What if they ask me a question I can't answer?

I often coach student teachers assigned to teach topics they have not worked with in a long time. The last time many of them had Algebra or Trigonometry was in high school and some "rust" obscures their understanding of the subject. They are understandably concerned about making a mistake while working through examples or demonstrating solutions to homework questions. 

I can empathize having had to teach College Algebra many, many years after my last encounter with the material. Before each lesson I had to reteach myself the topics. (It didn't help that my initial interactions with the College Algebra content were what Skemp would call instrumental.) And when it came time to address homework issues, I was always concerned that I would make a mistake in front of the class. Turns out I had my own issues with math-phobia.

While I am comfortable with the idea of making mistakes in my mathematics education classes, because it represents the learning process, I have found college freshmen and sophomores taking a required math course less understanding than my preservice teachers. Students in College Algebra often have certain expectations of what mathematics teaching looks like and when they encounter something different (mistakes), they can shut down. So early on I want to establish a certain level of confidence for myself and for them.

I share this story with preservice teachers so that they can feel comfortable with the fact that any nagging doubts they have about teaching a topic they need to relearn can be expected and dealt with. There are two suggestions that I make to build their confidence. The first is to avoid answering off-the-cuff questions until they feel more comfortable with the content and the classroom. And the other is to always have the examples they want to share written out ahead of time.

When it comes to questions that arise in class, if it's not something the student teachers have prepared for I tell them it's alright to write the question down and tell the class they will get back to it. This models that all mathematical questions don't have immediate answers and hopefully helps students to become more comfortable embracing the patience required to be successful in learning relationally (see Skemp). Regarding homework questions, I suggest that the student teachers set up a procedure by which students can identify which problems they want support on. If this can be done beforehand (I used Blackboard), then the student teachers can determine which items caused the most confusion and prepare a whole-class demonstration to support student learning. Items identified by a single student can be attended to through a written example or individual conferencing. If there is no way to gather this information beforehand, then I suggest collecting it at the end of the class period when it is expected to be completed and preparing the support for the next period. In either case, have the work written out ahead of time.

When they share their examples, at least early on, I encourage the student teachers not to recopy the work on the board but to use the overhead or document camera to project their work. This addresses several issues that teachers trying to build their confidence often face. First, it tightens up time management. Writing on the board is time consuming and can allow students to get off-task. (Believe it or not, many of them are not copying it down.) I would simply project my work and add my thinking as I go over each step. Second, projecting previously written work alleviates the potential for making a mistake and eroding confidence for those already dealing with this issue. Multi-tasking when stressed is difficult, and I have found that the combination of copying and talking through my thinking can lead to errors even though I have written everything out correctly. Finally, and this is huge for new teachers in front of a class of teenagers, using written work projected on the board usually means not having to turn your back on the class. If you've ever taught in a secondary math class, you'll understand what I mean.

Let me be clear, I am not suggesting that this approach become the norm; it is just the place to start when teaching a new prep that might require some relearning of topics. Once a classroom culture of trust and respect has been developed, I have found that I can go back to responding to questions more immediately. But I still reserve the right to say, "I'll have to get back to you on that one."