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See also: NordplusProposal, Mathematics, MathEncyclopedia, AlgebraNotes
AndriusKulikauskas January 15, 2009 22:57 CET I'm creating mathematics learning materials in the Public Domain. I will be organizing them as ClassicMathProblems. A good overview is my NordplusProposal.
See also: WolframAlpha for ideas on using that.
Top Ten Math Ideas
AmountAndUnit Every answer consists of an amount and a unit.
CombineLikeUnits
ListDifferentUnits
ZenosParadox
ClockAddition 10 + 4 = 2
Coincidences
RepresentativePopulation We conceive fractions by switching between two views: number of atoms (for intuiting, comparing within the population) and percentages (for calculating, comparing with other populations).
BiggerPicture We can extend the domain of a function by considering what it would take for it to satisfy a constraint such as an addition rule. This approach lets us decide how to evaluate an exponential function, initially defined on positive integers, so that it makes sense for zero, negative integers, fractions, roots, real numbers, complex numbers. It also lets us decide how to evaluate a trigonometric function, initially defined for acute angles x (0 < x < 90) so that it makes sense for 0, 90 and all real numbers.
Scales Why do we use logarithmic scales?
RightTriangle A right triangle is half of a rectangle. The shape is thus given by the proportion of two sides of the rectangle, or the angle of the triangle. This is the basis for trigonometric functions.
PlottingData Fitting data nicely onto a graph is a good example of using proportions.
Graphing parabolas.
Other Ideas
 Cell references - using spread sheets.
Algebraic notation for chess.
More Ideas: What is the deep idea? And the practical illustration? Let's make them clear!
Numbers
BooleanLogic
Andrius's Notes
 Andrius's notes for teaching algebra with an emphasis on the deep, fundamental ideas. I prepared these notes for my 1992 class which I taught at UCSD and used them in 2008 to teach in Bosnia.
AreaOfATriangle
A First Course in Linear Algebra and many links for education
Sean's Applied Math Book
Connexions: Mathematics and Statistics, Elementary Algebra by DennyBurzynski
Open Source math books
Blended Learning Open Source Science or Math Studies, MIT videos for Jordan and Pakistan funded by HP and the Sloan foundation.
http://siyavula.org.za AlexWeir alerts us to Matthew Horn's work
Pedagogical materials
Using visualisation in maths teaching
Experiences of learning mathematics
Learning Materials
Useful book: When are we ever gonna have to use this?
Wolfram Alpha answer engine
Classic Problems
Classic Math Problems from the Dr Math Archive
Famous Problems in the History of Mathematics
Michael Shackleford's math problems, see also Acknowledgements and Links
Nick Hobson's mathematical puzzles and more links to problem collections
Puzzles and Riddles
600 Algebra word problems
Theories, Problems, Solutions
Project Euler thank you, EdwardCherlin!
When will I ever need this (math)? by MariaMiller with links to:
Julie Harland's math videos
Books
Resources
Beautiful interactive graphic of cell size and scale
[ http://www.linkedin.com/news?viewArticle=&articleID=81216035&gid=1782421&articleURL=http://learn.genetics.utah.edu/content/begin/cells/scale/&urlhash=IqtU&trk=news_discuss S
Vision for a numeracy activity Calculator that inspires further creativity.
Mitchell Charity's projects such as Dot a day history.
Scratch language
Librarian Chick Wiki
Algebra work sheets
IXL Math Practice Site
Skoleo - PieterWykstra
http://www.urworld.nl
Mathematics at Wikiversity
The University of Chicago School Mathematics Project and materials including Applying Arithmetic: A Handbook of Applications of Arithmetic by Zalman Usiskin, Max Bell. See also: Paul Sally.
