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Favorite Books, Websites, Videos, and Quotes

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Favorite Books
  • For All Practical Purposes. COMAP. A superb text for introducing students to the breadth of mathematics subjects and their real-world applications. Promoted as a text for a liberal arts mathematics college course, most of the content is accessible at the middle school level and the rest is rich content for high school mathematics and computer science classes. There have been numerous editions. You can get a used copy for any edition that is no longer expensive.

  • Metamagical Themas. Douglas Hofstadter. Basic Books. Incredible essays on numeracy, default thinking, the ubiquity of the prisoner's dilemma as an explanation for societal problems, and much more.

  • Any collection of essays by Martin Gardner. His books, gathered from his many years of monthly columns for Scientific American, explore different topics in recreational math that so often raise fascinating theoretical questions. 

  • Math Games with Bad Drawings by Ben Orlin. This book is a brilliant collection that channels the spirit of Gardner's work. 

  • Flatland by Edwin Abbott. A classic, and strange, introduction to higher dimensional geometry by way of a satire of Victorian society!

  • Calculus In Context. The Five College Calculus Project (Callahan, Cox, Hoffman, O'Shea, Pollatsek, Senechal). An ambitious and successful rethinking of the order and focus of calculus topics. No text has ever found the interesting middle better than this one and the result is students with a deep grasp of what the fundamental theorems of calculus really mean and how to apply their skills in nimble ways. Available free here and used.

Favorite Organizations
Favorite Websites and Video Series
  • Quanta Magazine - An online site with accessible, sophisticated articles on the current developments and important history in mathematics, all fields of science, and computer science. A phenomenal site with a vast trove of essays. 

  • 3 Blue 1 Brown - Incredible videos that explain deep mathematics and computer science concepts graphically.

  • G'day Math - Teacher and Curriculum developer James Tanton shares his essays, math units, and problems with thoughtful examples of how to expand classroom practice.

  • Cut-the-Knot - Extensive collection of mathematics topics and puzzles.

  • Crash Course Computer Science - Charming and concise video collection on how computers work. Great for a course like AP Computer Science Prinicples (start at #1 and build up from there).

  • Veritasium - Well-produced and explained math and science videos.

  • PhET - 200+ interactive simulations of science and math settings can lead to great explorations.

  • NCTM Illuminations - A varied collection of interactive tools and games for teaching arithmetic, algebra, geometry, probability, and statistics searchable by topic and grade level. 

  • The Concord Consortium - Developers of interactive tools for learning topics in STEM (including dragon genetics).

Do you have any favorite mathematics or STEM websites? Please share them using the form below.

Favorite Humorous Math Songs
  • Tom Lehrer’s Lobachevsky (Note: Lehrer picked Lobachevsky’s name for the meter and not because he was a plagiarist – he was, among other accomplishments, one of two co-discoverers of hyperbolic geometry, the most influential non-Euclidean geometry).

  • Klein Four’s album Mathematical Fruitcake. The Klein Four were an acapella group of PhD mathematics students, so the references are of a high order. 

  • Grant Sanderson (of 3 Blue 1 Brown fame): Hallelujah and Ain’t No Twin Primes.

  • SOHCAHTOA sung to the tune of the title song of Oklahoma! I only provide the lyrics and not a recording. leave it to the rest of you to actually sing it for your students (they will appreciate you putting yourself out there, especially if, like me, you have trouble carrying a tune). 

Am I missing a great satirical math song? Please share them using the form below.

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Favorite Quotes about Teaching and Learning

John Dewey: Education is not preparation for life. It is life itself. 

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Norman Thomas: "Life is full of untapped sources of pleasure. Education should train us to discover and exploit them." An Elliott's Amazing Fruit Juices bottlecap. 

Neil Postman: We want a citizenry "who have freed themselves from the belief in the magical powers of numbers, [and who] do not regard calculation as an adequate substitute for judgment, or precision as a synonym for truth." Technopoly, p.184. 

