The last post discussed what goes on in my class on the first day of school. But what about the first night’s assignment?

I’ve not covered enough material by the end of day 1 that would justify assigning equilibrium problems. And, assigning math review is worse than useless – it’s harmful. I need problems for the first night that are doable without any in-class content, but that have useful pedagogical aims. (If I can’t justify homework as truly advancing students’ understanding, then I can’t assign it. There will be no busywork in my class.)

Consider what makes physics homework different from the homework that high school students are used to. A properly presented homework problem includes words, equations, diagrams, and a brief “comparison” in which the student shows an understanding of the physical meaning of a numerical answer. On the other hand, students habitually “solve” math problems by cramming a few numbers into the corner of a piece of notebook paper. The first day’s assignment should show clearly the level of thought, effort, and communication that will be regularly required.

So… here are two problems that I have assigned on the first night. The first is adapted nearly verbatim from a problem in Giancoli 5th edition.

1. 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? (Your comparison should discuss the size and/or depth of the lake compared to bodies of water you may be familiar with.)

2. Which is faster – your hair’s growth rate, or the speed of continental drift? (Your answer – in words with mathematical justification – is your comparison.)

Then, on day 2, here are two questions from the multiple choice quiz I give at the beginning of class. Note that the choices to the first question are local references… I encourage you to use this quiz with descriptions relevant to your class.

• How big is a 50 km2 lake?

(A) It would cover Woodberry and Orange, together

(B) About half the size of Woodberry’s campus

(C) About as big as the lakes on the golf course

(D) Would cover Woodberry and Charlottesville, together

(E) About one-tenth the size of one of the Great Lakes

• Which is faster, your hair’s growth rate, or the speed of continental drift?

(A) continental drift

(B) hair growth

(C) they essentially are the same

While everyone is working on these problems, I collect the homework. It is easy to flip through the papers to find all of the crazy answers to problem 1. I’ve had people tell me the lake’s depth dropped by as little as .8 mm, and as much as 87 million kilometers. As soon as I've gone over the quiz, I pick one egregiously silly depth and discuss why that can’t possibly be a correct answer. Thus, even before I graded anything, the homework problems have served a purpose: they’ve provoked a discussion of physical reasonability, and shown better than the best-written essay the difference between physics and math.

GCJ

I’ve not covered enough material by the end of day 1 that would justify assigning equilibrium problems. And, assigning math review is worse than useless – it’s harmful. I need problems for the first night that are doable without any in-class content, but that have useful pedagogical aims. (If I can’t justify homework as truly advancing students’ understanding, then I can’t assign it. There will be no busywork in my class.)

Consider what makes physics homework different from the homework that high school students are used to. A properly presented homework problem includes words, equations, diagrams, and a brief “comparison” in which the student shows an understanding of the physical meaning of a numerical answer. On the other hand, students habitually “solve” math problems by cramming a few numbers into the corner of a piece of notebook paper. The first day’s assignment should show clearly the level of thought, effort, and communication that will be regularly required.

So… here are two problems that I have assigned on the first night. The first is adapted nearly verbatim from a problem in Giancoli 5th edition.

1. 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? (Your comparison should discuss the size and/or depth of the lake compared to bodies of water you may be familiar with.)

2. Which is faster – your hair’s growth rate, or the speed of continental drift? (Your answer – in words with mathematical justification – is your comparison.)

Then, on day 2, here are two questions from the multiple choice quiz I give at the beginning of class. Note that the choices to the first question are local references… I encourage you to use this quiz with descriptions relevant to your class.

• How big is a 50 km2 lake?

(A) It would cover Woodberry and Orange, together

(B) About half the size of Woodberry’s campus

(C) About as big as the lakes on the golf course

(D) Would cover Woodberry and Charlottesville, together

(E) About one-tenth the size of one of the Great Lakes

• Which is faster, your hair’s growth rate, or the speed of continental drift?

(A) continental drift

(B) hair growth

(C) they essentially are the same

While everyone is working on these problems, I collect the homework. It is easy to flip through the papers to find all of the crazy answers to problem 1. I’ve had people tell me the lake’s depth dropped by as little as .8 mm, and as much as 87 million kilometers. As soon as I've gone over the quiz, I pick one egregiously silly depth and discuss why that can’t possibly be a correct answer. Thus, even before I graded anything, the homework problems have served a purpose: they’ve provoked a discussion of physical reasonability, and shown better than the best-written essay the difference between physics and math.

GCJ

Isn't the answer around 1.92 x 10^-5 meters of depth change? When you say by as little as 0.8mm, that's still too much...

ReplyDeleteNo... the depth change due to the town's use is about 8 cm.

DeleteGCJ