Math and showing your work

[mamaraby]

Ds is in 4th grade. Mental math has always been a strength of his, and he is able to do fairly straightforward problems in his head (not long division necessarily). I'd say he's right 80-90% of the time. I feel like he should be showing his work more often if not most of the time and especially if it's a word problem. My reasoning is that in higher levels of math showing your work is pretty much a requirement and so I think it's a good habit to establish now. Ds is rather resistant to this.

 

Is my reasoning sound or should I let him continue as he is and then worry about showing his work later? Or is there a general guideline I can give him to both allow him to do what he's good at while also establishing good habits for later?

[wapiti]

It doesn't have to be all or nothing.  You could require showing work for one problem per assignment or something.  Or assign harder problems.  Either way, eventually the math problems themselves will demand writing.  (FWIW, for my mathy reluctant writer, he didn't hit that wall until systems of equations in algebra.)

[Tsuga]

You are right. He is being short-sighted, of course, but he's a child so that's normal. This is a regular battle in our home.

 

Many kids hate showing work because showing work is work. :) He is not alone. Empathy--yes, this is tedious, I get it, but it's necessary--could be helpful.

[Kuovonne]

To me, showing your work in math should serve at least one of the following goals:

- help solve a problem that you can't without written work

- provide a record of your thinking so you and others can follow your thinking

- prove that you are not cheating

 

My personal rule of thumb is you don't have to show your work if you can get quick, correct answers 100% of the time.

If you can consistantly get quick, correct answers, slowing down to show your work is busywork.

 

On the other hand, if the answer is wrong, written work is invaluable in determining what went wrong.

When an answer is wrong I always insist on it being redone on paper.

 

To encourage my DD to show her work in the first place, I won't tell her what went wrong if there is no written work;

but I will help her locate the error if there is written work. I am also quick to point out when she would

have gotten the answer right if only she had written down the steps.

[Arcadia]

He is making careless errors in his head if it's not 100% correct. I'll ask him to show his work for the harder, longer word problems just to get into the habit of it.

[Paige]

I make mine show their work once it gets to multiple step problems. Before that, I am not such a stickler. My reasoning is that it is a good habit that is hard to develop later. It's hard when you do algebra or something to concentrate on the new material and concentrate on remembering to write stuff down at the same time. I also require it because I need to know what happened if there's a mistake. If he saw 5+ 5 and wrote 11 instead of 10, when I know that he really doesn't have a problem with that, it's much different than if he didn't know that he needed to add 5+ 5 in the first place. 

[ikslo]

I only make DS show his work now if it is a new topic, or if he gets something wrong ("No, that's an incorrect answer.  Try again, and write it out.") 

 

But I also make him read the directions, and if it instructs to write it out, he has to cross that part if he choses not to follow it, so I know he read the directions.

[simplemom]

I like the idea of showing work if the mental answers aren't 100%. I also like the idea of showing the work for a portion of the problems (your judgement) if the mental answers are 100%. My ds just got to a point where the problems are too difficult to do mentally. He HATES having to write out his math work.

[SparklyUnicorn]

With word problems he should show work.  If it's a straightforward problem like 324x57 and he can do that in his head, power to him.

 

Definitely get him into the habit now.  It only gets worse.

 

 

[TheAttachedMama]

YES!  he needs to show work.   He will eventually get to the point in college or highschool where an entire 1 hour exam may be 1 or 2 problems.   Not showing work would mean a failure.   Showing work in math is SO, SO important.  You just have to do it.

 

I get that kids don't want to do.  I totally understand that!  And as a parent, I think it is important that you communicate to them your understanding of those feelings.  (Let them know you get it...they don't like to show work.)

 

However, let them know that this is just something you have to do in math.  Have to.  

