To Show Or Not To Show (Work)

Photo by Doviende

Have you engaged in a “show your work” battle with a gifted math student? Have you heard this line: “If I can do it in my head, why do I have to write it out?”

It might be worth it to quote an interesting study of gifted students and their teachers’ personality types by Dr. Jane Piirto. Piirto found that most teachers prefer Sensing while gifted students prefer iNtuition on the Myers Briggs Type Indicator.

If most educators tend to fall into the S type, how will they meet the needs of the N preferring students that exist in their classrooms…  S type relies on their senses for understanding and learning… If they can not use their senses, learning will be minimized. On the other hand, the N type is quite the opposite. They rely on their hunches or inner sense…

Many gifted students do “just get it” as a result of their intuitive personalities. Many teachers need to see the pieces to understand. This is a major personality conflict that teachers need to be aware of.

Writing Out Lesson Plans

Let’s switch our perspective for a moment. 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?

(Let’s get it straight though, a first year teacher may very well need to write out plans just as a student first wrestling with algebra needs to write out the steps to solve for x given 3x = 9).

The Solution: Increase Complexity

Rather than wrestling with students to “prove” solutions with “work,” simply increase the complexity of the problem so they must do the work out to get it right.

If students can “see” the solution to 3x = 9, first congratulate them on having such an intuitive mathematical mind. Then, differentiate the complexity of the problem so that the child is challenged. Have your student solve for x given 3x – 2 = 7.

This two-step problem may be complex enough to make it useful to a student to show their steps. This is the crux. Once a student believes in the usefulness of writing out the steps, then they have an incentive (beyond avoiding a nagging teacher) to do so. As adults, we know that it’s useful to write out steps because we’ve goofed up enough checkbooks to convince ourselves. But as teachers, we also know that writing out detailed lesson plans is only useful in certain situations.

Are your primary students refusing to write out the steps to solve 21+ 30? Increase the complexity to 35 + 21 + 30. Can they do that in their head? Congratulate them (because it is impressive) and then push the complexity another step.

I wrote more about increasing complexity here.

We must be careful not to admonish our intuitive learners for being intuitive. As teachers of the gifted, we must set up learning environments that our best for our students. And if they’re doing it all in their heads (and getting it right!), then the environment needs to change.

Read more about showing work in math here.