Why do we have to show the work?

“Why do we have to show our work when we do arithmetic?”

I had an interesting phone conversation with a woman this morning. She was a tele-marketer for service I had signed up for to help me with how to make this site better. As she asked me questions about Math Mojo and Magic and Learning, she told me an interesting story about her son’s experience with math.

When her son was about 18 months old, she realized that when she took him to the grocery store, as she read out prices of what she was buying, he could add them up in his head! That is pretty amazing. No one had taught him that. It was an example of a strange, and poorly understood phenomenon that occurs now and then, and produces “savants.”

What made the story even more interesting to me is when she told me what I knew what eventually had to come. She told me that when he got to public school, it  absolutely ruined his math experience by making him “show his work.”

That fact that he didn’t understand how his work “worked,” made it hard for him to do it. The teachers didn’t understand how he did it, yet insisted that he “show the work.” It frustrated him and turned him totally off to math.

I wonder how many teachers realize that asking a savant “to show the work” (work which the teachers themselves don’t understand) is equivalent of asking the child to discover the basic principles of mathematics, streamline them, then codify them and find a symbolism for them that even the teacher can understand.

Yeah, and while your at it, why don’t you demand that the child square the circle, trisect an angle, and solve the Middle East crisis?

The tragedy is not only does this kind of thinking turn many gifted and passionate people off to mathematics, it also totally misses the opportunity to work with the child to understand how the child does what s/he does and share it with others. It is the teacher’s duty to investigate the methods, and help draw them out of the child. It is not the child’s duty to do the teacher’s job.

If the teacher is truly an educator, s/he will realize that this is a special opportunity that many educators can only dream of.

“Und now you vill show us ze paperz!”

It’s a control issue; pure and simple. They will not give it up. They will not admit it. They will not even face it themselves or even consider that it might be true. They feel threatened, and they will use every bit of rhetoric and rationalization they can dredge up to try to legitimize it.

Of course it is best for a student to be able to show his or her work. Admittedly, many children have lazy habits and need a kick in the butt about showing the work, but that is very often not the case. If a child has a problem showing the “work,” there may be many factors involved.

Very often, the child actually does have a better method than the mediocre algorithm that the school teaches. Face it, if it’s what the school teaches is what the No Child Left Behind Act tests for, it most assuredly is an inferior method.

So what can a teacher do in that case? The teacher should try to help the child relax and explore the thought process s/he uses to come up with the answer, without the threat of a grade hanging over his or her head. Until the teacher understands how the child processes the answer, there is no way the teacher can grade “the work.”

This can be a very difficult task for the average teacher. Especially an elementary school teacher. Teachers (good ones) are overworked, underpaid, underfunded, understaffed and over-criticized. What’s more, almost no elementary school teachers get enough training in basic math education, and what training they do get is generally towards what the NCLB act mandates.

If you are a frequent Math Mojo reader, you should already know that there are more than one ways to skin a cat (picturesque metaphor, no?) For example, there is no way I would ever ask students to spend a lot of time with the “standard” algorithm for multiplication. (For why, check out Standard Algorithm for Multiplication.)

You’ll probably have read something like this from me before, but it bears repeating, “If you are teaching ten kids how to multiply, you should have at least ten methods under your belt.” One reason for why I say this is because if you know a lot of ways to multiply, and you meet a child who doesn’t do it the “standard” way, you’ll have a better chance of understanding of how he does do it. At least you’ll have the mindset of understanding that there are different ways. You’ll be in a much better position to help the child understand his/her own thinking. Now that is teaching!

At an absolute minimum, everyone should understand at least this: “You must show your work,” should not be a dogma to be accepted, with the student held punishable for not being able to do it. Showing the work can be as much a learning experience for the teacher as for the student. The onus should be on the system, as much as the student. 

Being able to show your work in any kind of mental endeavor is a good thing. I’m not saying that it isn’t a good habit to cultivate, and that it can’t help you in your mental development. Unfortunately that is not what the mantra “you must show your work” is about in the public school systems in the US. It is about making it easy to grade and assess. It’s about making it easy for the system to keep records. 

Never mind that what it is assessing is meaningless, and the assessments are inaccurate. Never mind that in the process it stifles actual thought. Never mind that it makes grading easy, teaching frustrating, and learning difficult. The administrators and legislators can feel like they are doing something, and that is what it’s all about, isn’t it? 

In a nutshell, my point is that asking someone to do something that 

There is a happy ending to the woman’s story about her savant child. It involves a very unique and brilliant Idea that the woman came up with. I want to pass it on to you in a post very soon. If you have an exceptional child (and every child is exceptional) you should be able to get a certain amount of inspiration from it.

Tune in later this week.

Tomorrows post: Why do we have to show the work? Part 2