Howard Gardner on standardized tests: "I have become one of the most insistent critics of such tests, feeling that, whatever they successfully assess, they miss much; that they often fail to pick up the most important human capacities and attributes; they favor the glib and the conventional rather than the profound or the creative; and that people who do not understand these instruments attribute to them much more merit than they actually warrant." To Open Minds, p. 30. 

Wendell Berry: It may be that when we no longer know what to do, we have come to our real work, and that when we no longer know which way to go, we have begun our real journey. The mind that is not baffled is not employed. The impeded stream is the one that sings. 

Andre Gide: One doesn’t discover new lands without consenting to lose sight of the shore for a very long time. 

Grace Murray Hooper: A ship in port is safe, but that’s not what ships are for. 

Albert Einstein: In the middle of difficulty lies opportunity. 

Piet Hein: Problems worthy of attack prove their worth by hitting back. 

Amy Poehler: Find a group of people who challenge and inspire you, spend a lot of time with them, and it will change your life. 

Judy Logan: "I believe in saying yes to my students. Sometimes I say no, but I don't say it lightly, and I try to give all my reasons. I believe that students have reasons behind their requests, and that it is important for me to learn about them in order to really teach effectively. Usually when I get to a place in the curriculum when I have to say no to a student's request, I have a fair amount of trust built up because of all of my yeses, so they are more likely to take risks." Teaching Stories, p.4. 

John Taylor Gatto: "I've come to believe that genius is an exceedingly common human quality, probably natural to most of us. I didn't want to accept that notion - far from it - my own training in two elite universities taught me that intelligence and talent distributed themselves economically over a bell curve and that human destiny, because of those mathematical, seemingly irrefutable, scientific facts, was as rigorously determined as John Calvin contended. The trouble was that the unlikeliest kids kept demonstrating to me at rare moments so many of the hallmarks of human excellence - insight, wisdom, justice, resourcefulness, courage, originality - that I became confused. They didn't do this often enough to make my teaching easy, but they did it often enough that I began to wonder, reluctantly, whether it was possible that being in school itself was what was dumbing them down. Was it possible that I had been hired not to enlarge children's power, but to diminish it? That seemed crazy on the face of it, but slowly I began to realize that the bells and the confinement, the crazy sequences, the age-segregation, the lack of privacy, the constant surveillance, and all of the rest of the national curriculum of schooling were designed exactly as if someone has set out to prevent children from learning how to think and act, to coax them into addiction and dependent behavior. Bit by bit I began to devise guerrilla exercises to allow the kids I taught - as many as I was able - the raw material people have always used to educate themselves: privacy, choice, freedom from surveillance, and as broad a range of situations and human associations as my limited power and resources could manage. In simpler terms, I tried to maneuver them into positions where they would have a chance to be their own teachers and to make themselves the major text of their own education. ... Once loose [these ideas] could imperil the central assumptions which allow the institutional school to sustain itself, such as the false assumption that it is difficult to learn to read, or that kids resist learning, and many more. Indeed, the very stability of our economy is threatened by any form of education that might change the nature of the human product schools now turn out; the economy schoolchildren currently expect to live under and serve would not survive a generation of young people trained, for example, to think critically." Dumbing Us Down, p. xi. 

Connie Kamii: A classroom cannot foster the development of autonomy in the intellectual realm while suppressing it in the social and moral realms.

Mary Catherine Bateson: "Ambiguity is the warp of life, not something to be eliminated. Learning to savor the vertigo of doing without answers or making shift and making do with fragmentary ones opens up the pleasures of recognizing and playing with pattern, finding coherence within complexity, sharing within multiplicity. Improvisation and new learning are not private processes; they are shared with others at every age. The multiple layers of attention involved cannot safely be brushed aside or subordinated to the completion of tasks. We are called to join in a dance whose steps must be learned along the way, so it is important to attend and respond. Even in uncertainty, we are responsible for our steps." Peripheral Visions: Learning Along the Way. Thanks to Jack Dieckmann for this contribution. 

Do you have any favorite quotes about education and/or mathematics? Please share them using the form below.

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