The above shell is a copy of Don's watercolor painting of The Nautilus shell; it is Don's logo. The shell is beautiful, its shape a mathematical curve, and can be obtained from conchking. Also see the equation for the shell , making a spiral , IES java applet making a Nautilus, Xah Lee's work on spirals (and other curves) and student work on the growth of the Nautilus (chapter 6), and Don compares the Spirals of the Nautilus shell, the Fibonacci numbers, and the Equal Tempered Chromatic Music Scale .
Why have your child study with Don Cohen- now?
Click: On Don's Teaching
Do you understand? Don asks his students- in different languages!
Refreshing insights into the learning and doing of some important mathematics, by young people (while doing lots of arithmetic, using many hands-on materials, science to math activities, and the non-trivial use of calculators and computers)-- for children, as well as adults Don assumes only that a student can count.
look for patterns,
learn to learn
Don retired from The Math Program
as of May 30, 2014
Sheri as a 4-6th grader; then she went to University High
as a 12th grader, in the Summer of 2008, to prepare for
worked with her for
3 weeks before school started. A week into her calculus class,
she told Don-
"What we did the last 3 weeks (derivatives), the teacher
did with my class
and I was like the only one in the class that
understood what she was talking about! It really helped for me
about the problems as I worked on them".
It's been a pleasure working with you Sheri, as well as your sister, your mother, 2 aunts, and 3 cousins over the years- what a wonderful family!
Don's new telephone # is 217.840.4559
Don's new address: 1905 S. Prairie Winds Dr. Apt. 204, Urbana, IL 61802
Jonathan, above, at ages 7 and 8, came from Connecticut for a week, each of 2 summers to work with Don. He worked on infinite series, solving quadratic equations (Ch. 8), iteration, ++. He is in Don's videos and in Don's worksheet book. And he received his Ph.D. in physics!
17 January, 2012
I thought you'd be
interested to learn that Charlie has been offered, and has accepted,
a three-year post-doctoral appointment at the Institute for the
Physics and Mathematics of the Universe (what a title!) of the
University of Tokyo in Kashiwa, Japan, beginning sometime this
summer. It comes with a terrific salary and benefits, and it was his
first choice. We're very proud of him!
He'll get his Ph.D. in Physics in May 2012.
are watching us through telescopes, they’re going to think the dogs
are the leaders of the planet. If you see two life forms, one of them
is making a poop, the other one’s carrying it for him, who would you
assume is in charge?” - Jerry Seinfeld
this email: Hi Mr. Cohen,
I wanted to tell you that I graduated high school last month! I wanted to tell you this because there is no way I would have survived my math classes without you! You were so much help! I even finished my last semester with a B+ in statistics! All of this is thanks to you!
I just felt that I needed to thank you!
Again, I could not have made it without you and I'm forever grateful,
-- L. S.
April 2013 A LinkedIn message to Don:
Yes Don - I brought my daughter Natalie to work with you in 2000 and 2001. Natalie is graduating in June with 2 BS degrees, majors in cell biology and math. She is going to attend the graduate program in biomedical informatics at Stanford University. Your work with her was a part of the love for math that I wanted to develop and it worked. [See Natalie's work that she did with don in 2000 ( at age 7) at http://www.mathman.biz/html/natalie.htmland what she did during the year, until she returned in 2001 (at age 8) at http://www.mathman.biz/html/natalie2.html !]
February 2013- some exciting Guess My Rule games by Sara K, Maya K, Jack.E, and Ratan - look out!
Hi Mr. Cohen! I just wanted to share with you that I am a Sophomore in
a 4 year university this semester and I'm taking 4 math classes and
doing okay. I think about your book all the time and your approach to
Sent at 9:13 AM on Thursday Jan.24, 2013
Asiya: You have really inspired me to go beyond the formulas printed on the page and think about math.
I have been told that my mathematical thinking is good, even when my calculations are off.
I got a job as a Math Tutor and am a Math Minor right now, when I complete the Math Minor (18 credits BEYOND calculus 3) then I may, in fact, go for a math major.
I just wanted to share that information with you and let you know how I am doing mathematically and to say THANK YOU!!!
Sent at 9:15 AM on Thursday, Jan.24, 2013 Don sent Asiya his Worksheet book about 4 years ago.
From a parent whose 2 children
came to work with Don for a number of years- a great description of
"Typical approach studies one simple concept at a time- boring- isolated, irrelevant. Instead- have a more interesting, complicated problem, that uses these concepts in finding the answer. This leads the student through math concepts, seeing them in their natural context and usefulness. Also, when the problem is finally solved, the "Look what I can do!" feeling spurs further exploration of math."
