why is showing work in math so important to teachers?

Showing your work is important in math. It lists the steps taken to answer the problem, which allows the teacher to see how the student came up with the answer. With this information, the teacher has insight in how the student is problem solving. If the student is having difficulties solving the problems correctly, the teacher can look at the steps to see where the error is being made. If a student doesn’t show their work, it may be that the student does not understand the concept or is using a calculator. The steps taken in solving math problems truly shows if the student is understanding the concept being taught.

Teaching means developing concepts, not copying answers from page A to B.
Teaching means giving students problem-solving skills which they can use independently and transfer to many other fields (many others besides math), not programming robots.

I continually tell my students that if I want a list of the answers, they are neatly printed in the back of the book and I can photocopy them any time. That is not the point of learning, is it?

As a math teacher, I am always trying to teach my students higher-order thinking skills: analysis, synthesis, comparison, evaluation, self-checking, creativity, interconnection of knowledge, perseverence, and many others. The PROCESS of solving the problem is the subject matter of the class. The answer is just one number at the bottom of the page; next time we can change the initial conditions and the number will change every time, but the *process* will remain the same.

Focusing only on correct answers means you are totally ignoring the subject matter of the class. Sort of like evaluating a gymnast or skater only on the bow at the end of the program.

I think with students with learning differences all the traditional rules deserve to be reconsidered. While I understand the rationale for needing to show the work in math, I would also understand that ‘showing the work’ should not take precedence over everything else including the student. The first rule in any class -math or not - should be to continually rexamine the rules for each and every student to make sure they are supporting the student best in their learning.

For dysgraphic students, for example, showing the work would be laborious torment. For students with attentional issues, it could be much the same. If in cases like that, the need to show the work actually works to prevent the student from learning the math, the practice of ‘showing the work’ needs to be reevaluted for those students.

All that said, giftedness is also a learning difference while it is not conventionally regarded as a disability. Gifted students are thought to deserve IEPs. While it would be very unconventional, thinking very much outside the box, I could see an IEP working to excuse some gifted students from ‘showing the work’. I’ve met students of such extraordinary and intutiive ability in mathematics that they operated on a different plane. Your sons might be among them. For those students, ‘showing the work’ becomes the same laborious torment as it is for the dysgraphic student. Some gifted mathematicians do work better in their heads than on paper demonstrating a remarkable internal calculator all their own. In those unusual cases, showing the work on paper can actually foul them up in their calculations.

Of course a teacher should be glad assignments are being turned in but the system rarely works on that alone. Most classrooms, math or not, draw a line in the sand so to speak and students are expected to toe that line. I’ve seen brilliantly written papers given an F because the student’s name was written on the left vs. the right side of the paper. Or flunked because they single-spaced when they should have doublespaced.

What you might be missing is that not all of the common practices of school support full learning in each and every student in each and every class. School can often emphasize the details such as single spacing vs. double spacing while looking past the concepts. It’s also true that teachers are given enormous freedoms in the small kingdoms that are our classrooms and the wishes of the teacher can be paramount to the needs of individual students. We live in an imperfect world.

Sara, I wish my child had a teacher like you when he was in school. He is gifted and cannot STAND to show his work. He doesn’t think in the steps like most people and finds it impossible to do algebra the “correct” way. I don’t understand how he does it but he does and his tutor does also.He is thinking so fast that it is hard for him to slow down long enough to write out every step. He shows a minimal amount and his tutor says that is fine. We homeschool so we can teach him the way that is best for him. He is a 5th grader and is taking 9th grade algebra. He was bored to tears with math until we got him in algebra. He is not good at recalling “facts” but can and does apply them to higher level math. Schools just won’t work with these kids. I sure wish they would because he has surpassed my knowledge and we have to employ a tutor which can get expensive. I feel my child deserves an education just like all children but schools seem to think that gifted kids aren’t important!I really don’t understand how LD children can get services but gifted LD can’t! It is very frustrating. Thanks, Jan

