understanding of the operations, I began to tank. I never did well after that. It's only now with homeschooling my kids that I'm starting to see why and fix all the bits that I missed because I could "pass" through half my school years.

[Nan in Mass]

I didn't worry about having him write any math until he was about 7. He did most things orally and I acted as his blackboard. He would figure part of the problem, tell me to remember a number (I was usually driving LOL), and then do the rest and double check with me to make sure he had remembered his in-between numbers correctly. Then we started doing PM, at 1B. At first, I didn't insist that he show his steps or memorize his facts (he could figure them out fast enough that he didn't need to). When he hit long division, he needed to recognize his multiples and found that he needed to memorize them. He also needed to write down a few steps. After about 3B, I tried (not always successfully) to make sure he could write down the steps if he needed to, but I still let him just write the answer, since I thought that in real life, being able to do it in his head would be more practical. When we began NEM (algebra/geometry), I began making him write out the steps, as shown in the book, and the first few months were a constant battle. He was very unhappy with me. He also discovered that if he didn't, he made too many small errors and got the answer wrong. His method was fine, usually; he just couldn't keep track of it all accurately. I fought him into writing the steps and by Christmas, he wasn't objecting quite so much. I still have to remind him. If I don't give him an example of how much "step" I want, I'm likely to get the problem written out, a few hen scratches, and a boxed answer. If I write out an example of how I want this batch of problems to look, he usually does it. He isn't having any more problems with NEM than I would expect. So, for my particular child, it didn't hurt. I was very careful to make sure he could tell me how he got his answers, though. At first, since he was using me as a blackboard and was excited about what he was doing, I could see that he was thinking about math correctly. This gave me more confidence. I knew the groundwork was laid properly. Then later, I just made sure he could do it both the Singapore way and whatever other way he had invented for himself. I think it will work fine, if you are careful.

-Nan

[klmama]

OP - at your dd's age, my ds couldn't explain how he got the answers. He just knew. As he got older, I insisted that he learn the "book" way, whether that was A Beka, Singapore, or something else. He could work it however he wanted in his head, but if his answer was wrong he had to do it the book way on paper. At some points he discovered that the way he had figured out didn't work consistently, or if it did, that not writing things down led to mistakes. Usually, though, he can still do it all in his head. He's doing BCM now, is actually kind of bored, but we are doing it as quickly as possible to make sure he has all the basics down the traditional way before starting formal algebra. He just plays with algebra now, and I don't make him write things down there yet.

Edited February 4, 2009 by klmama
typos, of course

[Donna]

and suggestions to just be careful. It has been helpful to me that she has taken to talking out her solutions. I like being able to know how she is doing her work even if she doesn't want to write everything out. It is also a fascinating window into her problem solving strategies.

 

We will just keep moving along and see how it goes. My next concern will be that at the rate she is going, she will be ready for Algebra by 8yo. I have bought a few supplements this year to slow her down including Singapore's Challenging Word Problems and Challenge Math. Any other suggestions would be appreciated.

[fractalgal]

My dd(6yo) seems to "instinctively" understand math concepts. She tends to be a whole to parts kind of learner in everything. I am a very sequential kind of person so I find myself having difficulty "teaching" her because she always seems to be a step ahead of me.

 

She tends to learn math in huge chunks that don't correspond to any grade level so fitting her into a math curriculum is difficult at best. (For example...when she was 4yo, I was teaching her what 1/2 and 1/4 meant because she asked...she took off with the tiny bit of knowledge I provided and by the end of her playing and questioning understood how to write any fraction...add and subtract fractions with like denominators...and figure out equivalent. That's just one example...she's done the same with subtracting and adding large numbers with borrowing and regrouping on her own, multiplication, etc...). I loosely follow a curriculum with her more for my benefit...so I know she isn't missing anything.

 

Because she breezes through math, she tends to do a lot of the problem solving in her head without writing down the steps and it leaves me wondering if she even knows "how" she got the correct number. Sometimes, she talks through her problems aloud so I can tell if she understands more from what she says than what she is writing down. Like today, for example, she had the problem (X-456=243). Instead of rewriting the problem to solve for X, she skipped that step and just added up from the bottom erasing the X and filling in the answer. So, I know she has the correct thinking but don't know if she understands why this is the correct thinking if you kwim.

 

I am wondering if people out there with older kids who seem to instinctively know math have found that later, for higher level math skills, they have difficulty?

 

I don't want to force her to learn my way because I know that is just not her way but I want to be sure she has the skills to do higher order math when the time comes.

 

Thanks.

 

If she is only six, there will be time for this eventually. I would encourage her to slowly start writing down her work, or at least explain her reasoning to you if she gives you a solution without you understanding how she got it.

 

I have a similar situation with my own daughter who resists writing down how she gets answers to problems. When I ask her her reasoning she will explain it to me, but doesn't understand why she should have to and then tells me she has her own way of doing math. :001_huh: I usually back off but it can be frustrating at times.

 

I notice that you are using Saxon 5/4. It may have too much writing for her at age 6. I would suggest Singapore for a break from Saxon because it has less writing involved. I see you already have the Singapore CWP, but I also suggest the Singapore Intensive Practice workbooks which I think also inspire creative thinking. Were you to use the IP you may want to use the Text and then the IP for clarity.

 

It matters that eventually she will need to show her work, so I would slowly move her that way.

 

Good Luck :)

[Donna]

 

I notice that you are using Saxon 5/4. It may have too much writing for her at age 6. I would suggest Singapore for a break from Saxon because it has less writing involved. I see you already have the Singapore CWP, but I also suggest the Singapore Intensive Practice workbooks which I think also inspire creative thinking. Were you to use the IP you may want to use the Text and then the IP for clarity.

