My nephew and his wife are expecting, so I am in the midst of a crochet project for the baby. As any needleworker knows, there is a point in each skein of yarn where there is a tangle. It's not the fault of the crafter; it's a design flaw in the way yarn is produced, which is why it happens every time. Caught early enough, it's an amusing few moments of trying to figure out which direction the yarn is facing, but more often that not, it isn't found that early; and it tightens into a stubborn knot.
I had one of those this week, and it was particularly gnarly, containing multiple catch points. As I pulled from one direction and pushed in another, I kept saying to the yarn, "I know there is an origin to this knot somewhere, but I just can't see where it is."
There were points where I could loosen it just enough to make a little progress on the project, but I knew I would eventually pay for that. Loosening it in one spot tightens the knot further down the line, but that's a problem for later me to deal with as I want to feel like I can move forward now.
Eventually, though, the piper must be paid. I got to a point where I had to fight with the yarn. Cutting it is an option, but I am determined to out-stubborn the yarn. I'm a little sister, so I don't give up easily. After half an hour of fighting with it and a few under-my-breath curses at the manufacturer, I did eventually free the yarn.
This happens in our classrooms too. The knot, in this metaphor, is a misconception. Caught early, misconceptions are easily corrected, but we don't often know they are there until further down the line. At some point, a student surprisingly stops making progress. We try to keep going, but the confusion only seems to tighten. The invisible misconception is preventing the student from going any deeper into the content because they keep running into wrong thinking.
When this happens, it is important to track down the center of the knot. Back up to the beginning of the explanation. Re-explain step one and ask some questions. If they are good there, move on to step 2. At some point, you find the tangle and can fix it. After that point, the student says, "Oh, I get it now. This is much easier now."
But of course, this only works if we take the time to find and out-stubborn the confusion. Depending on how far down the line you have gotten from the initial hiccup, this could take serious time.
Some knitters are proactive. They begin their project by unspooling the skein of yarn and winding it into a ball. It takes time and doesn't look like progress, but it ensures they find the tangles early when they easy to unravel and allows the project to proceed smoothly.
In your classroom, you can't untangle the knots ahead of time. Some of them came to you from a previous class (much like the yarn comes with an inbuilt problem), but you don't know what they are. Some arise during your teaching because you know what you said, but you don't necessarily know what they heard. So you can't necessarily prevent the tangles entirely, but you can take steps to prevent them from tightening by using formative assessment. Pausing your lesson to check for understanding can feel like it is taking time from your lesson, but it saves you time in the long run.
There are a lot of ways to check for understanding, but the way we commonly do it, asking a question and then calling on a student with his or her hand up, is probably the least effective. You probably aren't finding the knots because students who raise their hands are usually confident they will be right. The misconceptions of the quiet go unnoticed, and the knots tighten as you move forward.
In my class, the use of a mini-whiteboard by every student simultaneously was the game changer. I could get an answer from every student in the amount of time it took me to scan the room. When six out of twenty four kids had the same wrong answer, I knew I had found a tangle. It was a simple fix as I asked, "Did you put that because you thought . . . ?" When they answered yes, I said, "Okay, I can see why you thought that, but it is is actually . . ." It's not the only way, but I do recommend finding a method that allows you to get an answer from ALL students.
The thing you DON'T want to do is to keep going in the hopes that the knot will untangle itself. This almost never happens. Deal with it now or deal with it later, but you will have to deal with it.
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