15 June 2012
From a parent who just purchased Don's 2 disc set (now 1DVD) with all
"My children are 12 and 10. They are already in advanced math at their schools, but it was clear to me that they were learning aspects of math without knowing how or why it was useful. I just googled 'how best to explain calculus to kids' and came across your site. I wanted them to see math in a different way than just memorizing and doing worksheets.
Thanks for taking the time to put your set together and doing what you have done".-Sundar R., CO
What people are saying about Don's "A Map To Calculus"
To search Don's site, for say "iteration", google site:www.mathman.biz iteration
Translate Don's web pages into your language (also use the translator, the A in the upper right on any of Don's pages).
"Learning, Living and Loving mathematics.."- the core of Don's teaching and books, ;
observed by Seth Nielson (see LOVE YOUR BOOK below).
"Calculus By and For Young People-Worksheets" by Donald Cohen, is now under a CC license . Now it can be used on OLPC computers!.
by chapter, (chapter #s
are also shown
Map to Calculus™,
on a topic)..
Electronic delivery of Don's DVD, with all his materials, will be available soon. This DVD with all of Don's materials "Calculus For Young People" , with upgraded video formats, all on 1 DVD, is still available at PayPal Checkout , below.
Don is trying to find other ways to do the electronic delivery of his DVD.
Order Don's new 1 DVD with all his materials, @$70.95,
via PayPal Checkout below.
Note: Shipping is FREE in the US (IL add 9% tax).
To ship outside U.S. email Don for S&H or ask for free electronic delivery.
Exciting news- all the time
5 April 2013Don asked Julia to make up an equation which has NO answer. She gave up quickly, but Don pushed, and this is what happened: images\juliasequations.jpg
26 March 2013 Don, Maya (6th grade), Anleen (11th grade) and Alice (11 grade) are working on Ramanujan's expression for 1/Pi
16 March 2013 Maya, Sara (2), Jack and Ratan make up other rules for Donk
29 October 2012 MarieK shares 8 cookies between 3 people to get a division problem 8 divided by 3 = 8/3 (a fraction) = 2 2/3 (a mixed number)= 2.666... (an infinite repeating decimal) = 2 + 6/10 + 6/100 + 6/1000 + ... (an infinite series) and you could probably write it other ways! . You can view the video of Don and Marie doing this on youtube at https://www.youtube.com/watch?v=j4ZPKndDWs8&feature=plcp.
28 September 2012Don, Shouri (3rd grader), and Grant (HS junior), work on Ramanujan's Infinite Nested Square Roots
20 September 2012 Shaleen (age 14), asked: Can we rotate a sine wave 60occw? See how Don, Shaleen and Lori did it!
20 September 2012Zachary's math work with Don this Summer of 2012
an email: "Hi
I receive the DVD yesterday. Thank you. I am a high school math teacher and will be teaching calculus this fall. I was searching for materials and I find your material through this link http://www.awesomelibrary.org/Classroom/Mathematics/Middle-High_School_Math/Calculus.html
I look through some of the problems in your book and it emphasizes critical thinking skills. It is also presented them in a way that students or kids will not be overwhelmed with the math symbols and language.
Thanks for putting up lot of examples of hands on activity on your website. I will probably look through those for ideas too.
Enjoy your summer with your family
From a Facebook note from Barbara Maclay Cameron, a student of Don's from 30 years ago: "It can be hard sometimes to trust that unschooling really works. And then you find yourself having a conversation with your (very excited) children about multiplying positive and negative numbers. I'm not sure I would believe this if it weren't happening right in front of me. — with Donald Cohen and Joanna Hawkins Maclay [Barb's Mom]".
You can find the
postman stories in Robert B. Davis' books online
(Discovery in Mathematics- student guide Or teachers guide) at http://ceure.buffalostate.edu/~newmath/Madison%20Project/DiscoveryInMathematics.pdf
From Barb' Mom, Joanna
Hawkins Maclay: Oh I miss those wonderful smiling faces! And the
postman stories, YES! Thank you Don Cohen. [See Barbara's Facebook
page for further discussion].
2 July 2012:Brenda Works on a regular Pentagon
2012: Email sent to Don almost 20 years ago:Mr.
Greetings from Ohio! I’ve always meant to keep in touch but time seems to slip by. Now that I’m ready to graduate I thought I’d drop you a line to tell you how much I appreciate the few years I got to work with you in The Math Program. You instilled a love for math in me that was able to get me through many hours of boring high school math.
I will be graduating June 5th as valedictorian of my class. Through the Academy Program offered by the State of Ohio, I was able to attend the local branch of Ohio State my Jr. and Sr. years and will graduate with 65 hours of college credit.
I am a National Merit Finalist and am attending Ohio State Honors Program on a full academic scholarship.
