Many years ago when I was a student at Queen's University, I was fortunate to take four courses with Peter Taylor, a terrific Math professor. Dr. Taylor is a terrific mathematician but he also has side interests in Biology (I did not know theoretical biology existed until I heard him talk about it) and education.
Earlier this year, I was able to attend his "Last Lecture" entitled "God is a Mathematician", and speaking to him briefly afterward I heard about his web site. When I find time, I look through his web site to see what gems I can find, because he has so many fantastic ideas and makes so many neat connections. Yesterday, I found this Dialogue (it deserves the capital D) which sparked fireworks in my brain about some of the difficulties I have seen while teaching.
Dr. Taylor's point in the Dialogue is that if you look at the content of an English course, it is normally full of works of art. There are poems, novels, plays, short stories and more that all have been found to have value, a connection to life, by many people. So, an English course by nature contains subject matter that is intrinsically interesting. I think that we all understand that not every student is going to be impressed by these works of art, but it gives the course a starting point rooted in reality, the reality that there is merit to these pieces.
In Mathematics, we typically focus on the building of technical skills, mostly revolving around addition, subtraction, multiplication, division of different mathematical elements. First, we work with natural numbers, then we work with fractions, then we work with variables, then we work with algebraic expressions. In a sense it is the same stuff over and over again, and so there is little wonder that students get bored. The questions/problems/challenges that have an interesting connection to the students' curiousities and lives are often put in the "extra", "challenge", or "extension" portion of the textbook and are rarely assigned by the teacher, usually because they seem too hard. Dr. Taylor's point is that these problems are hard, the same way that writing or reading a good poem is hard, but we still find the time to do that in our English courses, so why not do it in Math?
As I said above, these ideas ignited some fireworks in my brain. I have made a first attempt to put together a mathematical challenge to students that is, in its small way, a work of art. If you are interested in having a look, it is called the "One Shot Challenge". It is intended for Grade 10 Applied Math (Quadratics strand) and you can find it here on my wiki.
I welcome any thoughts and comments on my "work of art" as well as other ideas from this post, or any other.