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 .
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.
Don's keys:
visualization,
look for patterns,
learn to learn
Don retired from The Math Program
as of May 30, 2014
Don
had
Sheri as a 4-6th grader; then she went to University High
School. She
came back
as a 12th grader, in the Summer of 2008, to prepare for
Calculus. Don
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
in one
day,
and I was like the only one in the class that
understood what she was talking about! It really helped for me
to talk
with you
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!
LATEST NEWS
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.
Jack
+++++++++++++++++++++++++++++++++++++++++++++++++
"Logic will get you from A to B.
Imagination will take you anywhere".
- Albert Einstein
“If aliens
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
6 June
2013Don received
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.
27
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 !]
Best wishes,
Natalya
February 2013- some exciting Guess My Rule games by Sara K, Maya K, Jack.E, and Ratan - look out!
Asiya:
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
math.
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
Don's teaching::
"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
his materials:
"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).
NEW!
"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
on the
A
Map to Calculus™,
or click
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.
PayPal Checkout
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
Very exciting!
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 60^{o}ccw? See how Don, Shaleen and Lori did it!
20 September 2012Zachary's math work with Don this Summer of 2012
21 August
2012 From
an email: "Hi
Don,
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
Xu"
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
22 May
2012: Email sent to Don almost 20 years ago:Mr.
Cohen,
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]
18 May
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,
3 May
2012 In
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.
Love."
--Jay.- father of 3 of Don's students, one of whom came for 12
years, the other 2 have come for 6 years
29
April, 2012
"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, 2012
Dear 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.
Thank you!
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:
that Don does with kids who have worked with exponents, to find 64^{2/3}
14
December 2011:
Don found the sample problems from chapter 11 of his worksheet
book, on the website of NSDL,
the
National Science Digital Library
(search "iteration"
or compound interest to E and I).
7
November 2011:
In a note from Tammy's
greatgrandmother: "Hi Don! Thank you, thank you for
instilling the
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
committed to
learning. It's a pleasure to see her confidence grow].
13
September
2011: Sarah's Mom worked with Don ~ about 30
years ago. See
what Sarah, age 6, did with Don in 5 days, 2
hours/day,
June 29-July 3, 2011.
27
July 2011 email: Don worked
individually with Zachary for
2 hours each
day, for 5
days.
Dear Mr. Cohen,
Thank
your
taking your time to teach Zachary last week. I must admit,
I
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
process and
make sure that he understands the issue by solving it many
different
ways, all hands on. Your course was more that of a
mathematics
apprenticeship than of a worksheet grind that we are so
familiar with.
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.
Sincerely
David K. (IN) -
Zachary's Dad
[David
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
I
think you might enjoy this story:
In his astronomy PhD thesis, our older
son, Alex, wrote
“Mom and
Dad (Jan S. and Tim H.), thank you for all the ways
you nurtured my
curiosity
(maybe even including the calculus book
in first grade)
….” We didn’t
remember giving him any such book, but our younger
son, Peter,
confirmed the
story and said the spiral-bound book had been handed
down to him and
was still
on the bookshelf in his old bedroom. Sure enough, I
found there
your Calculus
By and For Young People! So apparently Alex
remembered correctly
(or almost
correctly—it’s the 1991 edition, and Alex was in
first
grade in 1988–89).
Tim
6 April 2011 The following is an essay that was sent with his college application by an 18 year old:
I am no dunce at mathematics, yet from the time I was six years old, I have studied with a math tutor named Don Cohen. Math, while an extremely important skill, is not the most crucial lesson I have learned from him through the years. Don Cohen, a renowned math teacher and a winner of many teaching awards[2], is known for his unusual approaches to teaching. My math instruction has been no exception. I have not memorized a single formula, and instead, I have learned to approach math problems from different perspectives. Simple lessons that I have learned, such as any problem can be broken down into a simpler form of the same problem, have uses outside the field of mathematics. I have learned the analytical thinking that is essential to mathematics. At the same time, this discipline influences my other thought processes to this day.
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.
Cordially,
Jennifer W.
Jennifer is the 3rd mother he had long ago, who now sends 2 of her children to Don!
Hi
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,
Becky
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
http://www.technicalmisery.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!
Peter Farrell"
"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.
Enjoy,
Dean E.
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
Hi
Mr.
Cohen,
I am a past student of yours and I was just thinking
about you the
other day and
thought I would see how you were doing. You taught me
about 11 years
ago until
my family moved to Chicago. I have since graduated
college with the
idea that I
would be premed, but found myself in a Master's of
Science program in
epidemiology and biostatistics. I haven't had a math
course since
freshman year
of college but I am loving statistics and I am
currently applying to
PhD
programs in biostatistics as well as medical school.
I wouldn't have the math abilities that I do today if
it weren't for
some of the
guidance you gave me early on. In fact, when I doubt
my math background
I always
remember your encouragement.
Before I moved you gave me a watercolor of a tornado.
It was the first
picture I
hung up in my new room and I think of you every time I
see it. I hope
you and
your family are doing well and you are still helping
students learn to
enjoy and
appreciate mathematics.
Thank you for everything you did for me in the past.
--Maggie P.
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).
http://www.ted.com/talks/hans_
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.
