Annotated Bibliography
Teacher Resources
"6.055J/2.038J: Art of Approximation in Science and Engineering." 6.055J/2.038J: Art of Approximation in Science and Engineering. Accessed July 31, 2015. http://web.mit.edu/6.055/. An excellent collection of course materials from an MIT class on approximation. Contains both readings and exercises.
"CCNMTL MSE | Frontiers of Science." CCNMTL MSE | Frontiers of Science. Accessed July 31, 2015. http://ccnmtl.columbia.edu/projects/mmt/frontiers/web/index2.html. A chapter of an electronic textbook that expands on the ideas of relative size and some of the uses of order of magnitude calculations.
"How Should Mathematics Be Taught to Non-mathematicians?" Gowerss Weblog. June 8, 2012. Accessed July 31, 2015. https://gowers.wordpress.com/2012/06/08/how-should-mathematics-be-taught-to-non-mathematicians/. This is a discussion of the role of mathematics in the education of non-mathematicians, with emphasis on the usefulness (and process) of Fermi estimates and using probability correctly.
Howe, Roger, and Susanna Epp. "Taking Place Value Seriously: Arithmetic, Estimation, and Algebra." November 1, 2008. Accessed July 31, 2015. http://www.maa.org/sites/default/files/pdf/pmet/resources/PVHoweEpp-Nov2008.pdf. A paper with special emphasis on arithmetic and estimation. Especially good is its treatment of lattice multiplication, a technique that your students may be familiar with that clearly illustrates the diminishing value of successive decimal places.
"Order of Magnitude Physics: General Information." Physics 103b: Order of Magnitude Physics (Winter 97). Accessed July 31, 2015. http://www.inference.phy.cam.ac.uk/sanjoy/oom/1997/. The course materials from Cambridge undergraduate course on order of magnitude in physics.
"Physics on the Back of an Envelope." Physics on the Back of an Envelope. Accessed July 31, 2015. http://www.lions.odu.edu/~lweinste/courses/309s08.html. The course materials (readings and exercises) from an estimation course taught at Old Dominion by Leonard Weinstein, one of the authors of Guesstimation.
Polya, G. How To Solve It: A New Aspect of Mathematical Method. Princeton, NJ: Princeton University Press, 1945. This is an excellent text on the mentality and process of solving problems. Polya establishes a methodology and breaks down the thought process involved in solving difficult problems.
"Powers of Ten (1977)." YouTube. 1977. Accessed July 31, 2015. https://www.youtube.com/watch?v=0fKBhvDjuy0. A fabulous video that illustrates the differences in size of powers of ten in a fluid and intuitive manner. Don’t let the publication date sway you, it’s excellently done.
Stadel, Andrew. "Home." Estimation 180. Accessed July 31, 2015. http://www.estimation180.com/. Estimation 180 is designed for middle school math students, but I find the daily estimation tasks to be extremely appropriate for high school students just getting started in estimation. They also provide work sheets, lessons and additional resources to support the material. The first time I looked at the site, I sunk about 45 minutes into the estimation tasks because they were just plain fun.
Problem Collections
Harte, John, and Leonard J. Soltzberg. Consider a Spherical Cow: A course in Envioronmental Problem Solving. Sausalito, Calif.: University Science Books, 1988. Estimation exercises in Environmental Science. The early questions are quite good, but the level of difficulty quickly surpasses high school mathematics as the book progresses.
Santos, Aaron. How Many Licks?: Or, How to Estimate Damn Near Anything. Philadelphia: Running Press, 2009. A simple and to-the-point book of Fermi Questions, where each problem comes with a list of guiding questions and hints. Far less explanatory text than the Guesstimation series, making it an easier read for students.
Swartz, Clifford E. Back-of-the-envelope Physics. Baltimore: Johns Hopkins University Press, 2003. This is a book of estimation questions and solutions that are heavily rooted in physics content.
"University of Maryland Fermi Problems Site." University of Maryland Fermi Problems Site. Accessed July 31, 2015. http://www.physics.umd.edu/perg/fermi/fermi.htm. A collection of Fermi Problems curated by the University of Maryland physics department.
Weinstein, Lawrence, and John A. Adam. Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. Princeton, N.J.: Princeton University Press, 2008. A phenomenal book of Fermi Questions with very well explained solutions and a starting chapter on problem solving techniques. Highly recommended.
Weinstein, Lawrence. Guesstimation 2.0: Solving Today’s Problems on the Back of a Napkin. Princeton, N.J.: Princeton University Press, 2012. The second book in the Guesstimation series. Longer than the first, but I don’t like it quite as much.
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