I am sure we have discussed this several times - does anyone have a link on hand about how to help gifties understand the necessity of showing working out in traditional schooling? (It's for a friend)

Well, we've discussed it. The general consensus is that most of the time this is a losing battle until kids are doing more advanced mathematics. Through algebra and in some cases a lot of high school geometry, your average EG/PG person simply doesn't need to write each step out, if they have the working memory capacity not to.

Until they see some real dis-incentive for not doing so, nothing much WILL convince them. We're hoping that calculus will supply the necessary motivation, because thus far, only physics has been sufficient inducement for our DD.

She really can do matrix algebra steps in her head that neither her dad nor I can. She's just not like most people.

How on earth to convince her that she "must" show those steps?

Uhhh-- we don't. She's proven that she simply doesn't NEED to. Why make her do something that she has mastery of, and doesn't need to do for herself?

We have finally moved into a phase where she sees her own limitations better in this respect, and has the ability to self-check, and -- where she is in error-- correct by reducing steps done in her head on the next iteration.


Tutoring other more typical students has helped her to understand what OTHERS need to see to "follow" her work. But I still wouldn't say that she is "good" about it without someone actually asking her "Hey-- wait a minute-- how did you get THAT?"

Interestingly, DD10's teacher this year (who totally gets gifties) does not require that they show work. So DD doesn't. She LOVES this, of course, but I wonder if it will just make it harder when she goes back to having to show it again.

The best argument I know of for showing work is that it will help you get partial credit if you make a dumb arithmetic error.

Exactly this. When you show your work, you get points no matter what the answer is - lesser points if the steps are correct and full points if the answer is correct too.

In my child's school, they are "taught" how to show their work for both word problems and numerical calculations. They expect a certain format and show the kids how to do it and they get point deductions if that is not followed.

My DS is adpet at mental math (regrouping mentally and doing anzan calculations in his mind), but he still does the manual steps on the paper as the teacher wants him to. I tell him to recheck his work using his mental math strategies while still showing his work on paper.

If your friend is in a homeschooling scenario, I don't think that showing the steps is necessary in the early elementary stages because who really wants to draw bar graphs or pictures for all addition, subtraction, multiplication problems? In such a case, I think that showing steps only for word problems is good enough. But, that is just my opinion...

ETA: just noticed that you said "traditional school" - sorry, the giftie needs to learn that the teacher is the person giving out the grades and they need to do things the teacher's way in the classroom

This doesn't necessarily help for a traditional school situation, but when I homeschooled my son (high school), I told him that I would give full credit for a correct answer even if work wasn't shown. But if he got the answer incorrect and no work was shown, he would lose all points for the problem. If work was shown and the mistake was a simple arithmetic or copying error that was carried correctly through the problem, I would give partial credit. If the error was conceptual or there were multiple sloppy errors, he would receive no credit. This did seem to motivate him.

On homework, which I did not grade except to mark it complete, I told him that if he didn't write out his work a certain way (and I posted a detailed list of instructions in his work area), I would make him do the assignment over. That also motivated him. I did this in response to his making multiple sloppy errors when he got to Algebra II. He has dyslexia and his working memory is not stellar--even he saw the benefit of writing out the work properly, but the lazy side of him didn't want to do all that writing.

I'm still struggling with this issue with my younger son. He has a more severe antipathy for writing (bordering on dysgraphia) and his working memory is phenomenal. He is motivated by grades though.

With both of them, I keep stressing that math isn't just about getting answers but also about showing your thinking. The question becomes how much thinking do you need to show? Everything? Just the non-trivial stuff? I'm sure there is some standard, but I never went far enough in math (or paid enough attention) to learn the answer. Perhaps a math person here can enlighten me.

Kai, this is where tutoring others has proven invaluable for my DD. She now understands what the "average" person NEEDS to see in order to follow her thinking in a mathematical sense.

It's been great for her. Nothing else convinced her.

This problem has been exacerbated by the implementation of the common core. Our district now routinely requires students to write out in English explanations of simple arithmetic operations. Such as why 2+2=4? They are also very proud of the fact that Kindergarteners may never see a equation. This is beyond the legitimate requirement of showing your work. It really bores everybody except maybe the few truly verbal but not mathy kids. Sadly, a lot of those kids have grown up and are in charge of our curriculum now.