 

I even make my 1st and 2nd graders show their work under story problems....JUST so they get in the habit of doing it.   So it won't be questioned.    My advice to people reading this is start with the habit of showing work in math as YOUNG AS POSSIBLE.  The earlier you start, the more of a habit it becomes, and the less it will be questioned.  I equate it to wearing a seat belt in the car.  If you were to take a 5 year old who has never seen the inside of a car and told them they had to wear a strap across them, they would probably hate it!   BUT--we've been strapping our kids in since they were babies.  A seat belt probably isn't even questioned in most families any more because of this.  You just do it whether you like to or not.  The same should go with math.  You just gotta show your work.  :)

 

We have lots and lots of talks outside of math of why you have to show work, how I understand they don't' want to, but you just gotta do it.  That type of thing.  I explain to them how they have to get in the habit of showing work without even really thinking about it.  That way they can do well in higher math.  Because they WILL get to a point where the math can't be done in their heads.  

[boscopup]

My oldest is finally seeing why showing your work is so important, now that he's doing Prealgebra. He is even drawing diagrams and labeling angles in the geometry section! :D It's been a long work in progress.

 

My younger kids are starting out showing their work from the beginning, since they use CLE. I think it will be easier with them. But even though my oldest didn't start early with it, he's seeing the light now that the problems really require showing work. More than once recently, he's worked through a lengthy problem and gotten a wrong answer, and I was able to show him that since he showed his work, it was easy to see he just subtracted wrong at the end our something like that. On one diagram the other day, he'd labeled every angle correctly, then made a silly subtraction error at the end that made him 2 degrees off on the answer. :lol: He was glad he hadn't just done all that stuff in his head.

[Tanikit]

My DD does not want to show her work either. What I did was give her a book marked scrap paper that she uses for both spelling and Math to solve anything that needs thinking about. Then she can write her answer without work in her other book. I do expect her to know how to "show her work" neatly too, but do not expect it for every sum. Word problems she must at least show what sum/s she is doing though she can solve these sums mentally if she wants.

[4KookieKids]

I've taught math at a variety of levels (primarily undergrad, but also some graduate level and some high school), and I feel like what work needs to be shown really depends on the problem, and it might be hard to figure it out on any given day. In general, I agree with this:

 

To me, showing your work in math should serve at least one of the following goals:
- help solve a problem that you can't without written work
- provide a record of your thinking so you and others can follow your thinking
- prove that you are not cheating

 

And I completely disagree with the premise that you need to get into the habit of showing work now because you'll have to later. Yes, they'll have to show work later, but math is not the time to make an object lesson out of perseverance and how life involves unpleasant jobs that you don't want to do (not if you want your kid to like math, at least). The point of showing work in those later years is mainly to serve the first two goals in the quote above (and the third in the case of an exam). I think that teaching kids to show work on problems that are really elementary only teaches them to dislike math because it's boring, tedious, and pointless (some of my gripes about how boring we make math education in our country, in general, and how it's amazing anyone even likes math despite that, but that's a whole different soap box...). "Showing work" should be motivated by mutli-step problems, the realization that this is how you learn to keep track of more and more pieces as the puzzles get more complicated, and by considering how you can communicate concepts to others if they don't know or understand them, rather than by the rationale that "you'll have to show work later."

 

Who among us here really finds it satisfying to ask "why?" to an unpleasant task and be told that it's just a good habit to have for later. I sure know what I'd be thinking: So we have to do boring, pointless work now so that we'll be good at doing boring, pointless work later??!! Well that's why I'm not going into THAT field! :)

[ikslo]

DS had to "show his work" for a word problem in MiF, which was essentially a simple 5+3=8 type of problem.  He looked at me strangely, and asked - how do you show your work for something you brain just knows?  I told him he should draw a picture.  So he drew a picture of himself, with a thought bubble in which he wrote 5+3=8, and then a speech bubble in which he wrote "Duh!"

 

That was one of my "Ah Ha!" moments in homeschooling, and why I disagree with PP who feels one should always show your work, and completely agree with deanna1ynne, above.  For some problems, it is just pointless.

