Math Advice Please -- Not Curriculum Related

[Haiku]

My dd12 is very good at math and has an intuitive sense of numbers and how they work together.

 

She also doesn't like to follow directions.

 

These two things combined are turning math into battles for us.

 

She is using Dolciani Pre-Alegbra, which she likes. I go over the lesson with her, and we work some or all of the classroom exercises together, and then she does the assignment independently.

 

If I were keeping a grade in math, I estimate that she would have a C. This is not because she doesn't understand or can't do the problems. It is because she always wants to play around with the problems to see whether she can find her own way of doing them. Sometimes this works out for her, and she makes discoveries and connections that I haven't. Sometimes it doesn't work for her, and she just gets the wrong answer.

 

I'm getting tired of looking at pages of calculations that don't make sense to me because they are the product of her mental meanderings and not of the process she was taught in the lesson. If her answer is right, it's ok, but if it's wrong, I don't know why because I'm not privy to her process.

 

I know that the simple answer is to require her to work each problem the standard way before she plays around with alternative methods, and I have asked her to do this, but she says that if she does it the standard way first, the excitement is gone and she no longer wants to try different methods. So frequently she just skips the standard method and does her own thing, resulting in a decent amount of wrong answers.

 

I don't want to quash her curiosity and creativeness, but I'm starting to feel like I am wasting my time going through lessons with her if she's just going to do her own thing anyway. And it's causing lessons to take longer because we have to go back and correct the ones she got wrong by using an invented process that didn't work.

 

Please do not suggest that we try AOPS. We've both sampled it, and we both hate it. I want to stick with Dolciani, which we both like and which I feel is an excellent text, but I want to find a happy medium that does not result in us arguing over math.

 

Suggestions?

[LinRTX]

Would it be possible to do it her way first, then do it according to the lesson. She could see if she got the same answer both ways. If not, maybe she would like to look at why her way did not work.

 

Linda

[Dana]

When I grade student tests, I tell them they won't get credit for just the right answer... they have to show the work.

They don't have to use my method, but they do have to have the work written out clearly enough that someone else in the class who got the question wrong would be able to understand why the answer was correct just from the written work.

 

Part of writing math correctly is the explanation.

We have formalized and standardized certain procedures. If you're using something different, you need to write (in words) more explanation of how you arrived at your answer.

 

I would mark an English paper written in text speak wrong.

Same for math where there are just meandering numbers and not a clear flow of logic.

 

Boy and I went some rounds on this for a while, but I kept showing him student work and he's come around.

[regentrude]

If I were keeping a grade in math, I estimate that she would have a C. This is not because she doesn't understand or can't do the problems. It is because she always wants to play around with the problems to see whether she can find her own way of doing them. Sometimes this works out for her, and she makes discoveries and connections that I haven't. Sometimes it doesn't work for her, and she just gets the wrong answer.

 

I'm getting tired of looking at pages of calculations that don't make sense to me because they are the product of her mental meanderings and not of the process she was taught in the lesson. If her answer is right, it's ok, but if it's wrong, I don't know why because I'm not privy to her process.

 

I know that the simple answer is to require her to work each problem the standard way before she plays around with alternative methods, and I have asked her to do this, but she says that if she does it the standard way first, the excitement is gone and she no longer wants to try different methods. So frequently she just skips the standard method and does her own thing, resulting in a decent amount of wrong answers.

 

I don't want to quash her curiosity and creativeness, but I'm starting to feel like I am wasting my time going through lessons with her if she's just going to do her own thing anyway. And it's causing lessons to take longer because we have to go back and correct the ones she got wrong by using an invented process that didn't work.

 

I consider her approach EXTREMELY valuable and much more valuable than simply following the recipe given in the lesson. If you do not want to spend the time or are unable to follow her calculations and ideas, you might want to find somebody who is able and willing to take look over her work and discuss where her approach has merit and where she went astray. This is how she will gain a deep understanding of math. If she is encouraged to think about the problems her own way and not forced to simply jump through hoops, she will eventually also master the book's way of solving the problem - but somebody needs to take her thought processes seriously and make the effort to discuss math with her on the level that is needed for her to evaluate her ways of solving. With good feedback, her problem solving skills will improve. With no feedback and discouragement of her independence, she may become turned off math altogether, and that would be a shame.