I happen to be one of those advanced math students, and have a coordination/writing problem that made elementary arithmetic a real trial to me.
Nonetheless, when I started to learn real math (as opposed to mechanical number/formula crunching) I was very very lucky to have a few good teachers who did teach all the steps.
Gifted students who have learned that they are too smart to do all that stuff hit a real crash and burn when they hit their first real math course — when they have to think creatively and produce a logical proof, in particular. They can see that A equals D, they know for sure that it’s true, and they simply cannot explain how and why this works, because they have skipped all the learning steps that would have led them up to this ability.
It’s a disaster for the student and a hopeless frustration for the teacher. The student does two and three step mechanical problems quickly and easily in his head, and is obviously bright, but come those five and six step problems, and the ones where you need to bring in outrside information, and the proofs and arguments and demonstrations, and the student goes blank. The teacher in senior high or college simply cannot teach what is needed, because what is needed is the thinking habit of analysis, which takes extensive practice to learn. The student blames the teachers and drops out of math just when he should really be getting into it.
For a rough analogy, what if you passed the child on reading for pure mechanical pronunciation and factual multiple-choice, and never graded comprehension until Grade 12? Do you think this might cause a few small problems?

I dont have the solution, but know how my 12 th grader reacted to what he saw as ‘pickiness’-he stopped taking high school math classes! This hasnt helped his elegibility for computer science in college-his overall ACT was 29 but math was his lowest score

I guess I would rather see a kid hit the wall as late as possible because maybe then they will have the maturity to see the reasoning behind the philosophy. My freshman sure doesnt get it and probably doesnt have the overall life experience and maturity to do so-and he certainly isnt going to believe an adult ;)

I worry he will fall into the same trap the 12 th grader already did-minimum math to graduate-period

I agree vehemently that there are valid reasons for having students “show all work.” However, I also agree that it can make for math-hating students. I have watched students who were those intuitive whizzes get to that point where the problem was suddenly one step too complex to intuit — and they really struggled. (It also costs *big* in the partial credit world. If you’re at all prone to “careless” calculation errors, and you haven’t shown work, your answer is wrong, sorry, n o points.)
Learning to understand that informatoin can be organized in several different ways is a critical higher-thinking skill that is applied wonderfully (if painfully) when you have to figure out how this teacher organizes things. As Sara said, though, when we’re talking LDs we have to reconsider assumptions. If a student’s LD means they don’t have the cognitive structures to organize things a certain way — but *can* do so in another way — then we can take the time to build those cognitive structures or decide they’re not necessary, or of course do the old-fashioned thing and say “you fail.” Lots depends on why they need that particular math skill/course.
One possible compromise is to ask that “all work be shown” on several of hte more difficult problems — and perhaps have a price tag on accuracy, too, so that for every wrong answer, work has to be shown on another problem.

Well, the answers-only students I had by the hundreds also hated and feared math, and they sat in the room copying answers from point A to point B and hating every minute of it, so that isn’t much of a solution. While teaching junior college for five years, I had literally hundreds of students who had “taken” a class named Algebra 2 and sometimes more. Their transcripts looked OK for college, but the colleges had learned better and instituted placement tests. Unfortunately when they took the college placement test, they failed basic algebra and tested lower than Grade 9 level. So tell me what is the advantage of keeping them in the room for three extra years while they learn absolutely nothing? And getting them into college classes which they then proceed to fail in droves? The average rate of passing in those developmental math classes, across the board, is around 40% of entering students.

If you have a good math teacher (admittedly a rare breed), any logical method to solve the problem is generally OK. A good math teacher does NOT look for exact copies of the exact same work — that’s actually a sign of cheating. A good math teacher looks for use of some appropriate methodology.

However there are exceptions even to that.

I had one student in college algebra who worked very very hard to get the answers — without ever using any algebra. His arithmetic skills were good, his logic was good, and he absolutely refused to write and solve an equation. Since I was teaching a course whose major goal was the solution of equations, a necessary skill in many following classes in business and statistics and science, I had to fail him. He simply refused to learn anything new; he already knew everything he was going to learn about math and his mind was set in concrete. Sure, I could have passed him because his answers were right — and set him up to fail his entire next semester, not exactly a kindness.

In various math courses, you are often asked to use a certain method in order to learn a concept illustrated by that method. Two classic examples are solving quadratic equations by completing the square and finding a calculus derivative or integral by using the definition. In fact both of these methods are very much the hard way and are never used in everyday work, where we have formulas. But you need to understand the method in order to go on and learn further topics, so every standard test requires a demonstration of the method — once.

