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This post by Dan is fabulous because it brings up the ultimate point that we as educators should pay close attention to: everything we teach in our classrooms has a history that came about from a problematic situation.
When we are teaching a topic or idea, we should seriously consider the original motivation for the concept. What situation caused a problem that these computations now solve. It’s tempting in math to give everyone the solution to the problem and practice the exercise of solving the same one over and over again. Another common endeavor is to do the same computation or algebra over and over to get proficient without ever having a clue to what the original problem could be that would motivate such a process.
Student: Awesome! I know how to graph equations in slope-intercept form.
Parent: when would you need to know how to graph an equation in slope-intercept form?
Student: when my teacher asks me to graph one.
Do teachers have enough time to teach all the concepts this way and still have time to cover the material expected of them? Do they have enough time to research or discover motivations behind all the topics they are teaching? Is there curriculum out there that has this done for you already?