Even though my math teachers tried to put me down for my odd ways of performing math, I managed a 790 on my Math SAT and am planning on majoring in both Math and Psychology.
I’ve always regretted having to move away from your program but what you gave me really helped mold what I am today.
Many thanks. I’m sure our paths will cross again some day.
Thanks for your inspiration,
Kohler [click on Map at Archimedes to see some of Kohler's work]
2012From an email: "Hi
Don, I found this by accident. Wolfram posted previews to the
animations I did of your dog!!!
Short link: http://bit.ly/JFEb0W".Lori Johnson Morse,
an email: "Hi, Don,
I just watched the You Tube video of your James Scholar Award. So amazing!! So well deserved!! You are a true inspiration.
At a time when people do not really know, or care to understand the meaning of the word “hero” or “role model”, you are a testament to what it means to live an engaged, meaningful and inspiring life.
--Jay.- father of 3 of Don's students, one of whom came for 12 years, the other 2 have come for 6 years
"Don Cohen, the Mathman, is
simply the best educator I have ever met. He taught me more about
teaching mathematics and calculus to young people than I have
learned from any other person or book. Watching him work with his
students is like nothing you've ever seen.
Don is more than an educator to me. His is one of the most generous and kind people I have ever met. He always gives his best to his students and believes in their abilities to learn extraordinary things. I wish all my teachers could have been like him.
Congratulations, Don!" from Lori Johnson Morse, a great friend and great math tutor in K.C., MO
28 April, 2012Dear Mr. Cohen,
Thank you so much for the beautiful painting
& for helping me so much with math! I love being
able to save my questions about my homework until
Saturday because I know that I will be able to understand
what I'm doing in class after I leave your house.
Love, E (a HS junior)
21 April, 2012 Don was asked 2 weeks before, by his son Mark, to join him for lunch Saturday April 21, 2012. Don had to reschedule a group of students, and did so. Mark didn't tell him, nor did anyone else, where the lunch was being held. We ended up at the UI football stadium. [A little behind the scenes action had been going on without Don's knowledge- Associate Dean of Education Chris Span (in charge of the program), 3 weeks before, had signed up his 6 yo son Langston, to work with Don on math, was excited about what he saw, and soon found out Mark's telephone number from his brother. Mark's wife was a UI alum and a James Scholar and they all worked together to get this done. The Dean wanted a member of the community to receive one of the awards and found Don who has been tutoring in the C-U area for about 36 years!] Needless to say it was an exciting & humbling luncheon and Don thanks all the people involved. To see the Don receiving the award from Dean Span go to this youtube link .
16 April, 2012Don worked on this problem with a student in Algebra 2: Simplify (1/27)1/3. We came out with the answer 1/3. Don looked at what we had and immediately asked when will we get the same answer as the original exponent ? The next day he gave the problem to Shaleen, who thought about it for about 2 minutes, and came up with his rule below. After that Don solved the equation: (1/x)(1/y)=1/y
3 April, 2012 , Don received a Facebook message from Maggie Q. "Hello Don! I hope you remember me. I just wanted to send a message to let you know what a positive influence you had on my life growing up.
I just watched a documentary about the Mandelbrot equation, and it reminded me that you always had a picture of it in your basement and would
refer to it occasionally. I never really understood it, but I think I get the basic gist of it now.
While I didn't grow up to be a mathematician or anything like that, you helped me feel more comfortable around tougher conceptual ideas. You always had me doing such cool stuff. It made math seems more accessible to me, and increased my self efficacy and self esteem. The basic understanding has helped me connect with the world and have a better understanding of current events. I ended up going into business, but work on the business and user end of software development, so am around technical people every day. I actually got called back twice for a job at Wolfram Alpha, but eventually decided to move to Vancouver, BC to be with my family.
I have never told you before how much I appreciated your help growing up. It meant a lot to me to have someone on my team and rooting for me. I had a rougher time as a teenager, perhaps because Champaign was so quiet and small, but things have been going really well since then. I try to stay current on math and science events, and am fascinated by all of it, even if I don't fully understand it. I don't know if I can truly express the positive impact that your influence had on me, but I tried! Please take care and I wish for all of the best for you and Marilyn! Regards, Maggie Q"
1 March 2012:
<Take a look at this lesson
that Don does with kids who have worked with exponents, to find 642/3
Don found the sample problems from chapter 11 of his worksheet
book, on the website of NSDL,
National Science Digital Library
or compound interest to E and I).
In a note from Tammy's
greatgrandmother: "Hi Don! Thank you, thank you for
power to learn, to Tammy and the fact she's enjoying
it. Enclosed is my
check for 10/29-11/28". [Tammy came for one month,
twice a week;
she is 15 yo, with a weak background in math, but is
learning. It's a pleasure to see her confidence grow].
