HOW EDUCATION DEPARTMENTS CAN HELP: PEDAGOGICAL CONTENT COURSES

Our Education Departments need to pick up exactly where the mathematical content courses leave off. Ideally, now that pre-service teachers have deep content knowledge in mathematics, pedagogical content courses need to develop ideas that are pertinent to teaching mathematics. This course should not be a course in preaching about traditional versus constructivist methods; strong educators that understand each method has its time and place in the context of learning would be the ideal candidates as instructors of such a course. Ideally, a pedagogical content course would cover topics such as presenting mathematical ideas in a clear and concise way, selection of purposeful representations, understanding and directing common student misconceptions, sequencing of mathematical ideas, modifying tasks to make them easier or more challenging, and evaluating mathematical explanations and notation. This set of topics, taken from this article by Deborah Ball, is not intended to be an exhaustive list, but a place to start conversation. It is important to include in-service teachers in this conversation, as they often have specific ideas that would be beneficial to heed when it comes to training our future teachers.

In addition, a good pedagogical content course might cover the cognitive processes behind learning; or, at least, the direct applications of cognitive psychology to education. Teachers could make more informed choices about how to present information to students if they received instruction on the basics of learning, including but not limited to: the lack of evidence for learning styles; the benefits of spacing practice over time; different ways of implementing retrieval practice; and how to train students to self-explain while problem-solving. Perhaps this could even be its own stand-alone course!

As I did some searching through some highly respected education programs in the country, I noticed that one of them did not have a specific mathematics pedagogy requirement. Rather, what was offered was a 500-level course in general science that doesn't even mention mathematics at all and looks like a vested-interest course (mention of inquiry-based methodology only and 21st century society claims). Also, although there are pedagogy courses that mention “learning” in the title, a quick scan of the course descriptions reveals that none of them actually address the cognitive mechanisms according to which learning happens! Instead, “learning” is discussed in a much more abstract and philosophical manner – for example, referring somewhat cryptically to “the ways in which teachers work within the parameters of prescribed curricula and assessment requirements”, and “current realities in society”.

Will those taking these courses realistically be prepared to meet the needs of their future mathematics students? Or would a more targeted approach that combines solid mathematical content with practical pedagogical strategies be more helpful? I would love to hear your thoughts.