 

Playing with math and THINKING about the problems instead of following a practiced procedure is not a "waste of time". It is the best way to develop an in depth understanding of math.

 

I would also work with her on clearly showing her work and communicating her thought process in a way so that it is understandable to another person. But you need to teach her how to do it - you can't expect her to simply know how to write out math.

ETA: When my kids developed solutions that I could not immediately grasp, I had them explain their thought process to me. You can use a whiteboard for this purpose. Talking through a mathematical thought process and explaining it to another person is also extremely valuable!

[JanetC]

Dana's on the right track here.  But, beginniers need step-by-step instructions on what "showing work" means.

Approach your DD's work with curiosity, not frustration.  Follow it as far as you can, then say, "I got lost at this step.  What's going on?"

 

There are two possible answers:

 

1. I forgot.  --> OK, do it again and come show me right away while you still remember.

2. I was doing X --> OK, here's how you could make that clear next time (demonstrate how to show her work)

 

Continue to the end, where you get to the answer or the mistake.

 

 

[Haiku]

I would also work with her on clearly showing her work and communicating her thought process in a way so that it is understandable to another person. But you need to teach her how to do it - you can't expect her to simply know how to write out math.

 

I have been doing this, and this is where things break down for us. Her usual answer is, "I just did it that way." She doesn't like having to explain herself and will resist doing so. Even getting her to write her steps vertically down the page or number them or do anything else to make them understandable is a battle. Sometimes she will do part of the problem on a whiteboard and part in a notebook, so when I go over her problems I don't even have her complete thought process, as she has erased the whiteboard and moved on.

 

I have talked to her many times about the "language" of math, and how people use who math need to have a standardized way of "speaking" and writing the language so that they can understand one another, and that she can't just make up her own format and expect anyone else to be able to follow it.

 

I recognize the value of her playing with math. That's why I posted this thread and asked for suggestions. But she is not really interested in having her style crimped in any way. She wants to do what she does without any sort oversight. I'm willing to work through her problem-solving process with her if she will make even the slightest attempt to make it readable, but she doesn't want to do that. And she's not so much of a math genius that she doesn't still need help now and then.

[unsinkable]

Can you pick out a certain number of problems to correct but then leave the rest for her to solve as she wants?

[regentrude]

I have been doing this, and this is where things break down for us. Her usual answer is, "I just did it that way." She doesn't like having to explain herself and will resist doing so. Even getting her to write her steps vertically down the page or number them or do anything else to make them understandable is a battle. Sometimes she will do part of the problem on a whiteboard and part in a notebook, so when I go over her problems I don't even have her complete thought process, as she has erased the whiteboard and moved on.

 

I have talked to her many times about the "language" of math, and how people use who math need to have a standardized way of "speaking" and writing the language so that they can understand one another, and that she can't just make up her own format and expect anyone else to be able to follow it.

 

I recognize the value of her playing with math. That's why I posted this thread and asked for suggestions. But she is not really interested in having her style crimped in any way. She wants to do what she does without any sort oversight. I'm willing to work through her problem-solving process with her if she will make even the slightest attempt to make it readable, but she doesn't want to do that. And she's not so much of a math genius that she doesn't still need help now and then.

 

In that case, I do not see a way to remove the battle. The battle over correctly writing down math is so important that you have to fight it. I'd give her choices: writing out the entire solution on paper, or working on the white board and narrating. Maybe it would help if you could be there with her when she does her math so she can narrate as she goes through her process.

But there is no way I'd let her get away with not writing stuff down. This is not negotiable. I'm sorry to have no easy answer here; you are correct in insisting that she writes it out. And again, maybe she would be more cooperative if you could outsource and this requirement were posed by an outside teacher who is not her mom.

I do not know what arguments will convince her. Maybe tell her that she will receive zero credit for her math answers in college if she can not document the process by which they have been obtained in such a way that the instructor will understand.