 

Although I did consider that his "Art Class" for the day. :)

[4KookieKids]

DS had to "show his work" for a word problem in MiF, which was essentially a simple 5+3=8 type of problem.  He looked at me strangely, and asked - how do you show your work for something you brain just knows?  I told him he should draw a picture.  So he drew a picture of himself, with a thought bubble in which he wrote 5+3=8, and then a speech bubble in which he wrote "Duh!"

 

Although I did consider that his "Art Class" for the day. :)

 

Awesome.

[kiana]

As an instructor, my policy has always been:

 

If it is a problem that I can solve in my head, and you have the correct answer without work, I assume you did it in your head and give full credit.

If you have the incorrect answer without work, you get a 0.

 

If I cannot solve it in my head and you have the correct answer without work, I assume it came from somewhere else and assign a 0. 

[mschickie]

As the math gets more complex the more I require dd to show her work.  When she was doing simple arithmetic I did not require her to show the work but now that she is in Algebra she has to because I know the material will be getting more and more complex.  It has been an up hill battle this year but I seem to be handing stuff back that does not have the work shown less often now.

[ikslo]

If I cannot solve it in my head and you have the correct answer without work, I assume it came from somewhere else and assign a 0. 

 

I don't get this line of reasoning - you are automatically assuming no one is smarter than yourself?

[MEmama]

I'm definitely in the camp of they'll show their work when they need to. Writing out solutions to intuitive answers isn't helpful, but would certainly be painful and tedious, not to mention pointless. If you can get to the answer mentally-power to you! When they get to algebra, there will naturally become a time when showing work becomes necessary. DS is slowly coming around to that, and while yes there's a learning curve involved (mostly learning that math won't forever be able to be solved instinctily), he also has the maturity (usually) to be able to deal with it.

[Garga]

Pre-algebra here.  The problems this week are things like:  Simplify: (6³x5)-(5²+54)x3

 

He got 9 out of 18 wrong. 50%.  That's an F.  He's been fighting me about showing his work, but he needs to do it so I can see where he went wrong in the problem.  (We figured out that he was calculating all his exponents incorrectly.)

 

I've just read posts 1 - 11 to him out loud after he'd calmed down from the frustration of his math problem.  He's a good kid and he genially rolled his eyes at me and said, "Ok! Ok!  I got it!  I understand. You can stop reading."  

 

I'm sure that when math rolls around again on Monday he won't want to show his work, but I think he's starting to see the necessity of it.  I think he's realizing this isn't something I'm personally requiring but is just the nature of pre-algebra.  Everyone has to show their work in pre-algebra and beyond.

 

I'm so glad that my youngest son is in CLE and they do a good job of helping you show your work by providing little boxes to write in for each step of a multi-step problem.  I'm hoping that by the time he gets to pre-algebra he won't even notice that he's showing work.  It'll be something natural to him.

[TheAttachedMama]

 

I've taught math at a variety of levels (primarily undergrad, but also some graduate level and some high school), and I feel like what work needs to be shown really depends on the problem, and it might be hard to figure it out on any given day. In general, I agree with this:

 

 

And I completely disagree with the premise that you need to get into the habit of showing work now because you'll have to later. Yes, they'll have to show work later, but math is not the time to make an object lesson out of perseverance and how life involves unpleasant jobs that you don't want to do (not if you want your kid to like math, at least). The point of showing work in those later years is mainly to serve the first two goals in the quote above (and the third in the case of an exam). I think that teaching kids to show work on problems that are really elementary only teaches them to dislike math because it's boring, tedious, and pointless (some of my gripes about how boring we make math education in our country, in general, and how it's amazing anyone even likes math despite that, but that's a whole different soap box...). "Showing work" should be motivated by mutli-step problems, the realization that this is how you learn to keep track of more and more pieces as the puzzles get more complicated, and by considering how you can communicate concepts to others if they don't know or understand them, rather than by the rationale that "you'll have to show work later."

 

Who among us here really finds it satisfying to ask "why?" to an unpleasant task and be told that it's just a good habit to have for later. I sure know what I'd be thinking: So we have to do boring, pointless work now so that we'll be good at doing boring, pointless work later??!! Well that's why I'm not going into THAT field! :)

 

 

I disagree with you.  