Kai, this is exactly how my sons math teacher does it. Regular home work they have the answer key in the back of the homework. So the homework IS showing your work (No Grade). They do have one turn in home work due with each quiz and test that does not have the answers (Graded). With your turn in home work if it is right its right, if its wrong you better show your work if you want any type of score. It is usually an easy mistake. Also, on your turn in home work you can do it when ever you want. If you turn it in early the teacher will mark it and give you a shot at correcting your mistakes. Turn it in the last day and you don't get a second shot at it.

I am not sure of the upside or downside of this, it's just how it is. My ds has conformed pretty well.

I remember the things that irked me most as a kid when faced with "show your work.":

First it is a dishonest request. I had no work to show. If there was work, it would be shown.

Second, a frequent argument for showing work is that it proves you did the work as opposed to cheating from someone nearby who tends to get significantly poorer scores on tests? Trying to persuade me to song and dance because you don't trust me = fail.

Third, the bait of partial credit, already being on the edge of thinking the whole grading system was ridiculous, that convinced me it was pointless, because it is math. If it is wrong, it is wrong. There is no subjectivity to it. Tell me it was wrong, I'd figure out what I did. If I can't I'd ask (Historically proven to ask questions anytime they struck me.)

Fourth, I proved I knew it seventy-three other times. Why was I continuing to prove it? One repetition was enough.

But I wasn't entirely as obnoxious as my thoughts on the subject, and would comply up to a point. The persuasive answer would've been along the lines of tutoring. "Show how to get the answer in a way that someone else in the class could reuse to solve a different problem."

Oh yeah, and it was partially about the burden of writing.

p.s. DS8 enjoys the heck out of trying to do everything in his head. He thrives on that challenge. In addition to the so others can learn, I've suggested doing it in his head first and using the long way to double-check his work, and since he is interested in programming, I've pointed out that decomposing problem is a critical skill in programming.

I can see both sides of this argument, with the "show work" side in a sort-of kind-of way.

I get that the teacher needs to know that my DD understands a concept. But IMO, "following the algorithm" does not necessarily mean "understanding the concept." And I'm certain that her teacher's OCD-level requirements for showing work are detrimental to DD's ability to understand said concepts. As an example, let us take "What is 15% of 50?" They have to write it out as follows, mental math (5 + 2.5) being BANNED:


What is 15% of 50?

n= the number that is 15% of 50. (it has to be n)

n = (0.15)(50)           Do calculation on the right.

n = 7.5

The number 7.5 is 15% of 50.

7.5 (Answer must be at the bottom, not circled)

Problems are marked wrong if they don't follow her recipe exactly, including lack of capitals in sentences and so on. Even work for 12*4 must be shown. DD gets so wound up about following the steps, she gets into a muddle about how to obtain the answer. I get that she's trying to teach them to be tidy, but she goes overboard and just sows confusion.

IMO, there are only two valid arguments about showing work. The first is that it shows that you know how to do the algorithm (value of which is noted above). But teachers can keep a list of who gets it and allow algorithm-savvy kids to start taking shortcuts (which will presumably lead to increased understanding of the material). The other argument is that it helps you learn how to explain things to other people. This skill is important in adult life, especially at work if you want to convince someone about your cool new idea or teach a subordinate how to do something. Fine. But this doesn't mean a student should be required to write out each step on 72 problems that all require the same steps.

The other side of the argument is that by not forcing a student to show steps that are trivial to her, you allow her to focus on the meat of the problem. Which I think is a more important consideration for gifties. But teachers don't generally get gifties, which brings us back to

12
*4
48

Well, this is something that teachers in our school drum into the students from 1st grade. A substantial portion of our standardized state testing as well as district testing require constructed responses. I am not sure whether it is even possible to score more than just proficient on the state exam without crafting constructed responses. As a result, the classwork and tests always include long and brief constructed responses and for good measure, the students are told to show work on multiple choice answers as well. At times, it is rather a bit of an overkill. If the student doesn't care about doing well on the state/district testing or getting good grades, then there is little incentive to comply. My children generally went along as required by their teachers although there have been a few occasions when I had to issue a challenge borrowed from one of their highly regarded GT teachers who believes that if you can't explain to someone else how you arrived at your answer, then you have not acquired a deep enough understanding of the concept. Fortunately, this same teacher also believes in many ways to arrive at the same answer.

