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
Don has found someone who can make his A
Map to Calculus™ into an APP !!! (as of 13 April 2011)
He has also initiated plans to make his 3
books into Google Ebooks- in about 4 months.
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!
19 March
2011 From an email:
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?
6 March
2011: From Don's facebook
conversation with
Barbara, his student from 31 years ago, about the pyramid her
daughter Maggie made.
4 March
2011: I
found
a formula to find the area of shapes on a geoboard, then graphed it in 2D and 3D; by Irisa, a 6th grader
22 February
2011: Jack,
a 4th grader, draws a Penguin & asks Don to help him describe it
using the graphs of
equations!
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.
com/2011/02/cylinder-fun.html
N.B. The
student is much smarter that the
teacher now!]
14 January
2011: Ed Cherlin, from OLPC (One
Laptop Per
Child) asked Don if he was interested in having his calculus for young
people
materials be part of their 2 million computers under a Creative Commons
License.
Don has agreed to do this.
17 December
2010, from an email "Hi,
Don,
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"
10 December 2010: From
Ashley's Mom, describing in part how Don teaches:
"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™ ].
13
November 2010 Don has worked
with Sara
since she was 5 yo, now 9 yo. He came down to the Mathroom one day to
find her
writing on the chalkboard:
Do
you see why Don loves to teach?
25 October
2010 from
a letter: "Hello Don Cohen,
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 hapy 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.
21 October 2010 "why small animals are nocturnal (SA/Vol
ratio)" See Nanako's
work on this problem and on the MAP.
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
9 October 2010 from
an email to Don:
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.
9 October 2010 Our
granddaughter Tara and fiancee Tyler, won "favorite commuter/travel
biking blog"-
at http://www.goingslowly.com
. You can see their bicycle route from Glasgow, Scotland, through
Europe and north Africa,
with a journal, pictures, and sound bytes along the way.
Congratulations guys! We are proud of your fine work and hard bicycling
around
the world. They bought a car in Berlin then drove to Ulan Bator,
Mongolia, with bicycles in the trunk. They took a plane to Bangkok,
Thailand today and will go to LopBuri where Don's Thai son has a room
for them at he and his sister's restaurant. After bicycling around
Asia, they plan to leave for home from Kuala
Lumpur, Maylasia.
29 September 2010 See
Don's new page containing hands-on
materials, lessons, puzzles and games he uses
with his students
A test of Don's calculus program
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).
4
August 2010 The
recording of Don's virtual "talk" is now up on the page at the Math 2.0
wiki: http://mathfuture.wikispaces.
com/Calculus+by+and+for+Young+
People There were about 35 participants from around the world
(New
Zealand, UK.., one of Don's students Ashley, and her Mom, Lori Johnson
Morse from KC, and a teacher who Don had as a student circa 1970 in
NYC). Don
introduced people to his clickable A
Map to Calculus, showing Donna's graphing of x2 + y2
= 25, then changing something in the equation and seeing what
happens..very
exciting!
Best
stats presentation you'll ever see, at
http://www.ted.com/talks/hans_
rosling_shows_the_best_stats_
you_ve_ever_seen.html
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.
2 June 2010 Congratulations
Lori Johnson Morse!! Her new, fine,
Wolfram Mathematica Demostrations Project submission: ChangeTheDogMatrixTransformations has been
accepted for publication.
It does the matrix transformations
Don has in his book Changing Shapes With Matrices, in a new way!
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"
17
May 2010 an
email to Don:
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
19 December 2009 From a holiday
card: Dear Don, The boys (and I!) have learned a lot this year and are
looking forward to more math in the New Year! We are blessed to have
you in our lives.
- Shawna N. [the Mom]
3 November 2009 Anna
L., a 4th grader, does some fine mathematics
1 November 2009 Don
has worked on math for 9 years with Jay, now a HS Jr. Don and his wife
Marilyn were invited to
Jay's Vedic ceremony
BRAHMOPADESHEM, celebrating a period of education or preparation for
life. In
the photo below, his father, considered the ultimate guru, imparts the
"secret" of the Gayathri
Mantra to his son Jay, with the help of the Priest.
It was a beautiful ceremony.