 

The writing in Saxon is not the problem. I write out the problems that she needs to do and she just fills in her "work" and/or answers. She happily does 1-3 chapters a day and never complains about writing (she writes chapter books in her spare time...if only I could get my boys to write half as much as her :glare:). I tried Singapore with her previously and she didn't like the cartoons and such in the book. She wants "big kid" math. Probably at the level she is now it would be more mature looking but I used Saxon 6 with my oldest after someone suggested it was better than Saxon then quickly switched back because he hated it.

 

So, we are fine with the program and adjust as needed. I was just worried about what comes later for a kid like her and if I should start expecting her to show work or just wait awhile and see if she stumbles upon it naturally when things get difficult.

 

Thanks.

[ajjkt]

I was like that. So is my son. I found that I continued to do very well at maths all the way through high school. However, when I hit calculus there were no more numbers. I couldn't "instinctively" understand the relationship of greek letters in the same way I could numbers. As I had always resisted showing reasoning and working out, I could not go that next step into calculus.

 

I explain this to my son when he whinges about having to show me his working out. My daughter is just as bad. "but how do you know that there were ten apples and John ate three that there are only seven left?" "That's how many there are. You asked how many apples are left. I told you."

 

I push it pretty hard, because I feel like I failed myself in refusing to show working out. It didn't become apparent until calculus and by then I didn't want to go back to really basic level maths to learn how I knew the answer.

[fractalgal]

The writing in Saxon is not the problem. I write out the problems that she needs to do and she just fills in her "work" and/or answers. She happily does 1-3 chapters a day and never complains about writing (she writes chapter books in her spare time...if only I could get my boys to write half as much as her :glare:). I tried Singapore with her previously and she didn't like the cartoons and such in the book. She wants "big kid" math. Probably at the level she is now it would be more mature looking but I used Saxon 6 with my oldest after someone suggested it was better than Saxon then quickly switched back because he hated it.

 

So, we are fine with the program and adjust as needed. I was just worried about what comes later for a kid like her and if I should start expecting her to show work or just wait awhile and see if she stumbles upon it naturally when things get difficult.

 

Thanks.

 

I understand now. I thought maybe she was copying all the problems out of Saxon and then not showing her work. That makes sense that you copy them out for her at this age.

 

By the time she is 8 or 9 she will likely show more work naturally, but at that time she will possibly be in Algebra...so yes I'd have her at least begin explaining to you how she got her answer and then maybe have her write a number sentence on paper.

 

I formerly taught math (Calculus and others) at the university level. Showing one's own work becomes very important at this stage - especially when the teacher grades the work. No work shown means no partial credit if the answer is incorrect. For some of my students this meant the difference between passing and failing tests and had a domino effect on the student's final grade.

 

I think you are on the right track with encouraging her this direction.

Edited February 7, 2009 by fractalgal

[LizzyBee]

I used to think Math was something you either get or don't get. I always got it, and I could show my work, but I couldn't always explain why math works the way it does. It seems like people who teach math are those who just get it, and they usually don't do a good job explaining it. With my kids, I am most concerned about whether they understand why a procedure works and they can verbalize it. That, to me, is much more important than writing the steps every time. I make them write the steps often enough to show that they can, then it's optional for that concept. Oh, and when they make mistakes, they have to write the steps with me sitting by their side so that I can identify and show them where they made the mistake.

[JeanM]

You are describing both my myself and my oldest son. He's 9 now (almost 10), and really gets things instinctively. I spent most of my school years fighting teachers because I hated writing things out. I do make my ds write some things out, but he understands why he needs to do that. I don't make him write things repetitively until he hates math.

 

FWIW, I didn't run into trouble in math myself. I took math through 3rd semester calculus. My DH is an engineer and very good at math, but he marvels at the way that ds and I just "get it".

 

Hope this helps,

Jean

[Storm Bay]

My dds are like this, particularly my 10 yo. I still don't insist that she write everything out, but she has to be able to write at least some of it out. Since she's nearly ready for Algebra, I'm working on her learning to put together problems into one long equation instead of steps, but she doesn't like it. However, she doesn't get to do Algebra until she'll do it (she'd like to move on, so it's incentive.) She's not as math savvy as that of the OP (she's more into art and history), but she definitely can do many aspects of math in her head and has her own way of doing things. As long as it will work consistently, I allow her to do things "her" way, but if it's evident it won't, she has to learn the book way (or my way if it's different, whichever works better for her.) fwiw, my eldest does show her work in Algebra. I insisted, and now it's a habit for her.

[lighthouseacademy]

I am a major stickler for showing work. The reason is because my dh is an engineer. I know that the habit of writing the process down is important because if there is an error at the end, then you can go back and find out where you made a mistake and easily fix it rather than solving the whole problem. At first my son balked at me, but since he wants to be an engineer, showing his work wasn't too tough of a sell... also, as they get into more complicated math, there are cases where showing work will be graded (like in college). I won't matter if they can find the answer if they don't show the work too...

I also find that by forcing my son to show his work, I can catch small cases where his instinctual way isn't quite working and then teach that concept. For example, like your daughter, he could get the whole 1/4 plus 1/2 but didn't know exactly what he was doing. When he got to 2/3 plus 5/12 he couldn't quite expand his understanding until I explained the process that he was using instinctually. Had he not shown his work, I wouoldn't have caught that part as easily. I should clarify, I DON'T require obvious things to be written out or things I expect he would do in his head. For example, I wouldn't make him write out 89+56 and show the trading etc. I expect he will do that in his head. I will require the 4698 +5899 to be written though because it is much easier to make an error even if the process is known.

Edited February 9, 2009 by lighthouseacademy