2011: Sarah's Mom worked with Don ~ about 30
years ago. See
what Sarah, age 6, did with Don in 5 days, 2
June 29-July 3, 2011.
July 2011 email: Don worked
individually with Zachary for
2 hours each
day, for 5
Dear Mr. Cohen,
taking your time to teach Zachary last week. I must admit,
enjoyed watching the light bulb go off in his face the
many times that
it did. Not many teachers have the technique that you use.
You do not
correct the error in his problem. You correct his thought
make sure that he understands the issue by solving it many
ways, all hands on. Your course was more that of a
apprenticeship than of a worksheet grind that we are so
Your one and one teaching challenged him, made him go just
a little bit
farther and made him excited about math. Again my hat is
off to you.
David K. (IN) -
followed up and has brought
Zachary back for one
weekend (four hours individually with Don) in
each of the 4
months, September, October, and November 2011].
11 June 2011- from an unexpected email: An acknowledgement
think you might enjoy this story:
In his astronomy PhD thesis, our older
son, Alex, wrote
Dad (Jan S. and Tim H.), thank you for all the ways
you nurtured my
(maybe even including the calculus book
in first grade)
….” We didn’t
remember giving him any such book, but our younger
story and said the spiral-bound book had been handed
down to him and
on the bookshelf in his old bedroom. Sure enough, I
By and For Young People! So apparently Alex
correctly—it’s the 1991 edition, and Alex was in
grade in 1988–89).
6 April 2011 The following is an essay that was sent with his college application by an 18 year old:
29 March 2011 From an email: Hi Mr. Cohen,
I wanted to know if you are still teaching. If you are what is the current rate structure of the program? My children have just started school and I wanted to ask what you would recommend as far as getting them started with mathematics. My daughter will be in first grade and my son will be starting Kindergarten in the fall. I would love for them to be able to come and experience the “Mathman” environment. I too was a student of yours and thoroughly enjoyed every minute of it. I would love to come back.
Jennifer is the 3rd mother he had long ago, who now sends 2 of her children to Don!
This is Becky W. - about 30 years ago, you knew and taught me as Becky E. I'm excited to see that The Math Program is still trucking away after all these years; I know Sheri (my niece) really loved it!
I am writing because my own daughter Sarah is now 6, and I would love for her to meet you and spend a week over the summer in The Math Program while we're out visiting family. She's doing great at math in school, but the program doesn't spark her imagination or give her the courage to experiment. Besides, how cool would it be for her to be taught by you? I'd love to share that with her. Anyway....is there an application process? Are there better or worse weeks? It would be in late June or in August; we're booked through July already.
All the best,
The article below describes what Becky (above) did, when she was 8 yo, working with Don at The Math Program. D.S.F. was David S. Fielker, the editor of the Math Teaching (England) journal at the time.
Can you generalize Becky's rule?
February 2011 From a parent and son:
While watching my 26 year old son with Don aka "the mathman" this morning at breakfast, it was de ja vu only with a twist. This morning, Jonathan was going over material and making drawings to illustrate to Don some things that he may not have known instead of Don doing the illustrations and making explanations for him as Don had done many times and many years ago.
You see, Don was highly recommended to me by a very good friend who sent her daughter to him when she struggled with math before becoming a teacher years later.
I called him and explained that my son was 12 and was being made to feel he was stupid in school when it came to math, even though he excelled to a level far beyond most in his class and many other classes above him in every other subject. I knew something was terribly wrong and I had to do everything in my power to prevent his failure, knowing how intelligent he was. I just couldn't seem to help him because he needed to learn math in a different way from the one and only way it was being taught in the schools. I was also taught that one particular way which was why I never excelled in math and really wasn't ever excited about it even to this day.
To make a long story short, a meeting and first 2 hour lesson was set up with "the mathman" and when I dropped my son off, all I could do was pray that this might be the help he needed. Lo and behold, when I picked Jonathan up from his lesson and he got into the car, he excitedly began to tell me about the things he did and learned in that two hours and he never stopped talking about math from that day and couldn't wait to get out of school for the day to get to Mr. Cohen's lessons so he could actually learn something.
You see, Don has a special way of relating to all of his students that gives them self esteem and makes them realize they can not only learn to do math, but they can also enjoy math and do more than they ever dreamed they could, like calculus. He knows not every child learns in only one way and Don lets the students know that that does not make them wrong OR STUPID!
I heard someone ask Don to explain what his method of teaching was. "How do you do what you do with so much success?"
Until I actually observed some of the sessions and could see the excitement of his students including my own child, I couldn't have pinpointed any obvious teaching method per se. I can only say that Don opens the minds of his students and expands their horizons in such a way that is simply unbelievable. My explanation is that it is his personality.
