What is Mathematics and Why do We Teach it?

I decided to follow my path of mathematics because I ultimately enjoyed it and was pretty good at it.  It was an easy ‘A’ elective at university.   Then when I decided to become a teacher and I settled into a math job, I never once wondered why do we teach math?  Obviously I was faced by this age old question in class by many students.  But, I always had an answer.  There was something that I could relate the topic to in real life and if I couldn’t then I would tell students they would need it for harder topics down the road.  I was a strong believer in many aspects of Lakoff and Nunez’s (2000) the “Romance of Mathematics” and felt as Davis (1995) describes this question to be one classified as rhetorical.  Why did I feel we were teaching math?  My answer would have been very close to how Davis (1995) answered, “[b]ecause we have to...” (p. 20).  

My beliefs about math have begun to change and this process started when I began my masters in education almost two years ago.  Many of my previous courses got me thinking about the structure of the education system and why we are teaching the things we are and the way we are.  As Ken Robinson stated in his video about creativity and education, we are unaware of the future, students need to be creative and learn how to solve novel problems.  Students will need to learn to be learners, it’s the only way to prepare them for the unknown.  He described creativity as coming up with something original and useful whereas our education system dictates what the students will learn and how they will learn it by illuminating mistakes.  We need to allow students to ‘discover learn’ more often and students in mathematics in particular are often told the exact method to use to solve a problem, they are given step by step solutions and teachers will often mark solutions wrong if they have not followed proper procedures.  How is mathematics preparing our students for the future of the unknown?

Previous to the readings for this week, I believed that mathematics consisted of known facts, a truth, and always having a correct answer. Again similar to Lakoff and Nunez’s (2000) “Romance of Mathematics” I felt that math existed in the universe whether humans did or not.  However, I can now see Hersh’s (1997) that math is a part of the human culture, without our human consciousness it would be nothing.  Although we can see small numbers in nature, numbering something is the same as giving it a name.  Without humans, there are still four flowers there but the word four is used to help us humans classify and sort objects.  We are the ones that find the need to manipulate the numbers and it becomes very complex and confusing to question something that you have always believed.  Sometimes it just takes a different perspective to open your eyes and see a different view.  I think I would like to know more about the history of mathematics, even as a math minor none of my courses delved into where the many of the mathematical ideas came from.  I would also need more information different philosophies of mathematics, I am very easily lead by ideas and I would certainly like to learn of more ideas about what exactly math is all about.  

References:

Brockman, John. (1997). What kind of thing is a number? A talk with Reuben Hersh.

Davis, B. (1995). Why teach mathematics? Mathematics education and enactivist theory. For the Learning of Mathematics, 15 (2), 2-8.

Lakeoff & Nunez. (2000)  The theory of embodied mathematics. Where Mathematics Comes From.

Robinson, Ken. Do Schools Kill Creativity? Feb 2006. Keynote Address.

Math Autobiography

Math was always my favourite subject in school.  I went to a one room school which included students from kindergarten to grade 3 and all students would be doing the same subject at the same time. It was very easy for the teacher to provide extension work because when you completed your work you would move on to work for the next grade  I remember getting a lot of praise for completing my math work quickly and correctly.

The math book for primary school certainly stands out.  It was a work book with bright pictures and many interactive lessons.  I can vividly recall spending classes cutting out base ten blocks and then gluing them on the next page to correctly display the correct number.  I always found math so much fun and loved when it was math time.  It wasn’t until I was in grade 3 that I realised I was much different from other students in this regard.  This was when math began to get difficult for some students and I felt so frustrated with my group members if they did not understand a concept or a simple multiplication fact.  I can also recall my teachers displaying similar emotions when students were expressing difficulties.

In elementary school mathematics was more of a memorization subject.  I think I did understand the underlying reasoning to some extent but for the most part had memorized how to complete certain questions by repeating the process.  That’s how I remember math class, completing the same type of question over and over.  It wasn’t until high school that I remember being challenged by math again.  In grade ten my teacher would give me hard math puzzles to complete when I had my work done.  Myself and another student in the class would race to see who could solve it first and it was always something different, something that did not contain curriculum content.  

It also wasn’t until high school that I saw a passion for math coming from my teachers.  There was a statistics half credit course offered as an elective and of course I took it.  Our teacher would always make real life connections to the content of the course.  He even brought in Proline tickets for us to use for a full month.  We discussed odds and probabilities while completing a full class competition to see who could “win” the most money.  He would post up our scores every Monday and had a prize for the winner.  That activity is still one of the most influential and memorable activities in my school career. 

However, one of my worse memories of school also involved math.  The one and only time I was ever asked to stay behind after class was by my grade 12 math teacher.  We had completed a math test the day before and our school band had just returned from a trip to Toronto.  He had asked me to stay behind to tell me how bad I had done on the test and how disappointed he was.  I can clearly see the 74% on the test paper now.  I felt awful!  I remember dreading to tell my parents and finding it hard to return to math class the next day.  In hind sight the life experiences that I gained from the band trip were much more valuable and I really wish I hadn’t beat myself up over it.  But, I certainly remember working really hard throughout the next unit.

Another elective that I completed in high school was a Pre-Calculus course.  It made absolutely no sense to me what so ever as I was completing it but it certainly made Math1000 a lot easier in my first year of university.  I had to complete two math courses for my science degree and figured that since I found math so easy I should just complete it as my minor.  Little did I realize that it would lead me to my future career.  I had full intentions of completing medical school and it wasn’t until I finished my third year of my BioChem degree did I change my mind.  

One of the largest differences between math in high school and university was the assessments.  Assessments in high school mostly consisted of questions exactly like the millions we had completed in class.  Whereas, university assessments contained questions that were new and required techniques or even combinations of techniques learned; you had to fully understand concepts and know how to apply them to novel situations in university. This is when I fully understood the importance of understanding the mathematics as opposed to memorizing it and I try to emphasize this in my teaching every day.  

My university education training was in intermediate/secondary with a primary teachable in science and secondary teachable in math.  I thought that I would be teaching science in my career until I was awarded my first job in the UK teaching all math.  The school that I taught at had a high turnover rate of teachers.  It was a school that was known to have many behaviour issues and had recently received a bad review by the local education authorities.  Our math department consisted of five full time teachers, three of which were all under 25 years old.  Our teaching styles were interactive and fun.  We would try new teaching techniques together and experiment with technologies where possible.  Since the school was trying to improve its reputation, it awarded funding for materials and professional development in the most recently researched educational ideas. 

The three of us stayed teaching there for three consecutive years (which was basically unheard of) allowing us to attain middle management positions in the school.  I was awarded the department head of junior high math by my third year which gave me such an amazing experience and ultimately lead to me landing my job here in Newfoundland.  

Teaching all junior high math, my biggest challenge here is covering the vast curriculum.  We have common exams in all courses I teach, grades 7, 8 and 9 which also adds more pressure.  I often feel rushed through more difficult topics and I don’t have the time to reteach or try different methods to teach a topic.  The lack of sufficient time here is such a disheartening factor to me because I cannot teach in a manner that I enjoy.  I find myself wanting to try different activities with the students but not having the time to do so.  In addition, the math curriculum has just undergone yet another change that it will take a few years to completely feel comfortable in knowing what is coming up and to know what topics can be taught a bit quicker allowing for more time for interactive activities in other topics.