Should I die on this math hill?

[MamaSprout]

Dd is bright in Math. She's reluctant to do things conventionally. As a result she did PreAlgebra twice after I realized she "logic'd" her way through the first time.

 

Now she is in Dolciani Algebra Chapter 3. She is getting answers right about 85% of the time, but she is not setting up the problems algebraically, and starting to fight me on it. I think it's great she can see more than one way to go about solving something, but she is not learning what the book is teaching, either.

Edited May 10, 2016 by elladarcy

[wapiti]

Make her set up just one problem per day algebraically?  FWIW, my kid with handwriting issues strongly resisted proper setup until systems of equations... or maybe it was the second time through systems of equations LOL when he finally resigned himself to the fact that he was less likely to get correct answers mentally.

[The Governess]

I would require it for at least a certain number of problems.

 

My Dd grumbled about showing her work as well. It's one of the reasons why I put her in an online class that required her to scan and turn in her homework. Lo and behold, when the teacher required her to show her work, she had no problems complying. She was even praised for her neatness and thoroughness. ;)

[Zoo Keeper]

I've got one of those kids as well--very, very good at intuiting the answer, but hates to write out the thought process. 

 

I make him write it out anyway.  Math is a language, and he needs practice in how to write the language properly, or nobody will understand his thoughts as the thoughts become more complex. 

 

 

[Mike in SA]

Is it a problem solving issue, or a reluctance to write? Based on age, problem, and response, I could have very different opinions.

 

I have no qualms with asking a younger child to talk through the process. If they are "intuiting" answers, chances are high that they are doing some solid algebra in their heads, though they may be unaware of the fact. If so, I'd just as soon encourage them for it. Writing will come soon enough.

[MamaSprout]

Is it a problem solving issue, or a reluctance to write? Based on age, problem, and response, I could have very different opinions.

 

I have no qualms with asking a younger child to talk through the process. If they are "intuiting" answers, chances are high that they are doing some solid algebra in their heads, though they may be unaware of the fact. If so, I'd just as soon encourage them for it. Writing will come soon enough.

 

She's really not too young to show her work (almost 11). She definitely is doing some algebra in her head.

 

I know there are some steps, etc, that can be skipped, but sometimes her whole process is harder than it needs to be, although she gets the right answer. I don't want to kill her intuition, but I want her to learn the "regular" process too.

[Paige]

I give no credit if work isn't shown. It's a habit that is needed in higher maths. It organizes your thoughts, keep you on track, allows the student to get partial credit, and allows the teacher to see exactly where a mistake is made so that confusions can be cleared up. I die on that hill in Algebra because I need to know how they are thinking. I want to know if a wrong answer is because of a simple transcription error or if it is a serious misunderstanding of the concept that is repeated in other problems. 

 

I would enforce it now because it is somewhat difficult for some kids to get used to the format and structure of showing your work. I want my kids to learn and practice showing their work while the work is still a little easy so that it isn't too difficult. I think if I let them get to where the problems are so hard that showing your work is absolutely necessary or you are in a mess, then the kid has to focus on learning two things at once. They have to worry about the actual math and they have to worry about remembering how to format showing their work correctly. 

 

If the math itself is pretty easy for her, I'd let her do fewer problems if she shows her work to reduce her stress.

 

 

[SKL]

Sorry dp

Edited May 10, 2016 by SKL

[SKL]

My kid goes to b&m school, and boy was she surprised when she got an F on a math test (4th grade) because she refused to show her work.

 

Aside from being lazy/stubborn, she was confused about just what needs to be shown, which is actually a good question.  Maybe walk your daughter through this slowly a few times, even though she already knew the answer the second she saw the math problem.  :)  I always tell my kids that communication is key and if they haven't communicated what they did (when required), it's the same as not doing it at all.

 

FTR I had the same problem as a kid.  I wasn't called on it until high school, when I was awarded 0% for my brilliance.  :P

[domestic_engineer]

Yes - this is a hill to die upon.  If you are the most brilliant mathematician and solved the world's hardest problem, but can't explain your solution to the world, then it's not worth anything.

 

Regarding "learning what the book is teaching" -- perhaps present the method as just "another tool in your math toolbox."  She might not like it now, but there will be times that she'll need "the right tool for the right job."  So it's important to learn it now.  Later she can choose which "tool" to use to solve the problem.  I like to use the example of a woodworker who has a gazillion different tools ... all for specific purposes to solve his problem.

 

Another idea -- talk about getting an "elegant" solution.  Again - you'll need to right tools/methods to get an "elegant" solution.

 

[justasque]

I find it helps to explain that often the problems that are super-easy to do "the old way" or "in your head", are that way for a reason - the author deliberately chose a problem that would already be easy to do, to demonstrate the "new way" that they are teaching.  It deliberately helps you to see how the new way relates to the old way, so you can understand how the new way works.  

 

If you then use the old way instead of taking the opportunity to practice the new way, then you rob yourself of the chance to see what the author was trying to show you, and possibly of the chance to learn the new way at all.  The problem with that is that, generally speaking, the new way works on easy problems, but also on harder problems where the old way doesn't work.  Math, especially at the pre-algebra and above level, is about adding more tools to your toolbox.  If you're not practicing the new tool, it's not going to be in your toolbox.  

