Have you engaged in a “show your work” battle with a student? Have you heard this line: “If I can do it in my head, why do I have to write it out?”
You may be fighting the wrong battle.
Writing Out Lesson Plans
Let’s switch our perspective. Have you ever been forced to write out a lesson plan? Did you grumble to your colleagues that you can teach just fine without typed-out plans? That it’s a huge waste of time?
Then you understand the frustration a student feels when they’re forced to write out “the work” for a problem they already know the answer to. For a student who immediately sees that, given 3x = 9, x equals 3, writing out their work is as silly as demanding a 4th grader “prove” that 1 + 1 = 2.
Let’s get it straight, though; a first-year teacher will benefit from writing out lesson plans until they’ve developed mastery, just as a student first learning algebra may need to write out their work to get the solution.
Writing out our work is useful… until it’s not.
The Solution: Increase Complexity
Forcing students to write out unnecessary work is a fruitless endeavor. It masks the real problem, which is this:
If a student can do it in their heads, then the work is too simple!
Instead of battling over “showing work,” simply increase the complexity of the problem until the student needs to write out their thinking in order to solve the problem correctly.
If students can “just see” the solution to 3x = 9, first congratulate them on having such an intuitive mathematical mind. Then, increase the problem’s complexity until you’re pushing the kid into their zone of proximal development. Have your student solve for x given 3x – 2 = 7. This two-step problem may be complex enough to make it useful to show one’s work.
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 until the work serves a useful purpose to the student. Can we do 9999 + 99 + 9 in our heads? I sure can’t!
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 sometimes useful to write out our work because we’ve goofed up enough times while balancing checkbooks. And as teachers, we also know that writing out detailed lesson plans is sometimes useful in certain situations. I can estimate my grocery cart in my head, but I do my taxes carefully and double-check.
We must be careful not to admonish our intuitive learners for being intuitive! As teachers, we must set up learning environments that are best for our students. And if they’re doing it all in their heads (and getting it right!), then the environment needs to change, not the student.
Read more about showing work in math here.