Thursday, October 27, 2011

Today's Million Dollar Question

I have been struggling a bit this year with getting a student or two to show steps/process/work/setups (or whatever you call it when you say that it isn't okay to give a lonely answer with no justification). The silver lining is that this struggle forces me to think about WHY students should show work.  Here are a few reasons I have:

Showing steps . . .
Puts the focus on the process, rather than the solution.
Communicates your solution to others.
Makes it possible for you (or someone helping you) to locate your mistakes.
Slows you down, so fewer careless mistakes happen.
Gives evidence your answer is right.
Demonstrates your understanding.
Helps reduce cheating. (Some might still copy, but at least they must copy the work too.)
Finally, in my class an answer bank is given. Showing steps keeps practice from becoming nothing more than a matching game.

I am also asking myself some questions like . . . WHY do some students struggle with showing work?

Maybe because . . .
It takes too much time.
They can do it mentally.
They don't know how to show work.
They are bored.
They don't believe in its value.
They are cheating.

Writing this, I realized that when a student is repeatedly refusing to show their process, I tend to go straight to negative assumptions. I assume they are being stubborn and uncooperative, or that they must be cheating.

I am going to try to put the whole issue in a more positive light and see where the students are coming from. Maybe these students think that showing steps is just for the teacher's sake, and has no benefit to them personally.

Or, maybe they genuinely don't know how to express how they got the answer.

It also has me thinking about the types of questions I am asking. If someone can calculate the answer mentally, maybe the question wasn't challenging enough?

How do you motivate students to show their thoughts?


  1. I had a student call me ridiculous yesterday because I told him that he had you show the substitution accurately. I told him that it would be pretty ridiculous to loose points because he couldn't follow directions.
    I think it is something we all struggle with!!

  2. I've started talking about it exclusively in terms of communication. (This is also my go-to answer for why they must use correct mathematical notation.)

    Putting it in these terms has both made "winning" these kinds of arguments easier, and also made me clarify my own thinking-- sometimes you just don't need to show work. Showing work is not inherently a virtue, just a communication tool.

    As far as whether the questions are challenging enough, some of my favorite test questions are ones that can be done mentally, if you know what you're doing. The level of difficulty of a problem is not really tightly correlated to the amount of pencil lead necessary to solve it.

  3. I also struggle with this with my students and what I've noticed is it is due to a lack of confidence with vocabulary and understanding "the why." Many teachers they had before me only taught the rules and so for them to show their work or explain their thinking is a bunch of illogical regurgiations of things they've been told that they don't understand. I have students come up to the board everyday to work out solutions for their peers and the hardest part for them is to explain how they got their answer, even if it is right. One student was trying to explain how he subtracted two fractions with different denominators but he could not, all he could do was provide the answer. When I kept probing him his answers were not making any sense at all but were filled with common misconceptions (I divided 2 by 6 and got 3 when really he multiplied etc.). I think this disconnect between procedures, memorizations and what actually makes sense to the students stops them from feeling confident in their work as well.

    I also provide some partial credit for students for showing ANY work on homework, exams, and quizzes and I explain that it helps me see what's going on with them. Many students will simply show their work so they don't receive a zero on a question they know nothing about but what they don't realize is they are showing me so much by their crazy work.

  4. I have two students in particular who refuse to show work. One student is literally failing my class because he refuses to turn in homework and refuses to show any work on a test. I'm sorry but when we're doing things like the distance and midpoint formula, or solving for angle measures in triangles or angle pairs and he just writes an answer, I cannot justify that. And increasingly, he's giving me wrong answers but I have no idea where he went wrong. He is in Geometry, failing, and tried to get the counselor to let him take Calculus. Right. He prides himself on being a math genius and doing it in his head. If he does write anything down, he will erase it and write his answer over it, as if proving that he doesn't have to write anything down. I've talked to him about it, wrote a letter to his parents with a test enclosed, written notes on his test, etc. But alas, he cares not.

    Thankfully, for the most part, he is the only student like that. I think what has helped my students is that in middle school, the math teachers are very picky graders. If they don't show their work or write the correct units, the problem is counted wrong. That whips them into shape pretty well and carries over into high school years as well.

    What if you showed them examples of tests showing different amounts of work and had them discuss as a class what grade they would give based on the understanding shown? Maybe putting it in black and white in front of their faces would help them see a teacher's dilemma.

  5. Students who won't show any work really frustrate me, but I had two 7th graders in particular last year who consistently would not write anything down, but had answers correct. I frequently would pair the two together and give them increasingly difficult problems, for which they had to do SOME calculations and explanations on paper. This seemed to work, but they really didn't like being given "extra work". Both boys wanted to finish classwork ASAP so that they could get started on their homework assignments, which I have written on the back board before class begins.

    I love giving partial credit for work shown, especially on formative assessments, but there are still those students whose work has no logical reasoning...

    A continuing struggle! I plan to introduce the Mathematical Habits of Mind at the beginning of the year and stress the importance of "proving" your solutions through steps. We shall see!