 

I often drive home this point by making up a super-complex problem where the old way isn't going to work, but the new way makes the problem super-simple.  I write the complicated problem on the board, and solve it with much flourish, explaining that the author is laying a foundation for problems that will come two or three years down the road.

 

Knowing WHY the author is asking the student to solve easy-peasy problems with seemingly klutzy methods can help the student to accept the process.  

 

Smart kids can use mental math instead of written work for a long time, and the longer they go the harder it is to jump in and start using the written approach when they need to.  I've taught such students, and they were at a distinct disadvantage at a time when they should have been really rocking the subject.

 

[azucena]

I feel as though Lewelma wrote about this with her elder son ... maybe PM her?

[Mike in SA]

She's really not too young to show her work (almost 11). She definitely is doing some algebra in her head.

 

I know there are some steps, etc, that can be skipped, but sometimes her whole process is harder than it needs to be, although she gets the right answer. I don't want to kill her intuition, but I want her to learn the "regular" process too.

That's why we would still at least talk it through. At the beginning of algebra, it's common for a student to not show work as thoroughly as a teacher needs. It's more of an inconvenience to the teacher than the student.

 

That won't last long, though. Pretty soon, brain space will be needed for more complicated manipulations, and there will be no choice but to write or hit a dead end.

 

Early on, it is far more important to reinforce structured, thorough thinking. Writing everything out will not help without that pure, rigorous line of thought. This is a perfect opportunity to build confidence while ingraining the importance of that thought process.

 

You can even be the one to write it out, just to show exactly how many calculations she ripped through in a short time. Then congratulate her on her speed, accuracy, and natural ability.

 

After that, it's easier to explain that there are going to be problems which won't fit in her head at a single go, and besides, it helps you see where you can help most effectively.

 

Lots of kids go through this stage. As long as they aren't unduly pressured, almost all will grow out of quickly. Some respond well to pressure, but most will just learn to believe that math isn't their thing.

 

Both of our kids went through this, btw. I've had lots of students with the challenge even as late as calculus...

[chocolate-chip chooky]

My 10yr old resisted writing out working for maths too and still does as times. This is the cue for me to up the level to where she needs to write it. If problems have enough steps, then she really needs to jot it down. Some things, like algebraic inequalities, really need to be handled quite neatly.

 

When she was younger, I'd ask her to "talk me through" how she did it. She'd very often do things in intuitive ways that weren't what the book/program wanted. I viewed this as a positive. She was demonstrating a true understanding of concepts and not just parroting back a step-by-step process.  I'd then sometimes work a problem myself and ask her to watch me, to see how I'd tackle it. Same as someone above said, I emphasise that it is really helpful to have a range of strategies at hand, so you can choose the best tool for a particular problem.

 

It's also helped that she has two older sisters, both now at uni, one doing maths. She knows that mathematical communication is part of the assessment criteria.

 

So, at 10, I'm focusing on understanding, celebrating intuition, building mathematical communication skills gradually, and offering alternative methods to build up that tool kit.

[MamaSprout]

Okay, I will stand my ground on this, but maybe move some things to the whiteboard. That worked well when she was younger.

 

We're doing most of the problems listed on the maximum track in the TE. Maybe I could assign fewer from each lesson. We really like that selection of problems because there isn't much busy work other than some of the A level problems.

[chocolate-chip chooky]

My daughter's maths is always done on a whiteboard.

I think that it eases her perfectionistic tendencies a bit - it's so easy to wipe it away and start again, and it doesn't have the sense of permanency of pencil and paper work. She seems more willing to take risks on a whiteboard.

 

I take photos of her whiteboard maths for my records, sometimes a bit sneakily and sometimes with a 'wow, I really want to remember how you did that!'

[Xahm]

One way our high school math teacher got us seeing the value was designing very hard problems we weren't really expected to solve correctly. If we only gave an answer, it was either right or wrong (and would result in a grade that was dangerously low). If we showed our work and were on the right track, we got generous partial credit. This wasn't for all assignments, but it convinced some pretty stubborn teens to show work. Well, one boy did drop the class over it, so it isn't a perfect method.

[PinkyandtheBrains.]

Dd is bright in Math. She's reluctant to do things conventionally. As a result she did PreAlgebra twice after I realized she "logic'd" her way through the first time.

 

Now she is in Dolciani Algebra Chapter 3. She is getting answers right about 85% of the time, but she is not setting up the problems algebraically, and starting to fight me on it. I think it's great she can see more than one way to go about solving something, but she is not learning what the book is teaching, either.

 

Yes, I would fight this battle.

 

It will matter as she reaches even higher levels of math.

[MamaSprout]

Today I stood and worked with her (she has a counter instead of desk). I solved and she solved and we sort of worked together. She was very motivated to beat me, and things went very smoothly. She did finish before me on two problems, but one wasn't quite right. Anyhow, if she went about it by logic, we walked through the correct method, which was always faster. I also dropped two longer problems from the set.

 

We both thought it was fun. I don't always have and extra hour in my day, but I think I will try to stand with her on days when her work isn't review or a test.