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.

I had too long a response for the comment field, so I wrote a blog post in response:

ReplyDeletehttp://gasstationwithoutpumps.wordpress.com/2014/05/21/establishing-the-habit-of-writing/

That's a very nice and thorough response, one that's well worth reading. I've left a comment there, too.

ReplyDeleteI'm going to steal this as my first night's assignment also! I'll be delving into the world of AP Physics 1 in the very near future, after a much anticipated summer workshop over the class. I'm pretty intimidated, to say the least. Verbal processing of algebraic and mathematic skills isn't easy to utilize, much less teach to a generation that is used to instant, black-and-white information (myself included!)! Do you mind exchanging emails? I fear I may need the wisdom from a seasoned a veteran...!

ReplyDeleteChris, you can get my email through Woodberry Forest School... feel free to get in contact. Better yet, come to the free open lab July 27-29 2014!

ReplyDeleteI'm currently teaching an "Honors Physics" summer school class, which I'm using as my trial run for teaching AP Physics 1 this fall primarily using the modeling method. For the first summer school homework assignment, I gave the writing prompt mentioned in this blog, embellished slightly, and I have been giving similar writing prompts ever since. The biggest suggestion I can make regarding these writing prompts for teachers to establish with their students is to have them write it entirely without using any numbers, and to save the numbers for the actual calculation part.

ReplyDeleteAs an example, I gave a kinematics writing prompt about a sprinter running a 100 meter dash. I gave the maximum possible acceleration and the maximum possible velocity of the runner, and the students had to write a paragraph about how they would figure out how much time it took the runner to complete the 100 m dash. Then they had to say how things such as the length of the acceleration zone or the time spent running at a constant velocity were affected if the runner's maximum possible acceleration or maximum possible velocity were changed by certain factors.

Many of the responses to the first part came back with things like, "First I would divide 10 by 2.5 to get the time for the first part. Then I would square the 10 and divide it by 2*2.5 to get the distance for the first part, which gives me 20 m. I would then subtract this from 100 m, showing the the sprinter has to run 80 m at a constant velocity. Divide this number by 10 to get 8 s, and then add this to the time for the first part." For the latter part, the students recalculated new values based on the variables that were changed, and included these numbers in the writing as well.

Once I banned numbers in the written portion after this prompt, and then had them rewrite this entire writing prompt without including any numbers, the writing improved significantly, and it actually became clear in their writing what they were doing to solve for the sprinter's time, and how changing certain variables affected others.