How other sites use Don's ideas & his website
This site is still under construction, but good stuff here.
1. To see all the wonderful java applets of IES in Japan go to http://www.ies.co.jp/math/java/ You can now see Don's ideas in three Java applets at IES-
a. "Iterating I^(I^(I^I)).." from Don's ch. 11- a WOW!!
b. "The six trig functions"-all at one time!
c.The Japanese version of the "The six trig functions"
d. The version of "The six trig functions" in Denmark
e. The version of "The six trig functions" in Belgium
f. The version of "The six trig functions" at The Study Works
g. The IES version of Maggie's difference of two cubes
2. The following pages on Number theory starting at different places going through the same History of Mathematics site http://www.links2go.com/more/www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Frege.html and http://justbooks.co.uk.links2go.com/more/www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Frege.html have a link to a page on Don's website in which Paul divides by zero.
3. Antioch University in Seattle , uses Don's worksheet book as one of 2 resource texts in an INDEPENDENT STUDY COURSES THAT MAY APPLY TOWARDS A TEACHING SPECIALTY, taught by Dr. Nancy Murphy.
4. Don's book "Calculus By and For Young People (ages 7, yes 7 and up)" was given to all 40 teachers in UCSanta Barbara's Tri-County Mathematics Project (May, 2001).
5. Langara College in Canada uses the following references to Don's website, with links:
a. About the Snowflake Curve
b. Infinite Series
c. Sequences and series : "A nice pictorial demonstration of this (intended to be accessible to quite young children but still maybe useful for adults) is provided by "Mathman" Don Cohen (whose site includes many other examples of how calculus concepts can be explored by young children - which may also help older students see things a new way and avoid "drowning" in the algebra)".
d. Internet Resources for the preCalculus Student"Mathman" Don Cohen has a web site including many examples of kids (and adults) having fun with math. One of Don's pictures relates a geometric series to the area of a triangle. Can you see how to extend his idea to find the volume of a pyramid?
Don's picture leads in many directions - both geometric and algebraic
eg
Does the triangle have to be right angled? (isoceles is also pretty)And the factorization r+r^2+r^3+.... = (r+r^2)(1+r^2+r^4+...)
generalizes to eg (r+r^2+r^3)(1+r^3+r^9+...)
Is there a 3d picture corresponding to this?
Next thing you know we have the volume of a pyramid - without using
calculus.
Amazing!
e. Internet Resources for the Mathematics Student (Raw List ) under the following topics, with links:
i. Tutors- The Mathman
ii. geomSeries@mathman
iii. Sharing Iteration and Fractions and Real Numbers - fractions &expansions
iv. Series Paradox
v. Snowflake series (by Don Cohen)
vi. Harmonic Series (by Don Cohen)
vii. Relations and Functions -empirically determined functions
viii. Binomial expansion
ix. Cross-Subject Compendia -The Mathman
6. Charles Stuart University and New South Wales Dept. of Education in Australia
a. Series & Applications- Resources: Visual examples of infinite GPs (check answers)
An investigation on the summation of partial sums using grid paper.
b. Basic Arithmetic & Algebra-Tutorials; Equation solving by estimation & balancing
A worked example of using the substitution method for linear and quadratic equations
c. Binomial Theorem- Tutorials: Easy binomial expansions (concrete demonstration and link)
An investigation on deriving the terms of a binomial expression cubed through a concrete geometric approach. Resources: d. Binomial Theorem- Resources: Formula for Pascal's triangle value (by discovery)
A development of the formula for each term in the Pascal’s triangle.
e. Complex numbers-Resources: Link between i,e and pi (+ problem and imaginary powers)
Sample problems with links between compound interest and e and i.
f. Integration - Resources: Areas
A synopsis of the topic ‘The Integral’, with sample problems directed at developing the concept of finding the area under the curve.
g. Tangent to the Curve -Tutorials: Rate of change
A selection of sample problems on the slope and the derivative.
