I'm in the infant stages of planning my AP Physics 1 course. The big trick is going to be establishing my students' ability and willingness to write their reasoning, to get them to focus on communication rather than on getting a correct numerical answer. Once it's clear that they are not taking a math course -- once they see that the solution to a problem looks much more like what they've done in biology or economics than in calculus -- I think the students will be able to move along quickly and enthusiastically through the material.
Students must get comfortable with calculation. However -- as was correctly pointed out to me at the AP consultant meeting in April -- if we start the course with lots of pure calculation, students will think that getting the answer is the holy grail of physics problems. If instead we begin the course demanding description, explanation, and all sorts of prose, students may become accepting of the idea that a numerical answer is merely the result of careful reasoning.
Consider the very first problem set I assign. While I begin the year with static equilibrium, the first night's problem is not directly related to anything on the AP Physics 1 curriculum. Rather, I'm establishing tone. I'm showing the style of problem we will be solving, the interesting results that can be obtained via quantitative reasoning.
Here's how I presented the problem to my AP Physics B students:
An average family of four uses roughly 1200 liters – about 300 gallons – of water per day. How much depth would a lake lose per year if it uniformly covered an area of 50 square kilometers and supplied a local town with a population of 40,000 people? Compare your answer to the size and/or depth of bodies of water you may be familiar with.
But note how I've changed it for AP Physics 1, in order to evoke verbal reasoning and to de-emphasize the pure algebraic aspects:
1. An average family of four uses roughly 1200 liters of water per day. In the town of Bonk – population 40,000 – drinking water is provided from a lake that covers an area of 50 square kilometers.
(a) In a clear, coherent, paragraph-length explanation, describe how you would figure out how much depth the lake loses each year due to the town’s usage.
(b) Using the method described in #1, calculate the depth the lake loses each year due to the town’s usage.
(c) Describe as you would to a non-physicist the physical meaning of the answer to #2 by comparison to length of an object with which you are familiar; that is, something like “Each year the lake loses a depth equal to the height of a [foo].”
(d) Describe as you would to a non-physicist how much land area this lake covers compared to land references with which you are familiar. Justify your answer.
I'm still asking for calculation; I'm still specifically asking about the physical meaning of the result. What's different is part (a). I'm demanding, ahead of the calculation, a "clear, coherent, paragraph-length explanation." That's verbiage directly from the released AP Physics 1 exams. I think -- I hope -- that my students will see immediately that a bunch of algebra by itself will earn no credit.
Now, I will definitely recommend to those having trouble with the verbal explanation that they might just try doing the calculation first, and then come back to explaining what they did and why. A good number of students are substantially more fluent in the language of mathematics than in written English when it comes to quantitative problem solving. That's fine. It's my job throughout the year to bring my students to fluency in both mathematical and verbal communication.
Thing is, my students come to my class expecting the mathematical reasoning to dominate the course. I must establish from day 1 that verbal reasoning cannot be ignored.