Modifying Math Misconceptions

It is impossible to teach someone when they believe that they have nothing left to learn.

When I was a student, when I believed that I understood a mathematical concept, I would zone out in class as the teacher repeated herself for the third time, ignore the in-class activities, and then not do the homework questions. From my perspective, why should I waste my mental energy focusing on something that I don't need further clarification on when I could do something fun like doodling a new design? When we had quizzes or tests I discovered if I had actually understood the concept like I had thought, or not. More often than not I understood the concept enough to get around three-quarter of the questions right. Since I was doing well enough that I was passing the course with decent marks, I didn't care about the questions that I had gotten wrong, or if I hadn't actually understood the concept quite properly or completely.

One of the most important things that we need to accomplish as teachers is to engage our students in the lessons that we are teaching. I have always been interested in literature, and so I always paid attention in English class, even when we were reading novels that I didn't really enjoy. While I was in university, one of my professors showed us a certain TED talk, and I have re-watched this particular TED talk several times since. On YouTube I have watched informational videos on topics that I am already educated on but that I feel very strongly about just to see someone else's specific views on the topic. I have mentioned all of these examples to show that a student who is interested in a topic is much more likely to remain engaged when they already feel that they fully understand the topic.

Many students believe that it they understand a topic "well enough" that that is "good enough," because they care more that they pass the course with a reasonably good grade than that they completely understand a certain concept. This attitude is why so many students develop and maintain misconceptions about mathematical concepts. When these misconceptions are carried over from previous years, they can significantly affect how well that student succeeds when that mathematical concept is expanded upon in an older grade. The student can become confused when the teacher is teaching the lesson, because they are experiencing dissonance between their own understanding and what the teacher is saying. Often when these students ask for clarification, the teacher struggles to find a way to make the student understand when they don't address the misconception that is holding the student back. Other students will assume understanding of a topic, and if they are not engaged in the lesson, won't pay attention and so learn that they are wrong. When these students do badly on tests or quizzes, their low marks discourage them and cause them to dislike math.

One method to engage students while also correcting misconceptions is to directly confront common misconceptions that our students likely have.