This post is the third in a series of posts detailing the happenings of a math project. To better understand the whole story, please start reading at the beginning:

# Category: investigation

This post will make a lot more sense if you read the framework for the project in “Soft Drink Project Part 1: The Framework“.

I left the classroom energized; I could not remember a time that I was more pleased with a lesson that I had taught. In fact, I wouldn’t even call it teaching. I was observing. The process of brainstorming began organically. I had my doubts that it would continue the following Monday. Typically, students can’t even remember where they sit after a weekend–let alone what task they ended on.

## Unexpected Lesson Extension

It is very hard to develop an active atmosphere in a math classroom–especially at the high school level. I believe there are two main reasons for this: 1) Students have been slowly trained throughout their schooling that a “good” math student is one that listens, absorbs, and repeats. 2) The content often reaches beyond what most teachers deem to be “constructable”. Rather than fight with these two restraints, I began my implementation of Problem Based Learning in a class with manageable curriculum content filled with students who never learned to sit still in the first place.

I recently finished up a unit on sequences and series with my grade 11 pre-calculus students. The unit is somewhat of an enigma because it contains relatively simple ideas bogged down in complex notation. This coupled with the overlapping definitions makes for a fortnight of rather rigorous cognitive exercise.

The unit was supported through group tasks as the topics moved along. Arithmetic sequences and series were linked to linear functions through the toothpick problem. Students were asked to arrange toothpicks into boxes and record how many toothpicks it took to make ‘x’ number of boxes. Their results were extrapolated and tied to variables from the linear functions notation. From there, I introduced the new terms of “common difference” and “term one” instead of slope and y-intercept. The arithmetic portion usually goes smoother than its geometric cousin for two reasons:

I like to introduce each topic with a task or activity. These do not necessarily have to be long, but should activate mathematical thinking. The idea has slowly evolved for me throughout my short career. They are the amalgamation of the ideas of a “motivational set” and discovery learning. I felt that both components are positive things to include in a math class, but both had severe implementation problems.

The motivational set is far too passive. In my college, a picture, story, or conversation could serve as a motivational set. It was essentially a transition tool that was completely void of any mathematics. Every lesson begins with the same routine whether it be a national anthem, attendance, or a short time of homework recap, but each learning experience needs to begin with an active brain. I found that the purpose of the motivational set was important, but needed a stronger method to get brains engaged in the day’s learning.

I teach mathematics at the high school level, and know all about the various theories surrounding school mathematics. I can still remember the intrigue when the term “Math Wars” was introduced to me through some undergraduate reading. I immediately took to the history of my art, and found a very convoluted and bloody past. The constant pendulum between retention math, new math, back to basics, and now the new-new math is dizzying. Whenever I converse with a colleague about a new way of thinking in math education, I am sure to remind them that we are in a war. It is this idea that has appealed to the more militant teachers (myself included).

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.