I have blogged quite a bit about the theory behind my pedagogy; today I thought I would illustrate how I actually apply my philosophy to my teaching. Last week, I thought I would assess if my calculus students truly understood the critical thinking involved to solve a problem.
Using the methodology of Dan Meyer and an idea I read about on the AP Calculus discussion board, I gave the students a sheet that is illustrated in the photo above. No numbers, formulas, or guiding questions were given. The students were to collaborate on how to solve the problem.
The problem: The picture is a blue print, to scale, of a main floor of a prison. The circle is the camera that rotates in a full circle. Due to the difference in distances from the walls, when the camera pans over the two Xs, the speed will be different. Jailor Jimmy wants to slow the camera down, such that when it pans over the North X, it will be at the same speed it pans by the South X.
For the non-calculus teachers, I gave my students a question, with context, for which calculus is needed to solve. Acting like Jailor Jimmy, I answered any question the groups might have. Some questions, I would respond with “I don’t know”, or “Can’t remember”. Students were forced to decide what information is needed, and what information they can determine on their own. All groups where provided with ruler, protractors, and any other tool them deemed necessary.
At the beginning, students were frustrated and I heard comments such as “What should we ask?”,
“What do we need to know?”. I realized that these students were accustomed to being provided any and all information needed in the question, and usually in the order they needed it. This problem I have perpetuated by providing this information all semester long.
“What do we need to know?”. I realized that these students were accustomed to being provided any and all information needed in the question, and usually in the order they needed it. This problem I have perpetuated by providing this information all semester long.
After 5 minutes or so of struggling, the critical thinking started. Students started asking certain distances. Jailor Jimmy only remembered one distance. This information allowed for students to determine the scale of the diagram. Also, the current speed of the camera was given. These two pieces of information are all that is needed to solve the problem. I realized that is no longer what I COVER in class that sticks and makes sense, but what the students DISCOVER in class that carries the most meaning.
Students struggled at the beginning, but after 20 minutes, most groups were on their way. Measuring, on their own, the information needed and using formulas they decided were pertinent to solve the problem. At the end of class, I heard some students walking out expressing, “Man my head hurts!”, this made me smile as last semester I had students walking out saying “Man my butt hurts!”.
Video that inspired this:
This is a great example of the kind of story parents need to better understand what's meant by "critical thinking" and "stopping teaching".
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