Here’s an analogy for you: Suppose your child joins the community swim club. He can not really swim yet, but the club is very race-oriented and he wants to go in the races. So the next time instead of diving in and swimming, he runs around to the other end of the pool. He is certainly the first one there. Do you give him the gold medal? He achieved the goal of getting to the end first, didn’t he? Hey, I’m just being PICKY when I ask a person to win a swimming race by actually swimming, right?

and I 100% believe kids are coming into college with less prep than they should have

I suspect we share some of the same core beliefs but ‘see’ things differently in application-as a teacher, you see the good ones(and I suspect are one yourself) As a parent of 3, I tend to remember the not-so-good ones!

While I am confident any math teacher I would question on this issue would give the same answers given on the board-to see where the errors are, to help later math development, I think as a parent I have seen too many techers who do not make that kind of effort

To go WAYYY back to second grade, my son was in the gifted program-high achiever who suddenly started bringing home reg ed math papers with 4/10. After a couple of these, I myself went through to see where his errors(carrying/borrowing time) were. His answers and work were all 100% correct. Went in to the teacher; turns out he was copying actual problems off the board wrong; his answers were correct for problems he was writing. Ended up with much needed glasses. But why on earth would a ‘good’ teacher not have been alerted by such a drop in skills and taken 2 minutes to check his work for herself???

My son’s algebra tacher may indeed be one of the good ones who actually utilizes the kids efforts to further her teaching abilities. And I should give her the benefit of that doubt-for IF she truly is providing that feedback, she is helping him and I should be grateful.

Unfortunately, Ive seen too many bad apples who are just on a power trip of some sort-even questions answered in pen, odd in pencil or it’s a zero; science projects tossed because the wrong corrugation of cardboard was used; zero because February was abbreviated in the header.

So, my FIRST reponse to the math downgrade for work not shown is “here we go again”

I will give her the benefit of the doubt and speak with her if it continues

I’ve seen enough of the arbitrary teachers to suggest that if you could do it fairly easily and diplomatically (perhaps under the guise of ‘I would like to understand the work so I can help better at home’), that you find out just where this teacher stands. There are enough of ‘em who are of the “hard work is good for you — doesn’t matter what kind or how fruitful or fruitless or frustrating” school that it would be good to know. It would also commuicate to your child that you care about *learning* the stuff and also respect his reasons for being frustrated.
There are also all those teachers “in the middle” who are pretty good, great for lots of kids… but awful for some. I know my high school teacher who was great for me was not so good for others and some dropped back who could have succeeded w/ a different teacher.

You think I see the good students?? I worked as a “developmental” (read remedial) college instructor for five years, a high school teacher of the general population for eight years, and a private tutor (overlapping some of the above time) teaching the very, very failed students, the ones whose parents were desperate enough to spend hard-earned cash, for the past twenty years. One of the reasons I am so skeptical of easy answers is that I have seen every way to fail, at every grade and age level.
Writing down just the answers is among my top ten list of ways to fail; it appears to work, temporarily, just the same as as memorizing the pre-primer and pretending to read appears to work temporarily; it leads to the same false confidence, and when the rubber hits the road, it is too late to go back and learn the skills you missed. While you’re frantically trying to find out why you don’t understand and why your answers suddenly are wrong, the rest of the world is moving onwards ahead of you.
Students who have trouble need more help understanding the concepts, not less.

As far as good teachers and bad teachers, I’ve seen both and I’ve had both. I’ve also been both; you can’t be a good teacher in an impossible catch-22 situation, so you can only decide which way to be bad, to try to teach despite your students being totally unprepared and their parents attacking you for making them work too hard, or to play games and pass the students on to the next person.
Accepting the fact that an awful lot of the math teachers in North America are very poorly prepared and have very little understanding of math themselves — a lot being biology or gym teachers who are told literally to “keep a chapter ahead of the kids” in Algebra 1, and others spending four years of teacher’s college gluing together Monopoly games instead of learning any math — when you do finally get a math teacher who is at least trying to teach the math concepts by insisting on the work being shown, it’s a shame when that teacher who is trying to do the right thing is insulted and vilified. No wonder good people leave the profession in droves and the incompetents are ever more numerous.