7. Mathematics Associations
a. The Mathematical Association of Victoria (Australia) Other Problem Solving Sites: a link to The Mathman
b. The Mathematical Association of Victoria -Challenging Problem of the month 8/96: Share 2 cookies between 3 people from Ch.2 in Don's books.
c. The Mathematical Association-UK a link to The Mathman
d. The National Council of Teachers of Mathematics- US Don's book listed here.
e. NCTM Standards - functions: On Thin Spaghetti and Nocturnal Animals Ch.6 in Don's book.
f. Minnesota Council of Teachers of Mathematics - calculus: The Mathman
9. The Math Forum, the best mathed website on the internet. Don's website is linked under these topics:
The Binomial Expansion and Infinite Series - Don Cohen (The Mathman) Pascal's triangle of numbers, although named after Pascal, was known much before his time. If there is one piece of mathematics that exhibits many patterns, this is it. There are triangular numbers and tetrahedral numbers, and even the Fibonacci numbers ...more>>
Compound Interest to e and i - Don Cohen (The Mathman)
Continued Fractions, Infinite Continued Fractions, and Iteration - Don Cohen, The Mathman
The Fibonacci Numbers, Pineapples, Sunflowers, and the Golden Mean - Don Cohen (The Mathman)
Fractions and Infinite Series - Don Cohen (The Mathman)
The Harmonic Series - Don Cohen (The Mathman)
Students are to write a program on a calculator or computer to find the sum. A sample problem from Chapter 5 of Don Cohen's worksheet book. ...more>>
Ian's Proof that Infinity = -1 - Don Cohen (The Mathman)
Young children try writing the sum of an infinite series as a fraction. What's wrong with Ian's argument? Newton and Euler and those other mathematicians had made similar mistakes with infinite series! The problem is that the infinite series converges ...more>>
On Thin Spaghetti and Nocturnal Animals - Don Cohen (The Mathman)
Pi and Square Roots - Don Cohen (The Mathman)
Kohler (a 5th-grader) follows Archimedes. A graph and a program for iterating the square root of 10. Sample problems with some answers from Chapter 10 of Don Cohen's worksheet book. ...more>>
Share Six Cookies with Seven People - Don Cohen (The Mathman)
Young children (ages 6-7) discover fractions by dividing cookies - 3 cookies with 2 people, 2 cookies with 3 people, etc.. A sample problem with answers from Chapter 2 of Don Cohen's worksheet book. ...more>>
The Snowflake Curve, Perimeter and Area - Don Cohen (The Mathman)
Young children start with an equilateral triangle, then go 1/3 of the way along each side, then add a smaller equilateral triangle, protruding out from every side to get the next figure. A sample problem with answers from Chapter 4 of Don Cohen's worksheet ...more>>
Solving Equations - Don Cohen (The Mathman)
Fractions in Real Life Situations: Share 6 cookies With 7 People (MathMan)
- Young children (ages 6-7) learn to add fractions through graphing and partial sums, and about infinite series. A sample problem with answers from Chapter 1 of Don Cohen's worksheet book.
- Reference Materials:
- Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean (Mathman)
Mathematics from a Pineapple: Infinite sequences, limit of a sequence, ratios, fractions,and decimals. Also Looking at a Regular Pentagon. Sample problems from Chapter 7 of Don Cohen's book, Calculus By and For Young People- Worksheets
- Ian's Proof that Infinity = -1 (Mathman)
- Young children try writing the sum of an infinite series as a fraction. A sample problem from Chapter 3 of Don Cohen's book, Calculus By and For Young People-Worksheets
- Fractions and Infinite Series (Mathman)
- Seven-year-olds add 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + ... forever! A sample problem from Chapter 1 of Don Cohen's book, Calculus By and For Young People-Worksheets.
- Share Six Cookies with Seven People (Mathman)
- Young children (ages 6-7) discover fractions by dividing cookies: 3 cookies between 2 people, 2 cookies among 3 people, etc. A sample problem from Chapter 2 of Don Cohen's book, Calculus By and For Young People- Worksheets.
Fractions and Algebra:
- Continued Fractions, Infinite Continued Fractions, and Iteration... (The Mathman)
Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean (Mathman)
zz. Resources for Students: "Calculus by and for Young People (ages 7, yes 7 and up)"
Fibonacci Numbers, Pineapples, Sunflowers and The Golden Mean (Mathman)
Other things coming:
Homeschooling sites (Larson, OR, also the site where I talked to people+++)
Gifted websites with info (canada ++)
Countries with sites that have links to Don's website (also see Don's site in Arabic, Japanese, ..)
Topics that Don's website comes under: homeschooling, gifted, math, problem solving, K-12, High School Math, ...
Sites that refer to Don's books
Sites that sell Don' materials