Don can pull things out of the students by getting them to reach far back into their minds and find answers that they never would have considered looking for had they not been sitting beside him. If they come up with a different answer to something, he doesn't tell them they are wrong, he says let's look at this and see how you arrived at that answer.
What a concept!
Soon, the students are looking at mathematics in an entirely different light and looking to their future in a way that the never could have hoped for before knowing "The Mathman".
Don and his lovely wife Marilyn are known and loved by probably thousands of previous students and will never be forgotten. My son and I will always be thankful and privileged that we met them so many years ago and will always call them friends.
Carol Storm Gudeman and Jonathan Storm
[See Jonathan's calculus way of finding the volume of a cylinder on his blog at
N.B. The student is much smarter that the teacher now!]
It's Peter Farrell, a math tutor/teacher fan of yours from California. I've gotten an unbelievable amount of inspiration from your works. You have a unique way of making it seem perfectly normal to have little kids playing around with calculus, infinite series and matrices!
I've been acting like a little kid myself, trying to come up with fun ways to teach a short calculus course to homeschoolers next month. I plan to go straight to differential equations, since they're the whole point to learning calculus. I'm planning to use computer applications to circumvent the drudgery of taking derivatives and slogging through the algebra. I learned from you that the majority of the ideas in calculus are immediately accessible.
The attached word doc is an exploration in optimal design I came up with, but your influence is obvious. I wonder if calculus teachers would be interested in an elementary application of differential equations. Any input you have would be greatly appreciated.
Best wishes for the holidays and Happy New Year!
"The funny thing about the boy in our carpool was that a few days earlier he had asked Ashley if she knew her multiplication tables, which she does not, although she does know how to do "four fives" and count it up to get the answer. So he was explaining about the nines multiplication facts, and showing her a method of using your fingers to represent ten and then counting starting with your left pinky. Well, Ashley thought that was cool, and the next day she said she wanted to explain a math problem to him. I chuckled to myself as I drove, because I knew what she was going to explain. He kind of brushed her off, and he explained something he had learned in math that day, and when she took her turn explaining how to use bags of washers to solve equations with balance pictures, it really surprised him. He had put her at a certain level because she doesn't yet know the multiplication tables. But when students learn the way that you teach, you are building on whatever they do know and helping them figure out ways to solve problems with what they are already able to do, instead of thinking that someone can't do something because they haven't learned multiplication or division yet" :-) [ see Balance pictures to solve equations on Don's A Map to Calculus™ ].
Do you see why Don loves to teach?
I came across your book "Calculus By and For Young People" in the last few days, after not cracking it for some time. I happened across your note about Judy Silver, [a 1st grade teacher in Don's class for teachers at Webster College, who figured out the relationship between the derivative and the integral], and the tear in your eye. Though not in math, but in other areas, I have had similar experiences, and can appreciate what a great feeling it is. And I have not found others speaking of similar situations, so I was very happy to see your expression...
For sure, if there is reincarnation, I hope to remember to ask my mother to get your books for me when I am about 6.
Anyhow, I am going to pretend I am 6 or so, and play around with your material. I have a 3 year old grandson and I have great hopes that I can get him off to a good start in understanding mathematics.
Thanks for the inspiration and good ideas.
12 October 2010 See Lori Johnson Morse's 4 Wolfram Demonstration Projects, based on Don's book Changing Shapes With Matrices. Check out Lori's website at
The synopsis of a paper that was presented at the 23rd International Congress of Applied Psychology in Madrid, Spain, July 1994, by Janie Shaklee:
"A COGNITIVE APPROACH TO TEACHING CALCULUS CONCEPTS TO 10 YEAR OLD STUDENTS IN A MAINSTREAM ENVIRONMENT
SHAKLEE, Janie; McGILL, Karen; PULOS, Steven; COONEY, John and Teresa McDEVITT, University of Northern Colorado, Greeley, Colorado, USA.
D. Cohen developed a cognitive instructional program for teaching calculus to children. This study was conducted to systematically implement and evaluate the program's effectiveness in lower-socio economic status classroom environment. Twenty-six ten year-old students received instruction in the calculus concepts of limits and infinite series using Cohen's approach. An adjacent classroom, which also had 26 students, served as a control. Pre tests and post tests in calculus concepts understanding and attitudes to mathematics were administered to both groups. Results indicated that ten year old students can learn calculus concepts in a group instructional format. While the pretest indicated a lag in scores achieved by girls, there were no significant gender differences in the post tests. We conclude that the teaching and learning of calculus can be achieved in mainstream classrooms using the conceptual instructional program designed by Cohen".
