As our school’s Gifted Intervention Specialist, I often get questions from colleagues who need random resources or articles. Yesterday a question really got me thinking though. A colleague came to me with this request:
“Do you have any articles or handouts at the ready that help explain WHY it’s good to show your work in math?”
She explained that during a recent math test a student argued with her about showing his work, even going so far to say: “Your job is not to grade my work, your job is to grade my answer.”
It got me thinking – is he correct?
I jumped on this opportunity to do some digging, and Google searched: “Why gifted kids should show their work.” I expected to find articles stating the importance of showing the math process, or how explaining work proves they know concepts – all of the reasons I had been regurgitating to my own students over the years.
I found article after article about why it might be okay if gifted kids DON’T show their work. Ian Byrd’s post included a fantastic comparison that hit home with me, and probably will with many teachers:
“Have you ever been forced to write out your lesson plans? Did you complain to your colleagues that you can teach just fine without typed plans? Then you understand the frustration a gifted student feels when being forced to write out “the work” to solve for x given 3x = 9. For many of our intuitive gifted students, the solution for x in this case is as obvious as 1 + 1. And you wouldn’t demand proof for that, right?”
I totally get this; it makes complete sense to me. However, I still wanted to find a way to support my teacher. I know that (like it or not) our evaluations are based on student test scores, and the Common Core test includes questions that require students to “show their work.”
And – to be perfectly honest – I DO see some value in showing work. What I had to do now was get a little introspective and figure out why I found it valuable. Was it really just because it was what I had always been taught, and what I had always told kids?
After some thinking, I realized that to me, a student’s work is a snapshot of their brain. There are questions where they might guess, or where they might THINK they have a logical strategy down, but if I don’t see their thought process I have no way of helping them – either by reinforcing their logic or by helping them correct it.
Let’s say a question says: “Is 3 a prime number?” and a student answers with “Yes,” because in their brain all odd numbers are prime numbers. They get the answer correct, thus supporting their logic. The next question says: “Is 9 a prime number?” The student applies the same logic and but this time gets the question wrong.
If I had no explanation from the student, I would not know the mistake they made in their thinking. How could I interject to explain that prime numbers are numbers with two factors, and not all odd numbers are prime? I wouldn’t have known that was their thinking.
Because I agree with the sentiment that a gifted student’s intuitive thinking should be respected, while still understanding the purpose that showing work can serve – I decided to find some ways to compromise the two beliefs.
Want Your Gifted Kids to Show Their Work?
Suggestion 1: Give them harder problems that FORCE them to show their work. They know 6 x 9? How about 6 x 19?
Suggestion 2: Allow them to “show their work” in whatever method works for them. Let them use written out explanations, pictures and visuals, or simply math formulas.
Suggestion 3: Let them choose. Instead of making students show their work for every problem, let them pick a few to show their work for.
Bonus! You could even use this as an extra assessment if you state: “Show your work for ONE multiplicative comparison problem.” Now, you will also see if they can identify multiplicative comparisons!
Suggestion 4: Give them the option. They can choose to show their work or not. However, if a question is wrong and the work is not shown then they will not get a chance to redo for any credit. If they chose to show work, but still got the answer wrong, they will be able to go back and correct their work for partial points.
I would love to hear feedback from other educators – is showing your work a thing of the past? Also – do you have any other suggestions on how to balance showing vs. not showing?