Step one: Realizing what you don't know

Sometimes, you can’t even find the maze, let alone find your way out of it. (Image by Wokandapix from Pixabay)

Something had finally clicked for a student of mine.

Trying to find the side length of a square with a perimeter of 56, she said, “I just don't understand how I would get the answer by dividing and getting one number and know that the other three are the same.”

It wasn’t that she understood the concept of division. It was that she was able to articulate clearly what she didn’t understand.

Actually, division is a concept that many students seem to have trouble with. Division is first introduced in third grade, and students are able to solve problems involving it; however, they don’t always grasp the underlying concept. My seventh-grade student is not alone in her confusion.

Unfortunately, for so many students, it’s painful to admit, even to yourself, that you don’t get it. Therefore, the loose threads are tucked away and hidden from sight, unacknowledged. An important aspect of my work is to help make it safe for students to pull them out and examine them. A student has to feel like it’s okay to be wrong or ask a “stupid” question about something they first learned years ago.

That’s why my student’s comments about division were such a breakthrough. It showed me that she had overcome the shame of ignorance and had begun to embrace it as an opportunity for growth. Instead of just trying to quickly get the right answer, she took the time to describe the gap in her understanding. Once that gap was recognized and acknowledged, we could address it together.

The gap is not always obvious. A seventh grader wouldn’t necessarily think to look for it in the third-grade material. Without a teacher or coach to reflect things back to you, it becomes even harder to see these gaps.

That said, the first clue is discomfort. There’s a sense that all is not well, even if you can’t put your finger on what the problem is. Sometimes the discomfort is accompanied by a sense of resistance: “Ugh, I don’t want to do this!” We can spot the missing piece in our knowledge by observing where we might be going around instead of through. What are we avoiding? That’s where the problem lies.

Then, the challenge is to formulate a good question. Saying “I don’t get it,” is a start, but it’s passive. If we want to solve our problem (or enlist someone’s assistance in doing so), we will make more progress if we can figure out what our question is or what we don’t get.

If step one is realizing what we don’t know, then step two is acknowledging it. Then we can ask for help — and then we’re on our way. It helps if you have someone you trust to guide you — someone who won’t laugh and say, “Shouldn’t you know that already?” The fact is, we all have gaps. Systematically identifying them and addressing them, no matter how surprising they are, can be highly satisfying once we drop the shame of feeling as though we should already understand.