I'm curious whether I am the only one whose child is being allowed not to show work. I really do mean that. She can hand in papers with nothing but the answer, even in cases where one pretty inevitably does "work", such as those involving multidigit x multidigit multiplication (DD often will scratch these out on some random scrap of paper that is handy and not pollute her HW with it). Not only that, the teacher will sometimes instruct them to cross out portions of the HW that enforce tedious work-showing.

I also recently found out that kids in this class can take pretests and test out of any math unit (they get computer work instead). DD just hadn't bothered to tell me this. I don't always hear much from her!

DS11's homework is almost all in the online Borg Math environment. He can just click the right answer without showing any work. Apparently this is OK with the teacher.

I want him to have the skill of showing work, but it's not worth the struggle for me to insist on doing things my way when the teacher doesn't care about it.

Sigh.

Yes-- DD's math classes have pretty much never required it. WE have-- once she got into algebra, I mean.

She could STILL hand in twelve step trig problems with nothing but an answer, however, given that the computer only cares about the result.

Sometimes, she does. She claims "I did it all on my calculator anyway-- I didn't have anything to write down." Which is usually bogus, btw, but often not worth arguing over if she's doing the problems right (mostly she is).

This is what helped my son as well. But it takes till they are in at least doing more complex math.

I think if you are showing your work you should be able to show how YOU did it.

Therefore 50 is half of 100 therefore 15 % of 50 is 15/2 = 7.5. If they really want an algorithm then they should use something like 17% of 63.

My DD HAS occasionally been dinged by this policy. She fortunately had neat handwriting (I think it's sloppy handwriting kids who could get the worst results here) but sometimes writes very small, and a 5 becomes a 6, etc. Bing. Wrong answer due to copying error.

Interesting. I don't think this is required here. I was just going to point out that standardized tests don't care if you show work, but I guess I am incorrect.

[quote=ultramarina]I'm curious whether I am the only one whose child is being allowed not to show work. I really do mean that. She can hand in papers with nothing but the answer, even in cases where one pretty inevitably does "work", such as those involving multidigit x multidigit multiplication (DD often will scratch these out on some random scrap of paper that is handy and not pollute her HW with it). Not only that, the teacher will sometimes instruct them to cross out portions of the HW that enforce tedious work-showing.

Our school sounds very much like Quantum2003's. They require constructed responses, on every day assignments and on state assessments. But our kids have learned this way since beginning school, and don't find it problematic at this point. I don't feel they are required to show tedious busy-work, but do have to explain their logic. They also do a fair amount of writing about math. DS just finished an 18-page "portfolio" on the latest unit, where he had to do everything from discussing how various formulae were derived, to creating and then grading some parent problems we had to complete, to talking about which part of the unit he found most interesting and why. It is part of their differentiation; I assume many kids didn't have as much to say, but DS got quite involved. He really thought a lot about how the formulae related to each other. It is interesting to watch his "technical writing" evolve, by the way. in the past I considered him more of a creative writer, but this was very well-written.

This is indeed very unusual. Your DD has a unusual teacher and has not been corrupted by the commmon core standard. Explaining your work has been taken to a whole new level with common core. It literally means using English to explain your reasoning for every little thing from Kindergarten math and up. All in the mistaken view of this somehow teaches deeper understanding.

At the same time, showing the relevant steps in math calculation and particularly in word problems are good and often necessary when the problems get hard. I have no issues with that and will encourage my child to do that.

I am glad to hear that your kids enjoyed this assignment. I just think I would have hated it when I was a child. It seems just like you said it became technical writing and no longer mathematics. It really penalize the mathy but not necessarily verbal kids. I venture to say it may even have the harmful effects of making some kids feel turned off by math.

This is what we have too. Show how you worked the problem out then in written form explain what you did. It drives DD9 (and me) bonkers!!!