25 October 2009 an email to Don, used
with
permission:
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
14 October 2009 Van,
a 4th grader, graphs in 3D
6 October 2009 Jack invents new
ways of
looking at mathematics
5 October 2009 Do
you understand? In 16 languages so far; do you know another?
27 September 2009 Zion
made up the problem: 52.65 - 83.50 = - 31.15 Was he right?
20 September 2009 While
iterating a function, Laura, a 4th
grader, divides 7.75 by 2- WOW!
26 August 2009 And
Anushka, age 6, knew neither division nor graphs !
20 August 2009 Don
shows below that the limit of the infinite series 2/5 + (2/5)2
+
(2/5)3 + (2/5)4 + ... = the area
within the orange
triangle. Note that the terms of the series alternate being tall
rectangles (the odd powers) and squares (the even powers). Don
connected the orange diagonal line from the point
(0,1) through the upper right corners of the squares. He found the
slope of this
line to be -3/4 and the y-intercept 1; then he found the
x-intercept to be 4/3.
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.
13 August 2009 Don
received this email:
"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.
15 July 2009 Shaleen
moves a parabola 2 units to the right and something else happens!- or
an example of what the teacher does to allow good mathematics to come
from a
situation, when the student's answer is
different from what is expected or would be considered "wrong".
7 July 2009 Don
received an email out of the blue. "Freeman Hunter is now following
your updates on
Twitter". I
looked at her Twitter site with the update
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].
19 June 2009 Don
received this email:
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)
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].
2 June 2009 From
a note to Don from one of his fathers: Don, The kids had a very good
year with
you. In addition to all the things they learned about geometry, numbers
and
puzzles, I think they've absorbed the most important idea: math is fun!
I hope you have a
good summer, and I know the kids look forward to seeing you again in
the fall.-
Charles
22 May 2009 From
a note to Don from one of his mothers: "Thanks for helping Jesse to his
"A" in math! Fondly, K. [Jesse was taking
algebra when he started
with Don in Dec. '08 with an "E" (for failing- of course he didn't
hand in homework), and by the
end of January, a month later, he got an "A" and continued that until
the end of the school year!]
7 May 2009
-
a note from a
parent of 3 of Don’s students,
along with a check for May:
Hi
Don! I wanted to mention that we might send Jack to you this summer-
and have
Joe take the summer off. If Joe’s schedule allows him to go to
you, we’ll
send both boys.
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
1
May 2009
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.
28 April
2009 Don
and his students Jay, Chris, and Elizabeth find a new number- the Dottie
number
2 April
2009
Check out Don's
granddaughter Tara and fiance Tyler on their world trip by
bicycle at www.goingslowly.com
- they started April 1 in Scotland,
rode through England, France,
Switzerland, Italy are now in
Tunisia at this time (28
November 2009)! See the article
about them in the April
20 issue of The Champaign-Urbana News-Gazette.
30 March 2009 From
a note to Don from one of his mothers: Dear Mr. Cohen, ..We are
fortunate
that Mildred was able to work with you this past year.. We will always
happily
recommend your services to others and would not hesitate to contact you
in the
future if we should find Mildred in need of additional math tutoring.
Thanks for
everything. T.C.
23 March
2009 from an email
Dear Don,
..Ashley
received her letter of acceptance into the Radiology Program at Parkland College on Saturday, March 21,
2009 and is so excited
about that! Thank you again for assisting her with her
Math! If she
ever needs any future tutoring, we would certainly give you a call.
Sincerely,
Julie (Mom)
20 March 2009 From Michael's Mom: Don,
Thank you for working with Michael [8 months via email- see some of his
work
below]. Maybe we can come spend a few days in person with you this
summer...
Michael is really enjoying your
calculus
worksheets. Thanks again!! Sincerely, Theresa (WI)
26 February 2009 Dear Lori Johnson Morse, my friend and fellow
math
tutor wrote a little article about
Don which was accepted on an
eNY Times
page- take a look.
18 February
2009 See
Malcolm Gladwell's book Outliers The
Story of Success. Chapter
8 is entitled: Rice Paddies and Math Tests. Lots of interesting
connections and
without knowing these, Don had his Calculus.. book translated into
Japanese and sold much better
in 10 years in Japan than
the original English version
has sold in 20 years in the
US.
