After interviewing three high school students and three high school math teachers I have learned a lot about the practicality of teaching mathematics. In school we tend to get caught up in the theory of teaching, but this assignment really anchored everything back into reality. The following is a reflection on a few of the ideas that jumped out at me most from the interviews and how those ideas relate to my idea of how I will teach.
As a new teacher I will need a few years to get adjusted to my new position and everything it entails (i.e. lesson planning, marking, talking to parents, class management etc.), however there are various strategies I could employ to help my chance of success. While I am figuring out the basics of teaching I will have limited time for lesson planning so it is of great importance that I optimize how I do spend my time. I think the most beneficial focus at first would be on the mathematical content of my lessons and the enthusiasm with which I teach them. It is easy to get caught up trying to plan classes that are innovative, interesting and fun, but the time and effort it takes to put things together like that may not always be feasible in those beginning years. That’s not to say I should be happy lecturing for 45 minutes every class and never trying anything new, but there needs to be a balance. Perhaps later on in my career my lessons will most often involve innovative techniques, but in the first few years of teaching my style may lean mostly towards lecturing. During those first years when I am trying to figure everything out it is invaluable to have help from colleagues. Whether I have a specific mentor who gives me help and advice on a regular basis or I simply ask for help in the staff room at lunch, recognizing that I don’t know everything and that others have valuable advice and experience will be of immense help to me throughout my career.
Innovative lessons which integrate various mathematical concepts, technology and learning styles are the kind of lessons I assumed most teachers strive to create. From a student’s point of view, traditional lecture-driven math classes are not ideal; they are boring, solitary and restrictive. Creating a lesson that uses math in a new, interesting way or utilizes some new form of mathematical software will excite the students and possibly change their opinions about math class. Unfortunately, it may be only their opinion about the math class that has changed. It may be that the students still find math boring and the students’ sudden interest in their math class has more to do with the declining mathematical content rather than a shift in their opinion about the subject. In regards to weaving together different types of learning styles, this tactic can have positive and negative effects. Presenting the material in various ways may help some students in understand the concepts, but at the same time it could stifle other students’ individual learning. For example, in drawing visual representations of mathematical concepts you may help some students visualize it but you also direct what they will visualize. Directing their thoughts to one particular visual doesn’t allow them the chance to create their own personalized interpretation of the mathematics that would enrich their understanding, and instead the teacher has inadvertently directed their thoughts to mimic his/her own. As for integrating mathematical concepts together and showing how they are all connected, I have not yet heard one bad word said about it. The general consensus seems to be that there are no major downsides to showing the inter-connectivity of mathematics and that students will greatly benefit from seeing how everything fits together. When thinking about how to best teach a lesson - or teach math in general - the pros and cons of each strategy must be weighed and there will not be a single best way. Instead, there will be a plethora of ways all with different advantages and different weaknesses; the trick is to choose carefully.
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