[*Lulu*]

I agree wholeheartedly with Regentrude. You don't want to squelch her desire to look at math from a different angle than the one prescribed by the book.

 

In the short term, while you work on getting her to the point where she is consistently writing *her* method in a way you can follow, would it help to allow her to work it her way but any she misses must be reworked in the method the lesson outlined?

[Haiku]

I do not know what arguments will convince her. Maybe tell her that she will receive zero credit for her math answers in college if she can not document the process by which they have been obtained in such a way that the instructor will understand.

 

I did tell her that when she finishes Dolciani and moves into algebra, I will have to keep an official grade for her because she will be earning high school credit. I told her that each problem will be worth two points: one for a correct process, and one for a correct answer. I told her that if I can't reasonably understand her process by looking at the steps she took, she will not earn the point for correct process. I explained to her that this means she could get every single problem in the book correct and still fail the class by earning only 50%. She said that she understands and that she will do it when she's in algebra.  :rolleyes:

[Haiku]

In the short term, while you work on getting her to the point where she is consistently writing *her* method in a way you can follow, would it help to allow her to work it her way but any she misses must be reworked in the method the lesson outlined?

 

This is pretty much what we have already been doing, and it makes for very long math lessons.

[JanetC]

I have a fiercely stubborn kid, too, so I feel your pain.

However, she also takes a lot of pride in her work, so putting a large percentage grade on her assignment is enough to make her be a little more careful.  I've also found that I can be as rigid as she is when I need to be.  You aren't going on until you can get XX% or higher on this type of problem.  Period.  (I can google math practice sheets all year if I have to...)

 

Also, I know you said you hate AOPS, but their graders mark down HARD for poor style, even if the answer is correct.  There are articles related to showing work clearly on their website http://www.artofproblemsolving.com/Resources/articles.php?  Entering math contests and losing for sloppy work might work, too. 

[foxbridgeacademy]

I had one son try to go this route; he just wasn't neurologically developed enough to do all the writing for both solutions (the teacher's plus his alternate route).  I let it go and signed him up for math club which he loved.  He tried not showing sol'ns again in PreCalc...at that point I looked at him and asked him what he thought a class was for, and was he a teachable person. 

 

I would suggest assigning only the C problems and giving her the choice to do as many of the B problems as she wishes...all with solutions. Boardwork is fine, she can take a picture and turn that in.

:iagree: I would assign a certain number of problems, say 15.  Tell her that 10 of them MUST be done the correct way and 5 her way.  Grade her on the 10 and give extra credit for the others if she gets them right.  Later add in the stipulation that if asked she has to "show" how she got to the right answer, if you can't figure that out just by looking. I wouldn't stifle her creativity, no matter how frustrating it is.

 

 DS can do most math in his head(the quadratic equation is causing him a bit of trouble) but he often misses a step here or there.  So he ends up with the wrong answer.  So I let him do quite a few "in his head" but if they're wrong then he has to go back and "show" his work to get the right answer.  We also do a lot of problems together, I do it on my paper he does it on his and we see if we both came up with not only the same answer but also if we did it the same way.  We're pretty evenly matched speed wise.  He's better at math then me but I write faster and I show all my work so I don't make simple mistakes. 

[regentrude]

I would assign a certain number of problems, say 15.  Tell her that 10 of them MUST be done the correct way and 5 her way.

 

Please replace "correct" by another word, like "standard", "traditional", "from-the-book".

An alternative method of solving the problem developed by the student is not necessarily "not correct".

This goes beyond mere semantics and has to do with a fundamental attitude about mathematics.

[Catherine]

I've also dealt with something similar. I was able to eventually get around it by talking to ds. I explained that the book was trying to teach a method of problem solving that we would soon apply to more complex problems. Then I made sure we were doing those kinds of problems very soon. It took a few go-rounds, but eventually, he got the idea. I've had to return to this argument several times.

 

I think there's a fine line between encouraging creative approaches to problem solving, and making progress in learning NEW methods that seem harder at first.

[FriedClams]

In that case, I do not see a way to remove the battle. The battle over correctly writing down math is so important that you have to fight it. I'd give her choices: writing out the entire solution on paper, or working on the white board and narrating. Maybe it would help if you could be there with her when she does her math so she can narrate as she goes through her process.