2
February 2009 Email:
“I heard about your product (2 disk CD set) from a homeschooling
family that
is registered with the same DL school [in Canada ]
that my children are and they
recommended it”.- Karen T., after she purchased same.
23 January 2009
Email from Don's Facebook file
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!
November,
and 10 December 2008
Ann-Emily, 2nd
grader, adds fractions using complex
fractions and multiplies
mixed numbers-WOW! (and Don never taught her how to do any of this)
As a teacher, Don likes
this quote by an
anonymous writer who said: "We have not succeeded in answering all your
problems. The answers we have found only serve to raise a whole set of
new
questions. In some ways we feel we are as confused as ever, but we
believe we
are confused on a higher level and about more important things".
Mathematics
in Science: Michael has been
working through Don's
worksheet book and with Don via email,
for about 8 months. In
chapter 6 there is a
diagram of hinged mirrors at left,
below. Students are asked to look between the mirrors to see how many
images of
a red rod, say, that they see with the mirrors open at an angle of 90o
(3 + the original=4).
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!!
Fine applets to
interact with -you need to download free
Java program to view these:
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!
10
October 2008 Don received this
note
from the mother of her 11th grade student:
Dear
Mr. Cohen
Thank you for
being a teacher and an example to Elizabeth and other kids in math and
in
life.
Pat
1 -
3
October 2008 Mathematics in Nature: Aaron, Don's
grandson,
brought him a sunflower head cut from his garden; it was about a foot
in
diameter. The seeds grow in
spiral arrays
in 2 directions. See the photo
below that Don
took of the sunflower head, then added the numbers. Maddie, a 5th
grader, with Don,
counted the rows of seeds in the one direction going clockwise around
the
sunflower head (starting and ending in the lower left of the picture).
They colored the
starting or first row red
and every 10th row red,
to help keep track of the counting. The rows bend sometimes, not
perfect
spirals, which makes it difficult to count. Then Don and some other
students
finished counting those and the rows in the second direction, again
going
clockwise around the sunflower head, coloring the starting or first
row black
and every 10th row black.
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.
26
September 2008 Don received this email from
the mother of
a former student:
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 Boston . He is
very happy to be making $ and really engaged in
his work. In fact, he
seems all grown up and indeed an adult.
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 20 years (1988)
since
Don published his book Calculus By and For Young People (ages 7,
yes 7 and
up) . It was reviewed in the Dec. 1988 issue of Scientific
American magazine. It is still selling, now on CD Rom, and on his
2-disk CD set Calculus
For Young People . Then came Calculus By and For Young
People-Worksheets
with questions leading to the different ideas. Then 2 videos (Infinite
Series
and Iteration), A Map To
Calculus and Changing Shapes With Matrices. All items are
now on his 2-disk CD set Calculus
For Young People
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.
10 September 2008-
20 February 2009 Erin
has made 16- 3x3x3
cubes with the 7 Soma pieces and drawn the
layers
to help others make a cube. Erin is amazing; she keeps coming up
with new
ones, and can tell if it is different from the others- of course she
checks
them!
22 August 2008 From
Michael's Mom: "Do
you like to
see the parents involved..?" Don's
response: Yes, even to
have you child explain something to you. I had Sheri as a 4-6th grader;
now she is a
12th grader taking Calculus. I worked with her for about 3 hrs
individually
over the last month (August 2008). Today, a week into her calculus
class, she
told me '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'. On Don's main page, search
"Sheri" to see what she did as a 4th-6th grader!
11 August 2008 Sara & Maya,
age 7 (twins), find Patterns in
division
21 July
2008 Alex,
a 2nd grader, sees
an infinite series!!!
27 June
2008 Mom
and Dad with their 6 children,
drove down from North of
Chicago. Mom
and 4
children, 3 girls and 1 boy, worked with Don for 2
hours, while Dad and
their
two youngest children went off to the park. Click here
to see what they worked on.
17
June 2008 Don
received this
thank you note from Paul, who came to Don from 3rd grade through 12th grade:
Dear Mr. Cohen,
Thank you very much
for the beautiful graduation card, the gift card to Pages For all Ages,
and for
attending graduation. Even more significantly, thank you for
providing a strong foundation in mathematics and for helping me through
subjects
I found especially difficult. Your innovative approaches and teaching
styles
kept math interesting and fun, while the teaching methods in school
made it dull
and repetitive. This approach has been something that I can apply to
different
aspects of my life, by looking at a topic from a different angle, I am
able to
much more thoroughly comprehend the subject.
