Gifted Issues Discussion homepage Forums General Discussion Maths: showing working out?

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