But there is no way I'd let her get away with not writing stuff down. This is not negotiable. I'm sorry to have no easy answer here; you are correct in insisting that she writes it out. And again, maybe she would be more cooperative if you could outsource and this requirement were posed by an outside teacher who is not her mom.

I do not know what arguments will convince her. Maybe tell her that she will receive zero credit for her math answers in college if she can not document the process by which they have been obtained in such a way that the instructor will understand.

Totally agree.

 

BUT, I agree with the quote above - showing work is a hill worh dying on. In my house not showing it - even if the answer is correct - makes it wrong. When you get it wrong you do it again, and sometimes I add one for practice. I'd also start grading - for real - and have natural consequences for poor grades. Most transcripts require an Algebra 1 grade so if get her facing the music now.

[Ali in OR]

I taught high school math, I have an engineering degree, I worked in high tech, and I hang around with people who solve difficult problems for a living (like dh). The process of how a problem is solved is at least as important as the answer. No engineer can just say "the answer is 7.38"; they have to be able to communicate (by writing steps) how a problem was approached and solved. It is fine to have a non-standard or unique way of solving a problem, but it must follow mathematical rules and someone who is mathematically literate must be able to follow your steps and verify them. The process is at least as important as the answer. And frankly, if she is getting wrong answers than there is something wrong with her process--there is some error in her mathematical thinking. She needs to be showing her steps to find out where the thinking went wrong. 

 

 

DS can do most math in his head(the quadratic equation is causing him a bit of trouble) but he often misses a step here or there.  So he ends up with the wrong answer.  So I let him do quite a few "in his head" but if they're wrong then he has to go back and "show" his work to get the right answer.  We also do a lot of problems together, I do it on my paper he does it on his and we see if we both came up with not only the same answer but also if we did it the same way.  We're pretty evenly matched speed wise.  He's better at math then me but I write faster and I show all my work so I don't make simple mistakes. 

 

Don't let him do them only in his head at all. As you point out, that is how mistakes happen. But more importantly, his work needs to be verifiable. In real life, there isn't always an answer key you check. The thinking will be verified by someone else tracing your steps or doing the same problem in a different way. If the answers turn out different, you better be able to determine why. And as your son progresses in math, it will be too complex to do it in his head. It is better to learn how to show the important steps now in Algebra than to hit a wall and not be able to do any math at all because it is too complex to do in your head. People who are really good in math and problem solving don't do it all in their head--they work out the key steps on paper.

[Elisabet1]

I would continue to let her play with the numbers. She might be a mathematician some day! BUT, I would make her correct all wrong problems in the end to show she knows how to do each one. If she gets it her special way, great. If not, then she needs to show some way to get it.

 

Another idea is to pick, maybe half the problems, where regardless, she has to show she can do them the way the book said to. But, I always make my children correct all wrong problems. 

[kiana]

Rather than trying to figure out her work, I think that she should simply start over on the incorrect ones if sufficient work is not shown for you to easily follow her work. It is not the grader's responsibility to figure out what convoluted process the student was trying to use.

 

I would let it be up to her, though, if she wants to spend her free time trying to do the problem her own way instead of playing. This is a very valuable mindset to have.

 

Showing work IS something she needs to work on -- but don't let it come at the expense of exploration.

[Arcadia]

I told her that each problem will be worth two points: one for a correct process, and one for a correct answer.

For my older's algebra unit tests for his online school, the correct answer is worth about 20% of the marks for each question. When I was in high school, the correct answer was only worth 10% of a question.

 

The process has to be clear enough that no clarification by the examiner is needed. I'll make her redo only those she got wrong though else math might take forever.

[Serenade]

If her answer is right, it's ok, but if it's wrong, I don't know why because I'm not privy to her process.

I have one like this and it's so time-consuming. I once had to spend an hour on one silly problem, trying to figure out what my son did to get the right answer. When I finally did, I felt his method was OK, even if longer and more cumbersome than the traditional way, but geez, what a lot of time and aggravation for me.