Math Education Documents and Tools
rev. early June 2013

Donald Byrd
Woodrow Wilson Indiana Teaching Fellow
Visiting Scientist, Research Technologies, and
Adjunct Associate Professor of Informatics, Indiana University, Bloomington

Note: All of these are by me except for items whose titles are preceded by an asterisk ("*").

For Teachers (and perhaps a few others)

 Thoughts on Teaching: What I Learned about Why My Students Didn't Learn More How my lengthy career in software and music informatics led to a brief career as a math teacher, with quite a bit of reflection on my experiences as a teacher, plus a list of 11 things I learned and how I plan to respond to those insights in my future teaching. "Math is Cool, Fun, Wild, etc." Teaching Ideas A collection of wildly different ideas for teaching secondary math. What they have in common is I think/hope they have the potential of promoting intrinsic motivation by getting students to see that math can be cool and fun, wild and crazy. WARNING: Many of these ideas are half-baked, if that! DonsUpDownTimer_Distrib.zip A simple, easy-to-use timer that can act as a stopwatch to measure one or more intervals of time, then count down whatever length of time it's accumulated. Designed for occasions when you want to show unruly students that whatever amount of your time they waste, you'll waste the same amount of their time, but it has other uses, too -- for example, to convince those students that whatever amount of time they do something you want them to do, they can spend the same amount of time doing what they want.

Reference and General Information

 Meaningful Numbers and "Significant Figures" What significant figures are, why they're important, and how they relate to statements about accuracy like the plus-or-minus such-and-such percent form. Includes a photo of a remarkable hammer with its label: according to the label, the hammer's weight is known to five significant figures! Tips and Resources for Solving Math Problems A list of resources (in this case, Web sites) and a bunch of tips to help solve mathematical problems. The "Tips" are probably most useful for students in upper-level high-school and lower-level college math courses; the "Resources" cover a much wider range. Anatomy of a Term An algebraic expression is made up of terms, and a term is made up of a coefficient, a variable part, maybe an exponent, etc.; but students often have trouble telling what's what. This chart should help. Polynomials & Derivatives; Critical Points & Inflection Points Information about polynomials and their derivatives that should make it easier to understand the relationships between polynomials and their critical points and inflection points. Types of Triangles Shows the relationship among all types of triangles in a Venn-diagram-like way that I think is exceptionally clear. Small Powers of Small Integers I've seen students struggle with algebra problems I thought they'd find easy simply because they didn't realize that, say, 27 is a perfect cube. It'd be great if they were aware of such basic number facts, but that takes time, and there are more important things; hence I made this table available during tests.

Reference: Geometry & Algebra; Linear, Exponential, & Logarithmic Functions

 *S+C_QuickRefCard_Pg1 Page 1 of the quick reference card for a popular precalculus text (Swokowski & Cole's Algebra and Trigonometry, with Analytic Geometry; this copy from the Classic 11th ed.), with lots of useful formulas and diagrams for geometry and algebra. *S+C_QuickRefCard_Pg2 Page 2 of the quick reference card for the Swokowski & Cole text, with lots of useful formulas and graphs for trigonometry. Graphing Calculator Game A game to help students learn to identify logarithmic, exponential, and other functions by the shapes of their graphs, with a "chooser" graphing functions and a "guesser" identifying them.

Examples

 Exponential Model of Population Growth Excel spreadsheet to (1) demonstrate modeling population growth with an exponential function (the textbook example of Nevada in Sec. 1.5 of the Swokowski & Cole text); (2) show how to set up such a model in Excel with "synchronized" formulas, tables, and graphs; and (3) compare short- and long-term growth of a "slow-moving" exponential.

Wild and Crazy Stuff for Students and Others

 Infinite Bottles of Beer A few things you might enjoy even if you're not planning a long bus trip! I think you might learn something from this, too, just by the way :-| . *Price's Math Myths Some persistent myths about mathematics that will sound familiar to almost every secondary-school math teacher. Zeno's "Achilles and the Tortoise" Paradox and The Infinite Geometric Series The Greek philosopher Zeno devised several "paradoxes of motion" that baffled all of his contemporaries, but, armed with the 2400 years of mathematical progress since his time, we can handle them! Cantor's Diagonal Proof and Uncountable Numbers: To Infinity and Beyond! Georg Cantor set the late 19th-century math world on its ear with his mind-boggling but ridiculously simple proof that there are different sizes of infinity. PowerPoint slides for a talk to a high-school "math exploration" class. From Polygons to Elliptic Integrals: Progress in Computing Pi, 250 BCE to the Present The record for accuracy in computing pi is now 10 trillion decimal places. There's a great deal of history behind this remarkable feat, and, in fact, Beckmann comments in his fascinating book A History of Pi, "The history of pi is a quaint little mirror of the history of man." One Tenth of A Picture Is Worth A Hundred Words There's much truth to the old saw, "a picture is worth a thousand words". But there's a little-known discipline, graphic communication, that covers that idea and a great deal more. Many principles of graphic communication apply even when there's nothing like a picture in the normal sense, and that's what I mean by "one-tenth of a picture": using graphic elements in text, formulas, etc.