19 May 2010 From the Mom of Don's student from NZ, many years ago, on facebook: "Hi Don, It was William you taught calculus to. How he loved your classes! He is now grown up (mostly) and doing very well working in IT. Best wishes"
Dear
Don,
I was a student of yours about ten years ago.
I just wanted to
send you a
little note to let you know that I still very
often use the most
important
lesson that you taught me: when a problem is too
difficult, first think
of
an easier case of the problem and work from there.
I am now a student at the California Institute of
Technology, studying
Chemistry. I very much enjoyed working with
you when I was
younger, and I
don't recall whether I ever really got to thank
you, so I wanted to make
sure that I did that.
Thanks,
Geoffrey
Don was so pleased to hear from Geoffrey. See his work at Geoffrey, age 11, graphs the 6 trig functions , Geoffrey generalizes the infinite series, Geoffrey works on powers of powers, Geoffrey worked on the Fibonacci numbers. Search Geoffrey, above to see other fine things he did.
Time lapse here due to Don working on his MAP
1 January 2010 An email to Don from Japan
Dear Don and Marilyn,
Hello! How are you? I didn't have a chance to visit you
last summer, but I hope I can soon
I hope that both of you will have a
Happy New Year
These are some pictures of my dog Fluffy, and I!! Did you
recognize that your painting was in one of the pictures
?Love,
Nanako
-Nanako came to work with Don for a week in the summers of 2007 and 2008! See her work at www.mathman.biz/html/nanako.html , www.mathman.biz/html/nanakograph.html andwww.mathman.biz/html/nanako08.html
It was a beautiful ceremony.
RE: Mathematics - See what an Educator and young students can produce! FYI – I’m forwarding email sent to me by Don Cohen about his students’ recent work [ Van & Jack below]. Don wrote Calculus By and For Young People (ages 7, yes 7 and up) . I’ve known Don since the early 1990s, and I have used his materials in my classrooms.
· If you are a young person, studying mathematics with Don Cohen is a great investment.
· If you know a young person, point them to study mathematics with Don Cohen-- a great investment.
· If you are an educator – Don Cohen is a great mentor and a really nice guy.
- from Dr. Debbie Denise Reese, the senior educational researcher at the NASA-sponsored Classroom of the Future (COTF) within Wheeling Jesuit University’s Center for Educational Technologies in Wheeling, WV
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
Hi
Don,
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
[See
www.maa.org/devlin/LockhartsLament.pdf
for Lockhart's article "A
Mathematician's
Lament".]
[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.
Check out @TheMathman website, esp example probs. Could his method be one answer to The Mathematician's Lament (see Paul Lockhart's 25 page paper on math education)?
[WOW!! Thank you Freeman].
Dear
Don,
I don´t know if you remember us, but we came
to see you for a
week about six
years ago. My son Johann was five
years old. I have thought
of you
so often and how you inspired our family.
Johann loves math and now our
younger son Tristann is also learning to
love math through his interest
with
origami. I don´t know why we didn´t
keep in touch
with you, but somehow
life got in the way.
I would like to be able to bring my kids
back, I know they would love
it. I
am so impressed with how you teach and your
love of math. I would
love to
hear from you.
Warmly,
Svava (CA)
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<droujkova@gmail.com>
subject:
Changing Shapes With Matrices - in the
Math Clubs!
This
is
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:
http://www.mathman.biz/html/probcswm.html
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
…Kids
could
quickly test conjectures, such as: "What
makes the shape flip?
How
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
kids
- 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.
For
Maria’s
complete article, go to
http://groups.google.com/group/naturalmath
Thank you Maria, for sharing this activity with your google group.
Dear Don,
..Ashley
received
her letter of acceptance into
the Radiology Program at
Sincerely,
Julie
(Mom)
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 60^{o } 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.
Pat
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.
Hi Don,
For
ages I have been
thinking about getting in touch with you
- and hope that this e-mail
address
still works. I'm not sure that you'll
remember Andy from about 12-13
years ago,
but if you do I thought I'd give you an
update. He graduated from U of
I with
majors in math and physics in 2006 and
then went on to grad school in
physics at
Harvard in the Fall of 2006. He finished
his Masters in January 2008
and then
decided that he really didn't want to be
an experimental physicist. So,
he's now
on a 2-year leave from the program and
working as an energy analyst for
___ in
downtown
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.
Chris
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!
1.
"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 $70.95
PayPal Checkout above.Note: Shipping on all items is FREE in the US,
To outside U.S. email Don for S&H.
------------
Besides
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___________ $13.95
(also
on
2 CD set)
"Changing
Shapes With Matrices" (paper);
ISBN
9780962167430
__________$
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, MOSee 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!
About Don's materials (7 items) and how they are used. Especially see the write-up about Don's materials on the Rainbow Resource Center website and where Don's books are sold around the world!!
Send
email
to Don Cohen
concerning his
'Math by
Mail/Email'
with IM
and
video,
coming to
Champaign to
work with him
, ways he
could improve
his web site,
or other
issues.
people have
come in,
peeked,
glanced,
shook, were
curious,
skeptical,
impressed,
excited,
thought about
what their
children are
doing in
school
or as
homeschooled,
tried a
problem,
solved a
problem,
emailed Don,
called Don,
ordered his
material, ..
since June
6, 1996. Notice,
this site
slipped past
200,000
visitors in
early
2004- in less
than 8 years!
Thank
you for
stopping, do
try some
problems
before you
go!