Teaching advanced math classes is a blast. Students are generally more engaged in learning (i.e.. they do their homework!), contribute insightful ideas, and typically make classroom management a breeze. Teaching accelerated students can also present some challenges. One of my greatest struggles was getting advanced students to admit their misconceptions when they arose.
Every student struggles with grasping math concepts at some point. As teachers, we know the importance of diagnosing and fixing misconceptions quickly. I lead a pretty open classroom where discussion is encouraged and the general climate is warm and inviting. No one ridicules thoughts or perspectives (our students are taught manners at the beginning of the school year, including manners relating to small group communication). Yet when it came to getting my advanced students to open up about what they really thought regarding a concept, I found them hesitant to answer. Intrigued by their reservation, I began asking several students after class why they hesitated to open up more about their struggles with problems in class. Their response was simple, but had a profound impact on my classroom approach – my students were afraid of appearing “stupid” in front of others.
Although that conclusion may seem obvious to some, I thought that advanced students would be less susceptible to insecurity than other students. Their drive to be the best and master content would somehow override the common fear of inadequacy we all face. But it doesn’t. Why is that? As I examined common classroom practices, here’s what I discovered:
1. The arrival at a correct answer is celebrated more often than the process it took to get there.
We have all experienced this in our classrooms. Students are confident and eager to present that x=5 but cannot explain why x=5. Over the years, these students have typically found math to make sense to them naturally, without much effort. Most of the answers they’ve offered in previous classes have been right. The rare times these students were incorrect, I picture another student quickly raising their hand, offering the correct answer, and receiving praise from the instructor. I can see this experience molding students into a position that if they aren’t certain their answer is correct, they may not risk participating.
2. Mistakes are rarely celebrated.
We all want students to feel comfortable offering their honest thoughts regarding solution processes in class. For that to happen, mistakes need to be celebrated just as purposefully as successes. Every answer that a student gives, right or wrong, usually offers us a teachable moment. One creative approach to celebrating mistakes, and the teachable moments they provide, is to practice Leah Alcala’s method of choosing your favorite “no”. For those of you using Discovery Education’s Math Techbook, the student whiteboard feature offers the opportunity for students to send whiteboard images to you, allowing you to choose your favorite “no” quickly, easily, and anonymously. Combine that with the formative student data from your teacher dashboard to find struggling students even more quickly and discretely.
3. Students truly feel they are the only ones who do not understand a concept. There is a lack of connectivity.
It may sound simplistic, but here was my solution. Every time one of my students displays a misconception, whether through asking a question or through displaying incorrect reasoning, I state to the class how glad I am that it happened. I show genuine excitement when teachable moments appear. I then ask the class who else also struggled with that misconception. Surprisingly, once my students saw that they weren’t the only one who struggled, they readily raised their hands. Over time, making simple mistakes became routine, accepted, and sometimes applauded as they moved us forward in understanding concepts more deeply.
4. Students assume that if they’re wrong, they’re really wrong.
This was rarely the case with my students. Over time, we identified common small errors that throw off their calculations. Our greatest issues were errors with negative signs, incomplete distribution (not distributing to the back term of a binomial), and miscalculations when adding or subtracting integers. Most of the time, one minor miscalculation threw the whole problem off. Seeing this happen over and over taught my advanced students to be meticulous in calculations and gave value to clearly showing their work. They soon understood that they knew 95% of the solution process in most cases, and that the 5% they were missing seemed to center around common weaknesses. Seeing their proximity to mastery motivated them to focus on fixing the small things. Soon, they self-identified their weaknesses and began to consciously avoid them in the future.
It has been said that success is built on a mountain of failure. However, it is hard to build on that failure if it is never brought out into the open for review and reflection. Creating safe environments for students to fail constructively is paramount to running an effective classroom. Do you have any additional strategies you implement to achieve this? If so, please share them in the comments below!