Math Reflection Week 2: What Makes a Math Teacher?

No doubt many people when asked what their least favourite subject in school was would say mathematics.  Many people I’ve talked to often express a kind of anxiety or fear when encountered with the prospect of classroom math.  I believe this to be in part to how mathematics was taught to them growing up and bad experiences associated with math.  Both I and my colleagues in my teaching cohort have expressed a level of anxiety when it comes to the prospect of teaching math.  I as well as others I’ve talked to feel as though we lack the necessary knowledge, or are too “out of practice” to teach math.  However, we are all still operating under the basic assumptions that teaching math is simply the process of the teacher possessing large amounts of knowledge and imparting it on to their students.  This assumes that the greater the teacher’s knowledge in mathematics the greater their ability to teach.  This mindset leaves student teachers with little experience outside of high school feeling as though incapable of teaching math.  

So we must ask, does greater mathematical knowledge make better math teachers?  According to an article byDeborah Loewenberg Ball and Hyman Bass from the University of Michigan it may not be that simple.  According to their study, they found that teachers with past knowledge of advanced mathematics only produces positive effects on students in only 10% of the cases, and oddly enough produced negative effects in 8% of cases (p.3).  However, they go on to state that from observational studies “teacher’s understanding of and agility with the mathematical content does affect the quality of their teaching.” (p. 3).  Therefore there are difficulties when teachers are unfamiliar with the content.  So what must be done to teach mathematics effectively?  According to Ball and Bass a lot of what teachers need to do to teach effectively are pedagogical skills.  This means adjusting your mathematical language and definitions to fit your student’s knowledge and experience.  Teaching mathematics thus requires a kind of textbook understanding of mathematical elements, but also math that is less visible such as definitions or determining the validity of multiple methods.  For Ball and Bass the significant factors for teaching mathematics is the act of unpacking or compressing ideas into more usable forms.  Another idea is to connect mathematical ideas across different mathematical subjects (p. 11).  These are some of the basic concepts for what makes an effective math teacher.
   
Mathematical knowledge is something that emerging teachers will simply have to have, but it is important to identify what they do know and what they don’t know.  I believe that we have already started this process with the Elevate my Math online course.  In it all of us were able to identify what we knew and did not know.  Student teachers will have to learn mathematical knowledge specifically for teaching.  We must continue to develop our content knowledge while beginning to develop our pedagogical content knowledge.  For me developing both of these skills further will be important as I progress to becoming a teacher.