9 August 2010 Xander, 7 yo, came from SC to work with Don for a week, 9 August-13 August 2010. See his work here (not complete yet).
On this day 6 June 2010, Don & Mrs. Cohen met Sheri, on the way out of a restaurant where she was working. It was great to see her. She will be a sophomore at the U of Michigan in the Fall, loving it, majoring in Neuroscience, and aims to be a doctor! Her sister Amanda whom Don also worked with, will be a senior at the U of CA, San Diego, and is planning to go to law school.
Besides seeing his own children, grandchildren and greatgrandchildren grow up, it's also a pleasure seeing his students grow up. Especially when he has had their children; one former student helped Don set up his website and one, Jonathan, has helped make his A Map to Calculus clickable! Don feels very fortunate to have positively affected so many young people. Mrs. Cohen has been the greatest supporter of his work and the love of his life for the last 57 years.
21 May 2010 David, an 7th grader, is very good at figuring out hard functions (we've played a lot of Guess My Rule lately, instigated mainly by Jerry, Anna, and David). Don asked him how he did this. He announced to Don today that he had a way of doing it- his "Rule Generator" or how he can come up a function from about 7 pairs of numbers! He is presently writing this up for the world.. Stay tuned.
Time lapse here due to Don working on his MAP
1 January 2010 An email to Don from Japan
-Nanako came to work with Don for a week in the summers of 2007 and 2008! See her work atand
It was a beautiful ceremony.
Notice that the piece above the diagonal orange line in the tall rectangles, equals the area below the orange line above the square to its right. Notice also that the length of the base of the orange triangle = 2/5 + 2/5 + (2/5)2 + (2/5)2 + (2/5)3 + (2/5)3 +(2/5)4 +(2/5)4 ... = 2* [2/5 + (2/5)2 + (2/5)3 + (2/5)4 + ...]. The area within the orange triangle = (1/2)(base x height) = (1/2)(2x [2/5 + (2/5)2 + (2/5)3 + (2/5)4 + ...])x1= 2/5 + (2/5)2 + (2/5)3 + (2/5)4 + ... , the sum of the infinite series whose limit is 2/3. This is also 1/2x4/3x1= 2/3 and also 2/(5-2) = 2/3. This last one comes from doing lots of series and students generalizing A/B + (A/B)2 + (A/B)3 + (A/B)4 + ... -> A/(B-A).
Below you can see Lori Johnson Morse's applet for this, made in GeoGebra.
"Love your book
I ordered your book "Calculus By and For Young People" a few years ago, even before my children were ready for it (my oldest was just turning 5). It's a good thing I ordered it before they were ready because I wasn't ready for it yet. But my wife and I were homeschooling our children, and I was looking for new ideas for teaching mathematics, so I started reading them.
I'm not a math-phobic person. I'm currently completing my PhD in Computer Science. My wife isn't math-phobic either, and she earned a B.S. in Electrical Engineering.
Still, as I read your book, I felt like I was experiencing math in a whole new way. I felt like there was truths in the book that were mind-blowing. I read it several times before I started to understand that Calculus wasn't the main point of your book. Learning, Living and Loving mathematics were the core of your book and Calculus was just the vehicle.
This year, Alex is 7 and he's really advancing in his schooling. We were preparing (over the Summer) our curriculum for the fall and your book was going to be Alex's text. Then I was sent the Paul Lockhart article, "A Mathematician's Lament" by a friend. It had a powerful impact on me, but I couldn't have understood that article, without first reading your book. The two together helped me come up with a Math "method" that I am now using with Alex that is just amazing. He has a math notebook, similar to an engineer or scientist's notebook, that we use every day to explore math problems. We're currently exploring the math problems in your book "Calculus, by and for young people." As we learn new formulas, we add them to another section of his notebook we call the "Formula Toolkit". I do have Alex do some drill problems every day based on things that are in his "Formula Toolkit", but Alex knows that the drills aren't the math, they're simply the tools to help him do real math. Thanks to your book, and Lockhart's article, mathematics will never be the same again for me, or for my children.
Thank you again for your amazing contribution!
(PS, I have a home schooling blog at http://typehpersonalities.blogspot.com. It's not all about math, but you might like to read my post about "The Joy of Mathematics")."
-- Seth Nielson
for Lockhart's article "A
[Don thinks Seth really understands what Don's book is about! -and a second linking of Paul Lockhart's article and Don's works in 2 months. Check out his blog- a real math teacher in the making. Thank you Seth.]
11 August 2009 Guess who came to visit with Don and his wife? Yes Kirsten,
who was 8 yo in this picture, which is on the back cover of Don's Worksheet Book. Don worked with Kirsten from age 4 when she was at The Montessori School of C-U, through age 15 at UNI high (when she got a 5 on her AP Calculus test). She is now about 28 yo, having graduated form U of Munich (in German!) a couple of years ago, and is now teaching German and English in Beijing, China and engaged to be married next year.
