One of my pervious posts mentioned the problem of the balls and the bins. I got this problem from a source on twitter that I have since forgotten. Regardless of its origin, the question has been a fun one to pose to students and colleagues alike (I even asked my in-laws with some very interesting results). For those of you who haven’t read “Practice What You Preach“, The problem is as follows:
I have already expressed my views on the value of probability within the school curriculum. When posed in a creative context, the nature of the subject leads to excellent exploration. I tell this to every class that I teach probability to, and this year my explanation caught up with me.
Since my introduction to the twitterverse and blogosphere, I have been on the lookout for like-minded individuals who share my passion for the teaching and learning of mathematics. I have met numerous people who document their best strategies, and have already been very helpful to me. One such community of learners is the #mathchat gang that meets once a week (and re-opens discussion at a more European friendly time later in the week) to discuss a topic or theme in math education. Although it is often tough to express pedagogical beliefs in 140 characters or less, the conversation is incredibly fruitful. It was during one of the “mathchat”s that I was struck with a particularly convicting, and ironic, realization.
This morning on twitter, there was a problem that I just had to solve before going out the door. It is safe to say that these types of problems are my vice. Number Theory has always held a special interest to me despite, according to G.H, Hardy, having “absolutely no practical use.” (A Mathematician’s Apology, 2001). This has all changed with the inception of encryption.
There has been plenty of recent twitter talk about the process of moving the focus of mathematics education away from the “how” and toward the “why”. Traditionally, students have been trained to approach a question–usually given to them by an outside source like a teacher, textbook, or test–with the express intent to show the grader “how” it is answered. Such responses often include the use of algorithms, formulae, or memorized facts we know to be true. (These facts are in no way axiomatic, but constant repetition reduces them to that state. Students have answered them so often, the process loses meaning. Take 2×2 for example.)
There is widespread turmoil among teachers and students when it comes to the practicality of mathematics. School mathematics, at the middle and high school levels, has moved out of the elementary niche of rudimentary skills, but has yet to make it into the realm of complexity necessary to apply it back into the world. Our happy compromise, as teachers, is to go with a two-pronged attack:
Teachers in Saskatchewan, Canada have had a lot to deal with lately in the classroom. The ongoing political battle has effected hours of direct instruction in a very real way. I quickly noticed my classes becoming disjointed with large amounts of time between each encounter with the mathematics. Needless to say, I entered today’s lesson in Math 9 with a little apprehension. A Friday morning after 2 days of job action and a long weekend didn’t sound like the most nurturing of environments. I decided that the time was ripe to attempt a lesson that has been in my mind for a couple of months; the following account is the story of the task, presentation, student reaction, and important learnings.
This week marked my baptism by fire into the twitter world. It was not long until I was neck deep in tweets, favourites, re-tweets, and followers. The eternal nerd awoke inside me when I was confronted with my first NCTM “Problem of the Day”. A simple, yet dangerously deep, question was posed. Wanting to cement my reputation as a responsible twit, I sat down and began to tinker with the theory.