Once again, thank you so much for all you've
done.
Sincerely,
Paul
Thank you Paul, for
your dedication to excellence and being a wonderful human being, and to
Mom and
Dad, for making it all possible! You all have helped make the last 10
years of my
teaching very enjoyable.
16-21
June 2008 Nanako came from
Japan again to work with Don!
3 May 2008 Don
& Marilyn were in Albany, NY to accept his 2008 Excellence in
Education
award- see the program and Don
after his speech . Don
wants to thank the Alumni Association of UAlbany, SUNY, his friends,
students and parents of his students who wrote to
support his nomination. Don realizes though, that this award is not as important
as his work with individual students over the years-and for that he is
most
grateful. It has been a great ride!
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!
April
2008 Margaret,
an 8th grader, asks a great question!
Don's 2-disk CD
set, "Calculus For
Young People
(2 CD set)",
ISBN 9780977949311, contains all of Don’s
materials -3 books, 2 videos, map, & poster, listed here:
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 2-disk
CD ROM
set above, for PC and Mac users, sells
for $70.95
on Google
/PayPal Checkout above.
Note: Shipping on all items is FREE in the US,
To outside U.S. email Don for S&H.
------------
Besides the two-disk CD set 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 2 CD set)
"Calculus By and For Young People--Worksheets" (CD-ROM);
ISBN 9780962167478 ___________$35.95
(also
on 2 CD set)
"A Map to
Calculus"-- a
15" x 18" poster-flowchart;
ISBN
9780962167485___________ $13.95 (also
on 2 CD set)
"Changing Shapes With Matrices" (paper);
ISBN 9780962167430 __________$
15.95 (also
on 2 CD set)
See what Rainbow
Resource Center says about Don's materials.
1 January 2008 What
a way to start the new year! Don spoke to Jonathan (now 26 years old)
and his Mom and Dad who are in CT. Jonathan, at age 7, started
working in Don's book Calculus By and For Young People (ages 7, yes
7 and
up), with his Mom acting as his secretary. She sent his work to
Don. (This started Don
on his Math
By Mail/Email Program). That
and the following summer, his Dad brought him to Champaign for a week
to work
with Don. Some of Jonathan's work is in Don's worksheet book and
he is on his videotapes.
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 2007: Don
and his wife Marilyn celebrated their 55th
wedding anniversary today!
Marilyn
and
Don Cohen are excited about their part-time work as Shaklee
Distributors and
users of many Shaklee “in harmony with
nature”
products-100% guaranteed -nutritional supplements including the new
VITALIZER, Get Clean, Cinch
inch-loss program, air purifier and more!- and they want to share these
with
you. Please take a look at their Shaklee website
if you want to feel better, want a healthy home, a healthy planet, and
bring in some extra money.
19 July 2007: Don
received this email from a parent who had purchased his 2-disc CD
set:
"..I just wanted to say thank you again for inspiring me and helping me
realize that kids can understand and do so much more with
math than many
people are willing to believe..".
13 June 2007: Leah's
Mom called to tell Don that Leah got into UNI High School and
would continue to
work with Don in August when she returns to Champaign- Congratulations Leah!!
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!
9 February 2007 Don received an order for his 2-disc
CD ROM
set from Moscow, Russia !!
7
February 2007 Don spoke to Loralee
Johnson at "4 Your Mind" and told people during the
radio interview that Loralee is selling Don's materials in Edmonton,
Alberta, Canada and can be reached at 1-780-485-0969 or ljohnson@shaw.c
Check
out Lori's
website for her
"MathHead Tutoring Inc."
“..You
wrote an amazing book
(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
“
..Two roads diverged in a wood, and I - -
I took the one less traveled by,
And that has made all the difference.”
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!
To get around on Don's site,
choose from the menu below:
- Try sample problems
from Don's books, by chapter!
-
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!!