7 June 2009 A conversation between Maya, 8 years old, Don, a TI-84 plus calculator, and WolframAlpha, to find the sum of 2+1/2+4+1/4
4 June 2009 Just so you know that Don is not perfect. From a note to Don from one of his mothers: Mr. Cohen, Could you work on some basics with Sarah. Addition, subtraction, multiplication, division, counting money, and word problems. She still got a C- in Math.. Thanks, Frances C. [Sarah is continuing to work with Don through part of the summer].
I hope you have a good summer, and I know the kids look forward to seeing you again in the fall.- Charles
You have made a huge difference in Joe’s life! Certainly his confidence and skills in math have increased- but your (and Marilyn’s) influence goes beyond that. You model for him an attitude and approach to life that he very much admires. I believe it really does “take a village” to raise a child. I feel mighty good that you both are part of Joe’s “village”- that you have been a part of all of our children’s village. Thank you! Bernadette
from: Maria Droujkova<firstname.lastname@example.org>
Changing Shapes With Matrices - in the
an activity designed by Don Cohen-The
Mathman, in his book "Changing
Shapes with Matrices." You can find some
sample book problems here, and
follow links to other Don's materials:
The general idea is to start with a simple "dot to dot" picture on a coordinate plane, and then apply a matrix transformation to coordinates of every dot.
Like many activities involving massive number crunching, it works much better on computers. [That’s why Don starts with a simple “doggie” with only 9 integral points, and limits students to only 1’s, 0’s and -1’s to form the transformation matrix, so there is not a lot of number crunching]. You can experiment with this applet, transforming a doggie, on Don's site [made by IES in Japan] at: http://www.mathman.biz/html/dogtrans6/changing_shapes_with_matrices%20ies6.html
quickly test conjectures, such as: "What
makes the shape flip?
can you stretch the shape more? What
happens if you put opposite
numbers in the
matrix? Reciprocal fractions? Zeroes?"
This was some excellent math by
- the reason I love this activity so much.
…We did some very meaningful math and had a lot of fun with the activity. Don, thank you very much for your wonderful books, full of great activity ideas.
complete article, go to
Thank you Maria, for sharing this activity with your google group.
her letter of acceptance into
the Radiology Program at
Michael is really enjoying your calculus worksheets. Thanks again!! Sincerely, Theresa (WI)
Subject: Thank You!
I just wanted to drop you a line and tell you how much my girls and I have enjoyed your math program. Last year we bought the Calculus program at our home school convention, and my girls have not put it down since. They are so excited about math and it has become their favorite subject. Thank you so much! Julie, GA
Thank you Julie, for sharing this wonderful information!
Michael made the diagram at the right below, using an angle of 60o between the mirrors, and proceeded to show the path of the light rays as they leave the red rod, bounce off the mirrors (the angle of incidence equals the angle of reflection) and to go to the eye, He found the 6 images (5+original=6); and they all lie on the same circle!And there is a rule here.
Fine job Michael!!
The Nautilus Shell applet done by Lori and Don - you need to download free, geogebra
Area of triangle= limit of infinite series, applet done by Lori and Don - you need to download free, geogebra
Changing Shapes With Matrices applet done by IES in Japan to go with Don's book of this title
The six trig functions in one picture applet done by IES in Japan- upon Don's recommendation
The difference of 2 cubes (Maggie, 9 years old, builds a box..and does some algebra)- applet done by IES in Japan- upon Don's recommendation
(a+bi)^(a+bi)^ ... applet done by IES in Japan, inspired by Don's problem of i^i^i... in his Worksheet Book, Chapter 11 -IES as usual, did a great job with this, ending up with fractals!
Dear Mr. Cohen
Thank you for being a teacher and an example to Elizabeth and other kids in math and in life.
There were 89 rows in the one direction and 55 rows in the other direction, both Fibonacci numbers, including 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... see the pattern?
See the sample problems from chapter 7 in Don's worksheet book and you'll find that Don has his students use the infinite sequence of the Fibonacci numbers to get the ratios of these. They are working with infinite sequences, ratios, fractions, mixed numbers, division, decimals, infinite repeating decimals and finding patterns. The infinite sequence of ratios has a limit which turns out to be The Golden Mean or The Divine Proportion, 1.618033... which equals (1+ Sqrt(5))/2.
