Week 2 Reflection

         In this weeks readings we looked at the Ontario Math curriculum for grades 1-8, as well as an article by Ball and Bass titled “Toward a Practice-based Theory of Mathematical Knowledge for Teaching”. As brought up in the lecture slides, there is undoubtedly a generally negative public opinion of math. Generally speaking, math is usually depicted as a chore and everyone’s least favourite subject, except for what the media depicts as nerds. When ideologies like this are depicted on children television shows it fosters a negative opinion of math from an early age. I can definitely say that this was the case for me when I was a child. When I was growing up math was my least favourite subject, and as soon as math wasn’t a mandatory course I stopped taking it. Due to the fact that I never took any post-secondary math courses I used to think that I would not be as good at teaching math, as I would be at teaching English, my undergrad major. However, in the article by Ball and Bass an interesting point was made. 
             There was a study that was based on math teachers and their student’s grades. The general thought was that those teachers who took math classes beyond the mandatory courses would have higher student grades in math. The results, however, were much different. In fact, the teachers who took more advanced math classes “produced positive main effects on students’ achievements in only 10% of the cases, and perhaps more unsettling, negative main effects in 8%.” (Ball and Bass, 3, http://bit.ly/1iHjN5o) The teachers who took very advanced math courses could have a very advanced thought process about math and therefore might be conditioned to think about and explain mathematical concepts in a very advanced way. This conditioning does not necessarily convert into high student grades, as the advanced way of thinking and explaining may confuse some children. Ball and Bass suggest certain teachers might be very advanced at memorizing formulas rather than knowing the pedagogy of math or how to explain the concepts. Another example; if you ask your Dad who is an engineer how to solve an equation, he may just quickly tell you the answer without explaining you through every step along the way of the problem solving. The advanced knowledge can hinder your teaching. Therefore, an excellent math teacher is someone who can relate every mathematical concept to every student individually, and explain in depth how to reach the answer. An excellent teacher must also understand that there are many different ways to reach the same answer. He or she should encourage students to find the answer and understand math any way that they can rather than just teach that there is a right and wrong way to do math, as most of us were taught. That is why the mathematical process of problem solving will be my focus over the next few weeks. Knowing how to explain a child through a concept is incredibly important in effectively helping them understand and excel at math. It is also, “the primary focus and goal of mathematics in the real world.”(Ontario Math Curr., 12, http://bit.ly/1dVS6Ck) This is important because basic mathematical problem solving principals and functions are used everyday in life and it’s crucial to learn how to effectively solve problems. 
The process of problem solving can also include every single mathematical process stated in the Curriculum. Equipping a child with the ability and the confidence to use math in the real world may help motivate them to learn and work through problems becoming better students, and ultimately better equipped adults.

Coleman, Mary. (2009). Chess. [Online Image]. http://bit.ly/1PhtNML