When I first started teaching math, I followed the general wisdom of the time that the majority of independent practice should take place outside of the limited classroom time. As I was advised, I took grades on homework completion, quickly glancing at thirty-plus student papers filled with equations before going over the answers.
At that time, if you had asked me which students would be successful in algebra at the end of the term, I would have replied confidently, “Well, the ones who do all their homework, of course.”
I would have been wrong.
Because what I was unaware of at the time is how many of the students were completing their homework, yet because of some critical misconceptions about the topic, did every problem wrong. Even worse, when the class went over the assignment, they discounted their errors as one-time mistakes or simply careless omissions instead of the deeper misunderstandings that they were.
And by asking the students to complete their assignments in the relative vacuum of home, I was providing the opportunity for them to continue to practice the material incorrectly, thus solidifying the errors. Without outside feedback, they lost perspective on their choices and their progress.
Because if we do something enough, we begin to believe it’s right thing.
When the only voice we listen to is our own, we fail to account for our misjudgments and we lose track of improvement.
When we do only what we know, our established neural pathways and assumptions become deep-worn grooves, lessons practiced and mastered, even if the conclusions aren’t accurate.
It’s easy to operate like those responsible students, dutifully completing every task that crosses our path. It’s easy to believe we’re doing the right thing because we’re doing some-thing. And it’s easy to discount any missteps as purely accidental or careless when they’re really because of some deeper understanding.
Before my first full year of teaching was out, I changed the structure of my class. I gave more time in class for independent practice and I always devised a strategy for students to verify their answers before the bell. I emphasized the importance of mistakes and that refusing to admit one is the worst mistake of all. I focused more on the quality of work completed than the quantity, making deals with the more reticent students that low homework grades could be modified upon successfully mastering a concept on a quiz.
That year taught me the danger of doing only what you know. I initially modeled my classroom on what I had experienced as a student, and the results were suboptimal. My students were practicing the procedures they knew, reinforcing incorrect pathways.
Progress was made only when other perspectives were considered, assumptions were challenged, mistakes were admitted and risks were taken.
Because sometimes the best step to take is the one into the unknown.