- New discoveries, new student work
and Don's new
pages: Anna
L., a 4th grader, does some fine mathematics; Van,
a 4th grader, graphs in 3D; Jack,
a 3rd grader, invents
new ways of looking at mathematics ;
While
iterating a function, Laura, a 4th
grader, divides 7.75 by 2- WOW! And
Anushka, age 6, knew neither division nor graphs ! ;
Shaleen
moves a parabola and gets something different! ; 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;
Don and his students
Jay, Chris, and Elizabeth find a new number-the Dottie Number; Ann-Emily,
2nd grader, adds fractions using complex fractions-WOW!; Sara and Maya, 7 yo twins, find
Patterns in division; Alex, a 2nd grader, sees an infinite
series!!! Margaret,
an 8th grader, asks a great question!; Nanako
changes a graph without changing the equation-HOW!?; Katy finds the area under a sine wave from 0 to Pi
(after Archimedes); Donna, a 4th
grader, graphs a circle, then changes the equation!!!; 2 ways to rotate a triangle
90° CW - by Alvaro, Ian & Don; Using
trig to do rotations with matrices; Don
paints in watercolor with.. + + +
- Have
your
daughter/son study with Don,
here
in Champaign, IL. Don has stopped working with
students from afar on IM with voice. He
worked with 50 year- old Tim,
an M.D. from FL
for
over a year; he worked with 10 yo Tadeo from
Argentina;
7 yo
Erin, from ID,
for 5 mos; a Juku teacher in Japan came for the
month of September 2003 to study with Don. Grace, then a 6th
grader in Chicago, worked with Don using Email for about a year, and
came here twice. Don worked
with 2 students
from afar via
email during the AY '08-'09, but without voice.
- About Don's
teaching - Sample problems, new student work, patterns in
mathematics, the non-trivial use of calculators & computers,
beginning trig, ..
- About
Don's books in Japanese
: as
of 21 July 2006, 25,860
copies
of the Japanese translation of Don's book "Calculus
By and For Young People (ages 7, yes 7 and
up)" were sold by Kodansha Ltd. in 6 1/3 years and as of 2009 they have stopped selling
this book; and 8,012 copies of
Don's book "Changing
Shapes With Matrices" were sold by Kodansha Ltd.
in the first 2 yrs., 8 months!
- Patterns in
Mathematics (patterns in numbers, patterns
in graphs,
patterns in shapes,..)
and how Don's students work on
particular topics.
- About Don's
website - see the four or so Java applets at IES in Japan using
Don's ideas, like showing
the 6 trig functions on one diagram and
the new Java
applet by IES
on Don's website at "Changing
Shapes With Matrices" .
 Don's Materials
Will Teach You To: |
Discover
Patterns
-New discoveries &
Patterns in Mathematics
|
 |
Try sample problems from Don's
worksheet book, by
chapter!
Don's Materials
(all published and copyrighted by
Don Cohen-The Mathman)
- Book: "Calculus By and For Young People (ages
7, yes 7 and up)" (CD-ROM)
- Worksheet book: "Calculus By
and For Young People - Worksheets"
(CD-ROM) &
Table of Contents of books 1 & 2
- Videotape #1:
"Infinite Series"
- Videotape #2:
"Iteration"
- "A Map to Calculus"
- "Changing Shapes with Matrices"
- All of Don's
materials are on a 2 disk CD set (see above)
Science to math activities
The non-trivial use of Calculators and Computers in
Don's materials
The
important mathematics
The importance of guessing
Patterns in
Mathematics
|
 |
Visualize
Mathematics |
Learn to
Learn -
Tessa at 5 works with Grandpa ! "When
Grandma talks, everyone listens!" |
 |
What
parents, teachers, kids, Martin Gardner, Morris Klein, W.W. Sawyer, the
MAA, the ASCD, Kodansha, Mary Pride in her 'Big Book of Home Learning',
the July/Aug. 2000 issue of The Home Education Magazine, The Math Forum.. say about Don's materials
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 ?
Don's materials are for grades K-12, ages 6-8 with
adult help, up through pre-calculus students, adults, teachers,
teachers of teachers, and parents!
|
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!
Don's
web site was designed and started by one of his former students,
Jennifer,
while at MIT, and continued & maintained by Don, with some help
from his
grandson, Lian.
