Must it Always be True?

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. I wish just to present the problem and then muse on its educational significance both for my personal learning of mathematics, and for that of my students. N is the 4-digit integer 6_9_. If these …

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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 …

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Merit to Mathematics Labs

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: 1. Tell the students that the practicality comes later 2. Create word problems about trains leaving stations or people tossing balls off cliffs Every teacher of mathematics (from the wide-eyed rookie to the well-weathered …

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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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Fractions From Digits

This week marked my baptism by fire into the twitter world. It was not long until I was neck deep in tweets, favorites, 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. The question was as follows: How many different fractions can you write using only the digits 1,2,3 & 4? Be sure to include fractions greater than 1. Immediately, I …

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