What mathematical knowledge is needed to teach mathematics?

EDBE 8F83 BLOG THREE

This week’s reading and discussion really reflected on how I have often felt over the last 4 years of being in this program. There have been several occasions when I have thought to myself “why do I need to take this course to teach mathematics or physics at the high school level.” I have become an expert at the subjects not an expert at teaching them, which is what my goal is. I believe that teacher perspective programs should include more classes and experience in teaching. There are many required classes that I believe are definitely not necessary to take in order to be a good math teacher. There needs to be a balance in this program between learning how to each (with experience) and the content needed to do so. This goes for all subjects at the intermediate/senior level, especially in mathematics and science. Ball and Bass (2003) described this as Pedagogical content knowledge, which is a unique kind of knowledge that intertwines content with aspects of teaching and learning. There needs to be a balance of content and how to teach the content. There is no need for us to be taking courses such as linear algebra and differential equations when we are in a program to teach high school math. The only benefit to taking these courses is that you finish with a Bachelor of Science and a Bachelor of Education at the end of this 5 (now 6) year program.

Something that really does not make sense to me is that elementary school teachers teach math but may not have taken a math course since grade 11, while high school teachers take mathematics until 4^th year of university. There needs to be a balance established. I know many elementary teacher candidates who do not know how to compute simple mathematics skills, and these are important skills in which they are ‘qualified’ to teach. I do not think this is the case all of the time, but I have personally seen this on several different occasions.

Another thing that I have learned in the past couple years is that math teachers need to be open to different approaches. Growing up I always believed that to complete a mathematical problem, there is only one way to get to the answer. Through my education course and my in my experience tutoring, I have learned that there is definitely several ways to do a lot of things. The example Ball and Bass (2003) used was multiplying 25 x 35. They showed that there were 3 different ways to do so, and I’m sure there are more ways to compute this as well. I have noticed tutoring too that I will explain a concept and then realize, from the students confusion, that they were taught it a different way. In order to be a good teacher I believe that you need to be open to learning these different approaches from students, and be willing to teach the same concepts in different ways. One approach may make sense to some students and make no sense to others, while another approach would make sense to these students who didn't understand one option and not make sense to the students who did.

I think that a balance between mathematical content and how to teach mathematics needs to be put into perspective teacher programs, especially at the primary/ junior and junior/intermediate level. The content is important in order to have a good understanding of what you’re teaching, and choosing grade and level appropriate material and problems. And the way this content is taught is even more important, in order to maximize students learning of the subject. 

picture one from: https://larrycuban.files.wordpress.com/2013/12/images2.jpg?w=500
picture two from: http://orig12.deviantart.net/6171/f/2013/093/f/a/snoopy_teaching_math_by_sakurapetalwolf-d609pot.jpg