I often forget just how dysfunctional a relationship many of my weaker students have with mathematics.”It’s been a long time since I’ve been surprised at the extent to which such students harbour an unproductive and damaging belief that mathematics is nothing more than a mishmash of symbols and voodoo procedures. After all, this is understandable, what with students being taught that memorizing templates of questions and plugging memorized formulas into their fucking graphing calculators is homologous with “doing mathematics”.”What surprised me for a long time after – at least the first fifty times I encountered the phenomenon – was how resistent these same students are to seeing mathematics as anything other than a collection of disconnected formulas and calculator algorithms.”The other week, I found myself teaching introductory graphing to a handful of students. Partway through a lesson, one student asked me – how do I graph the line in this question? Do I find two points and join them, or should I just find one point and the slope and then graph it that way?”Giddy with delight at this hint of outside-the-box thinking, I replied: you can do it either way you want! It’s your choice! Both of these options are totally valid methods of graphing the line! Two points, point slope, it’s up to you! In fact, you can graph it one way, and then if you want to check your work, you can graph it the other way, and ISN’T MATHEMATICS SUPER?”Pregnant pause. Hesitation. The barely-perceptible tremours of a worldview beginning to collapse unto itself.There are two ways to do this question?”Yes! Not one, but two (2) ways to achieve the goal of graphing a straight line! Pick one! It’s entirely up to you!”But which way should WE do it?”EITHER way! The easy way! The quick way! Try