 

I am a big stickler for showing your work because I think it aids in a more clear and organized thought process.   Above all else, math is a lesson in thinking and logic.   Developing these thinking and logic skills is priority number one.    Showing your work does not have to be a lesson in "perseverance and how life involves unpleasant jobs that you don't want to do."  I feel sorry for people who think of math that way...whether they have to write a few numbers down on the page or not.  :)   I personally think that math is a beautiful thing.  I have a real love for it. 

 

We teach math the same way they do in Singapore.  (As close as we can replicate it living in a US household at least.)   In the US, we tend to teach math with the end goal in mind.  We simply care if they can get the right answer or not.   If the answer is right...end of story. 

 

In Singapore, the thought process behind the math is much more prized.   A teacher might first ask one child to explain their thought process and problem solving techniques.   Then the teacher might compare that to the way another child solved the problem.   Then other methods of solving the problem might be discussed.   While the answer is important, it is really secondary to the problem solving techniques used.   Math is thought of much more as a creative subject as different ways of tackling problems are taught, discussed, and cherished.   Developing thinking skills is the end goal in those classrooms. 

 

We tend to think along those same lines.   The method used to solve the problem is VERY much prized and cherished in our home.  We quickly spout out the correct answer, but we will often engage in long conversations about HOW the problem was solved, WHAT other methods could have been used to solve the problem, WHICH was more efficient or elegant, etc. etc.  

 

Showing work is a way to demonstrate and document that process...and it encourages clear, organized thought.   THAT is the reason showing work is important and a good habit to form early.

 

Don't get me wrong---Mental math is EXTREMELY important.  We do a lot of mental math activities in our house.  However, the ability to explain /show your problem solving methods and techniques is just as important skill in math.   A child who can write down and explain their strategies is a child who is thinking clearly about solving the problem. 

 

Also, I disagree that asking a child to show their work is a sure fire way to make them hate math.  At least, it doesn't have to be.   My kids show their work in math and they LOVE (LOVE!) math.  (ETA:  And these are kids who hate the physical act of writing!)  But, They beg me to do math first thing in the morning.   I think a large part of this has to do with the fact that we have developed good habits in thinking. 

----------

TO GIVE AN ANALOGY TO WRITING (for those less math focused):

Those who follow the WTM approach know how important it is to get the child in the habit of answering in complete sentences at an early age.   Why do we do this?  Is it to teach them a lesson on perseverance and life's unpleasant jobs? :)   No.  Is the point to teach them to dislike talking and conversation?  No.   The point is to train the child in the habit of clear and logical organization of their ideas into thoughts.  

 

Let's say you ask the child to describe their guitar.   

 

One person answers simply:

"Brown"

 

Another child answers:

"It's nothing fancy, just a Madeira folk guitar, all scuffed and scratched and finger-printed. At the top is a bramble of copper-wound strings, each one hooked through the eye of a silver tuning key. The strings are stretched down a long, slim neck, its frets tarnished, the wood worn by years of fingers pressing chords and picking notes. The body of the Madeira is shaped like an enormous yellow pear, one that was slightly damaged in shipping. The blond wood has been chipped and gouged to gray, particularly where the pick guard fell off years ago. No, it's not a beautiful instrument, but it still lets me make music, and for that I will always treasure it. "  (The Blond Guitar by Jeremy Burden)

 

Both answers are TECHNICALLY correct.  However, one shows a more organized, elegant form of thinking.   It is MY personal belief that this same elegance in thinking must be taught in math. 

 

Just my 2 cents (OK....4 cents)

[4KookieKids]

I disagree with you.  

 

I am a big stickler for showing your work because I think it aids in a more clear and organized thought process.   Above all else, math is a lesson in thinking and logic.   Developing these thinking and logic skills is priority number one.    Showing your work does not have to be a lesson in "perseverance and how life involves unpleasant jobs that you don't want to do."  I feel sorry for people who think of math that way...whether they have to write a few numbers down on the page or not.  :)   I personally think that math is a beautiful thing.  I have a real love for it. 

