My intern just started a unit on statistics with my favourite starter question of all time. (First blogged near the end of this post in 2011…)The question is simple: floor is very low, and ceiling is very high. Create a data set with the following characteristics: Mean = 3 Mode = 3 Median = 3 During the teacher rotation between groups, I picked up on some lines of reasoning. (Not being directly responsible for the teaching of the lesson, allows me to sit back, be inspired, and follow the lines of inspiration). Student justifications for their data sets were very …
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The Blue Jays Defense
Baseball is mathematically based. It is the best link between the generally nerdy domain of mathematics and generally manly domain of professional sports. The one downside to this statistically driven machine is that the stats can be selected and used to benefit almost any argument proposed. Major League Baseball keeps such extensive records of stats, that there is always an obscure one in support of your argument. Right now the league is in an uproar over the Toronto Blue Jays sign stealing controversy. Some anonymous players claimed that the Jays were stealing signs with a 3rd party and that effected …
Continue reading »The “Nearly” in Mathematics
Mathematics is the purest form of science, or at least that is what they tell us in university. This ideology carries over into the school staff; it wasn’t long until another member of the staff referred to me as a “math guy”. As much as this label is also self-imposed, I still struggle to understand what it means. The labels “english guy”, “phys-ed guy”, and “science guy” all persist within the building as well, but there is something that about the title of “math guy” that gets me. My friends and family quickly shunt all calculations to me when needed. …
Continue reading »Attaching a “Why” to the “How”
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 …
Continue reading »Playing With Mean, Median & Mode
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 …
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