For high school algebra students have to find the equation of a straight line perpendicular to a street to build a bike path to a park. Is this relevant for a high school student?
Today my students did not appear interested in this problem. I took teaching classes and I am afraid I did not follow the advice; first grab the students attention. What happened is that only those already interested in math, got into it. The rest did not seem involved.
The textbook authors also are to blame. Most students are not invited to the planning commission to build the next bike path in their town. I am not a teenager anymore, I really do not know what my students would rather do to learn math.
Vygotsky's Zone of Proximal Development (ZPD), as I see it, only tells me what the student knows, and how to work in that ZPD. It does not tell me what are the real questions he wants answered.
What do I want to know? The topic is parallel and perpendicular lines. The slope quotient of the first is 1, the slope product of the second is -1. I can argue my way to show those results, and it is a bit of an interesting challenge to do it. But do the students really see my motivation?
I guess I am the elephant in the room. My concerns are not close to those of my students, maybe I should run a more student centered class.
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