Mathematics for Sustainability 2

The Numbers Game: The Commonsense Guide to Understanding Numbers in the News,in Politics,and inLife: Michael Blastland,Andrew Dilnot: Amazon.com: Books via kwout

In Mathematics for Sustainability 1 I explained that I want to develop a new Gen Ed course "to enable students to develop the quantitative and qualitative skills needed to reason effectively about environmental and economic sustainability".  With this as the general objective, what are some of the specific content areas that the course should address, and what should be the specific objectives within each content area?

Right now, I see four mathematical content areas:

• Measuring
• Changing
• Networking
• Risking

Measuring - using numbers (including "large" and "small" numbers) to get an idea of the size and significance of things.  Including, for instance: physical units, prefixes (mega, giga, nano, and all that), percentages/ratios, estimation, reliability.  That's a list of concepts on the math side but of course the examples should be sustainability focused.  So I'd like the students to be able to answer questions like

• An inch of rain falls over a forest plot of an area 3.21 square miles.  How many tons of water fall? 
• Roughly, what is the total mass of carbon dioxide in the Earth's atmosphere at present?
• Suppose that a nuclear accident spreads 2.3 grams of cesium-137 uniformly over an area of 900 square miles. Compare the radioactivity from this source with the natural background.
• On average, how many gallons of gasoline per second are burned on the Pennsylvania Turnpike?
• A 10-acre farm near State College can produce enough food to support how many people on a vegetarian diet?  On a "standard American" diet?
• Roughly, how many birds do you think there are in the world?   How accurate do you think your estimate is?

 Of course, part of "being able to answer" such questions is being able to know what additional questions to ask in order to give reasonable answers.

I am looking at several books in order to get a handle on this part of the course.  Right now I am reading The Numbers Game by Blastland and Dilnot.  It starts with an arresting example: how many centenarians are there in the US?  That should be easy: just count, right?  In fact, census returns ask people to report their age.  But the self-reported numbers vary wildly and are estimated to be exaggerated by factors of 20 or more in some cases.  Starting from this example, the book seems to give a good overview both of the difficulty and the importance of measuring, both in absolute and relative terms.

Any more suggestions for this part? Thanks!


EDIT: I am thinking now to put the important distinction between stocks and flows in this section too.  (We have to know what we are measuring!)   Logically, it might belong in the Changing section but pedagogically it seems better here.  A reader on Azimuth sent me a link to this interesting paper which points out how important the stock/flow distinction is in public (mis)understanding of the greenhouse effect.