Common Core + enVision Math = ARRRGGHHHHHH!!!! Want me to explain that further in writing!?! lol

This is where I allow my DD to do things like;

Front-end estimation is a stupid skill. While I agree that ESTIMATION is a useful skill, particularly for estimating line items in budgets and for checking results of longer calculations-- a more useful one for fourth grade would be to teach that there are alternative ways of doing rapid computations to arrive at approximate answers in a hurry. That's not estimation. That's rough calculation. Why would you call estimation anything BUT "rough calculation" anyway? "Front-end" implies that there might be a counter-example of "back-end estimation." What possible purpose would such an asinine concept serve, anyway? 'I have calculated that I shall require $473.89 to pay my bill. Therefore, back-end estimation suggests that I shall require $470, whereas front-end estimates would place this value at $475.' See? Stupid. Why bother? Is this math for people that find adding 301.00 172.89 to be "too hard?"

But I'm a bad parent, and I've encouraged DD's snarky and irreverent side to an unhealthy degree, probably.

So I'm not the only one who thinks that front-end estimation is lame. I've never understood why people need to be taught multiple algorithms for something as trivial as "round the numbers and do the operation." Yet my kids have spent hours of their lives doing worksheet after worksheet of this stuff.

Just wait until your dd gets to higher-level "math" and has to write about how she "feels" about a problem - I kid you not!

And I'll be leaving this post now before I write out how I really feel about talking about how math problems make my dd feel......

polarbear

I think it is because the some teachers are fundamentally weak in math. They had a hard time using the short cuts to do mental rough calculation themselves. Actually lot of the math education problems are probably due to the facts our teachers are not math persons themselves. The problems with mathematicians embracing Every Day Math and the like is that they were good with math and forgot and did not know what it was to learn math for the time as a child.

This. What is your favorite number and why is that? Anyone thinks that this belongs to math class other than maybe preschool? Let's leave the feelings out of Math.

e, i & π are really some of my very favorite & most interesting numbers.

You got me there. I love pi too.

i8∑π it made me

e is my personal favorite.

lol the responses were interesting reading! thanks guys - it appears the issue is a world-wide one - this is a friend whose child is in a school in Germany. They are super strict there and he just does not see the point of showing his working out.

All the estimation stuff has made my DD insane. I really don't remember this obsession with estimating from my childhood.

Oh no! When we get to that point, I think I'll be afraid she WILL actually tell them how she feels, since by that time she will have had to endure many years of the writing and explaining how she got her answers.



DD9 brought home "estimation" sheets recently where they were supposed to estimate then divide. I have just been waiting to see those graded sheets come back home. None of the sheets told her how they wanted you to estimate - estimate up/down, to the nearest whatever, etc - nothing but "estimate". So in my opinion there was no answer that could be wrong because you can estimate any number of ways and each student can pick how they want to estimate.

DD9 basically just made it easy on herself and chose a number that the other number went into evenly, so she could do it all in her head. I warned her she may want to get a piece of scratch paper to actually work out the problems, then attach it to the worksheet. She didn't go for that. I assumed there was an answer key for grading these sheets and when one of her answers didn't match the key it would be counted wrong.

I haven't seen the graded papers yet, but if she gets counted off (other than doing the problem itself wrong) then I guarantee I will be bringing that up at parent/teacher conference.

Maybe those worksheets were just another form of "there is no wrong answer" - who knows!

Oh, no they aren't.

They're an evil kind of GUESSING GAME, though.




Thus the danger in asking children who are highly verbal and have been treated to this kind of thing how THEY feel about particular elements of the math curriculum.

DD, thankfully, had the emotional maturity not to SCREAM 'YeeeeeeHAW!!!!' into the phone at the Honors College advisor when informed that she didn't, in fact, NEED to show a transcript with MTH 112 on it to place into calculus next fall.

Just noting that this kind of thing takes quite a toll on kids who are not NT in their approach/thinking. It's sad to see. DD loves math. She just hates the math course. She's actually very excited by the material-- which makes her anger all the more intense when the crappy curriculum RUINS it and sucks all of the joy and real learning from it.

I love Tau. It's as good as 2 pies.