 

We teach math the same way they do in Singapore.  (As close as we can replicate it living in a US household at least.)   In the US, we tend to teach math with the end goal in mind.  We simply care if they can get the right answer or not.   If the answer is right...end of story. 

 

In Singapore, the thought process behind the math is much more prized.   A teacher might first ask one child to explain their thought process and problem solving techniques.   Then the teacher might compare that to the way another child solved the problem.   Then other methods of solving the problem might be discussed.   While the answer is important, it is really secondary to the problem solving techniques used.   Math is thought of much more as a creative subject as different ways of tackling problems are taught, discussed, and cherished.   Developing thinking skills is the end goal in those classrooms. 

 

We tend to think along those same lines.   The method used to solve the problem is VERY much prized and cherished in our home.  We quickly spout out the correct answer, but we will often engage in long conversations about HOW the problem was solved, WHAT other methods could have been used to solve the problem, WHICH was more efficient or elegant, etc. etc.  

 

Showing work is a way to demonstrate and document that process...and it encourages clear, organized thought.   THAT is the reason showing work is important and a good habit to form early.

 

Don't get me wrong---Mental math is EXTREMELY important.  We do a lot of mental math activities in our house.  However, the ability to explain /show your problem solving methods and techniques is just as important skill in math.   A child who can write down and explain their strategies is a child who is thinking clearly about solving the problem. 

 

Also, I disagree that asking a child to show their work is a sure fire way to make them hate math.  At least, it doesn't have to be.   My kids show their work in math and they LOVE (LOVE!) math.  (ETA:  And these are kids who hate the physical act of writing!)  But, They beg me to do math first thing in the morning.   I think a large part of this has to do with the fact that we have developed good habits in thinking. 

 

I agree with most everything you said, so I'm not sure what you're disagreeing with in my post, exactly. :)

Maybe I wasn't clear, so I would just clarify that I never argued that children shouldn't show work or that showing work will make them hate math. What I said was that children should not be forced to show work for elementary problems (what each person means by that probably varies, but broadly, I'd say these are problems with very few - like 1 or 2 - steps and/or firmly established concepts) but, far more importantly, that they should not be made to show work BECAUSE it's a good/necessary thing later (which is a good way of making things feel boring and tedious, since they have no *good* reason given to them for why they're doing this). They should be given more constructive reasons for doing it (e.g., what you gave about it aiding the thought process and what previous posters have said about following the logic/argument and identifying problem areas). 

 

Your previous post (before the above quoted one) made it sound like you fell in the camp of teaching kids to do it "just because you have to" (when you said stuff like "I know you don't want to... but you just gotta do it"), and that was what I was disagree with.

 

My main point was just that we need to find a better way to motivate young people to show their work than saying something things like "this is just what we do in math," "you'll need to be able to do this later," "eventually you'll see that this is a good habit," etc. There are so many *better* reasons to show work on problems that have more than one step - some of them being the exact ones you gave. It sounds like you do this, despite what it sounded like in your original post, but I know that a lot of parents don't. And it's because of that that I wanted to encourage parents to find better motivation for having children show their work. :)

[Momling]

I don't bother showing work with arithmetic, but started insisting on showing work when working algebra problems in the upper grades. I just explained that algebra is a game that follows rules and to play the game, you have to write down how you got from equation to answer. Spending time working on two-column algebraic proofs in Foerster was especially helpful in showing how each step is clearly distinguishable from the others.

[mamaraby]

lol, I didn't really think this would be that controversial. I'm going to continue to require ds show his work. My biggest concern is with word problems where, like I mentioned in my OP, he's probably running 80-90% accuracy on average meaning there are days where he makes more mistakes and it's worse. For the rest, I guess I'll just keep an eye on it. I'm still in the "it's a good habit to form" camp so it was nice to hear I'm not off on my own math island. :0)