The visual display of unfathomable numbers, images by Chris Jordan
Order of Magnitude puzzle
University of the People
MCM: Mathematical Contest in Modeling
Software
The Concord Consortium open source math software
Visions
The Concord Consortium alternative to textbooks
Examples
Take a look at Stephen Law's The Philosophy Gym: 25 Short Adventures in Thinking (on which an Oxford University online course has since been based). http://www.stephenlaw.org http://cfilondon.org/about-us/
Arguing that a speed trap camera was faulty
Math and Ethics
See: MosaicLaw
Mathematics for Ethics by Nigel Phillips inspired by JeremyBentham, webmaster AT utilitarian.org
Mathematics and Ethics blog post by DavidCorfield http://www.kyb.mpg.de/~dcorfield The Philosophy of Real Mathematics, Towards a Philosophy of Real Mathematics, david DOT corfield AT tuebingen DOT mpg DOT de The n-Category Cafe blog on math, physics, philosophy David's posts
Ethics for Mathematicians RubenHersh, hersh(at)gmail.com about the ethics of Math departments.
Doin’ the Math: On Meaningful Mathematics-Ethics Connections by KurtStemhagen krstemhagen AT vcu.edu
The Psychology of Number and its Applications to Methods of Teaching Arithmetic by John Dewey
JohnStuartMill and utilitarianism and Gottlob Frege's attack on that
Kitcher, The Nature of Mathematical Knowledge
Piaget
Greer and Mukhopadhyay (2003) What is Mathematics Education For?
Moses and Cobb, Radical Equations (2001), using algebra to filter in and out who qualifies for college
Gutstein, Reading and Writing the World with Mathematics (2006)
Lakoff
The Evolution of Ethics: An Introduction to Cybernetic Ethics by S.E.Bromberg
Math and Ethics: Senior thesis journal: Proposal, Blog, Bibliography
Philosophy Forums: Truth in Mathematics, Art, Ethics
Mathematics, Peace and Ethics by Ubiratan D'Ambrosio ubi AT usp.br and Marianne Marmé mam AT fiz-karlsruhe.de The plurality of truth. Mathematics education for peace.
Mathematics of Social Justice by Rob Root, robroot At lafayette.edu Course development workshop
Ethics in Science, Bad Science Dean H. Garrison, Jr., Gunhand AT aol.com
Aristotle and Mathematical Ethics for Happiness?
Wittgenstein, mathematics, and ethics by CoraDiamond.
Engineering Ethics Module by JimmyHSmith
Internationalisation and Globalisation in Mathematics and Science Education by Jim Neyland et al, jim.neyland AT vuw.ac.nz
A “Professional Issues and Ethics in Mathematics” course by j.franklin AT unsw.edu.au
St. James Ethics Centre, Intelligence Squared Live Debates
Contacts
Algebra.com is a remarkable community founded by IgorChudov with about 1,000 tutors who have solved more than 100,000 problems. There is a wiki where textbooks and lessons are encouraged. And a sensible copyright policy. Add self study courses is on Igor's to-do list.
The Math Textbook I would Buy by Dan Meyer, a high school math teacher near Santa Cruz, CA. RSS: http://feeds2.feedburner.com/dydan1?format=xml
Maria Miller Have Algebra Books Changed? RSS: http://feeds.feedburner.com/HomeschoolMathBlog
AnnMaria De Mars, posts on Algebra,
http://mathforum.org/
Math: Folk Wisdom in an Electronic Age
COMAP, the Consortium for Mathematics and Its Applications, an award-winning non-profit organization whose mission is to improve mathematics education.
Expert Voices
OLPC
http://www.ck12.org
http://www.hstutorials.net/olpc/olpcmath01_02_g.htm
http://wiki.laptop.org/go/Curators_and_maintainers
Funding Ideas or Partners
Mokyklu tobulinimo programa plius RasaKuodyteKazeliene
Friends of OLPC
Messages
Thank you, LinasPlankis! I have created two pages for your suggested problems: RepresentativePopulation, Scales. I look forward to more!
Sun, 15 Feb 09 10:08:34 +0000 EdwardCherlin: Project Euler, a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve.
Andrius: Thank you, Edward!
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