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In my own physics book, I no longer include any of the "magical"
kinematic equations (like x = x_0 + v_0 t + 1/2 a t^2) as I find
they just allow students to bypass understanding. Without them,
students must solve problems based on scientific laws (like Newton's
laws) and definitions (like average velocity). At least that is my
intention. Has anyone else tried this?
I have and have found it very exciting.
The equations generally taught are for specific contitions that the
students never see. They constantly used to plug instantaneous speeds
into equations requiring average speed etc.
I make students create a graph sketch of the problem and then derive
the equation that represents that graph.
They complain a lot, but understand much more. They also start
looking for salient points vs superficial elements.
In alg based physics we are more often than not, solving for a slope,
axis, or area under the curve.
first semester ...
Students usually (but not universally) get #32 right. A reasonably
large percentage even get #36 right. Less than 25% get 33, 34, and
35 correct (over the past 10 years) and only one or two students a
year will get all 5 correct.