Don's son Brian made a beautiful, wooden 3-D diorama for the story written by Don's granddaughter Tara, for her UNI HS geometry class, at age 15, entitled A Quest For The Sacred Golden Pineapple, Pine Cone and Artichoke. The diorama includes 1.) a figurine of The Old Mathman holding a golden pineapple, made by Tara, within a dome, 2.) a watercolor painting by Tara and Don of The Old Mathman's house in the woods, and 3). a shelf underneath with a copy of Tara's story.
ages I have been
thinking about getting in touch with you
- and hope that this e-mail
still works. I'm not sure that you'll
remember Andy from about 12-13
but if you do I thought I'd give you an
update. He graduated from U of
majors in math and physics in 2006 and
then went on to grad school in
Harvard in the Fall of 2006. He finished
his Masters in January 2008
decided that he really didn't want to be
an experimental physicist. So,
on a 2-year leave from the program and
working as an energy analyst for
I hope that you are well and still the mathman. Andy really benefited from working with you, and I always enjoyed talking with you too. Have a good October.
It has been 10 years (1998) since Kodansha Ltd. published the Japanese translation of the original book.
Mr. Sasaki at Kodansha Ltd., wrote to Don a month after they published the Japanese translation of Don's book Calculus By and For Young People (ages 7, yes 7 and up) in 1998: "We can say that your method was accepted to Japanese people as a kind of new text in which they could learn and understand math much more than ever before".
Needless to say, Don's Japanese book has sold much better in 10 years, than the original English version in the US in 20 years!
Back in 1988, Don felt his book was 20 years ahead of its time, and now in 2008 he still feels it is 20 years ahead of the math taught in schools- of course it's not just the book, but also his methods of teaching.
While in Albany, he and Marilyn drove past Bethlehem Central Junior High School (now Middle School) where Don started his math-teaching career in 1954!
"Calculus By and For Young
People (ages 7, yes 7 and up)”
2. "Calculus By and For Young People--Worksheets"
3. "A Map to Calculus"-- a 15" x 18" flowchart, overview
4. Video #1 "Infinite Series By and For 6 year-olds and up"
5. Video #2 "Iteration to Infinite Sequences with 6 to 11 year-olds"
6. "Changing Shapes With Matrices"
7. “On thinking About and Doing Mathematics”-11x14” poster
The 1DVD above, for PC and Mac users, sells for $70.95PayPal Checkout above.
Note: Shipping on all items is FREE in the US,
To outside U.S. email Don for S&H.
the 1 DVD above,
Don will continue to sell these, paid via PayPal/check only:
"Calculus By and For Young People (ages 7, yes 7 and up)" (CD-ROM);ISBN 9780977949304 ______$23.95 (also on 1 DVD)
"Calculus By and For Young People--Worksheets" (CD-ROM);
ISBN 9780962167478 ___________$35.95 (also on 1 DVD )
"A Map to Calculus"-- a 15" x 18" poster-flowchart;
ISBN 9780962167485___________ $13.95 (also on 2 CD set)
2 CD set)
"Changing Shapes With Matrices" (paper);
ISBN 9780962167430 __________$
See what Rainbow Resource Center says about Don's materials.
Jonathan has finished the course work for his PH.D. in High Energy Physics and is working on his dissertation, which he plans to finish next year!
Don is very pleased when his students do well!
What a wonderful year 2007 has been. If we could only have Peace, and no one should go hungry!
28 December 2012: Don and his wife Marilyn celebrated their 60th wedding anniversary!
3 March 2007: Geometric Sequences and the 88 Keys on a Piano by Don
17 February 2007 Five views of Don's Math Room - where it all happens!
“..You wrote an amazing bookk(Don's worksheet book). Every week what my kids learn puts smiles on their faces. It makes me smile, too. You make people smile because they can understand math better. It’s a gift and you share it with as many people as you can! And I am having a blast following in your footsteps. Much, much thanks! Lori”. KC, MO
See the internet links to Don's website and references to his books from around the world!
Homeschooling math by Don Cohen
From The Road Not Taken by Robert Frost. Don feels that what he has done is not the usual, and something that has touched many people, young and old, around the world, very positively, and has been very rewarding- and that has made all the difference in his life!
|Don's Materials Will Teach You To:|
-New discoveries &
Try sample problems from Don's worksheet book, by chapter!
Tessa at 5 works with Grandpa ! "When Grandma talks, everyone listens!"
MAA, the ASCD,
Mary Pride in
her 'Big Book
2000 issue of
On Thinking About and Doing Mathematics
Who was that Mathman?
'The Math Program'- Don and Jerry's great way of teaching math & loving it! (and what parents and students say about The Math Program)
How other sites use Don's ideas & his website
Don's Favorite Places on the WWW
Puzzles, Games, & Hands-On Activities Don Uses With Students
After 45 years of teaching math & parenting..
Links to this website- how many now ?
Thank you for stopping, do try some problems before you go!