On Don's Teaching

A student once told Don: Most teachers "stand and deliver",  you "sit and listen" - and we have fun!

From a homeschooling parent:

"Learning, Living and Loving mathematics.."- the core of Don's teaching and books..observed by Seth Nielson

 

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 2, 2013: " I was thinking today that 15 years ago when I bought your materials I never got to them because I thought of it as an add on to our regular math skills work books. I realized this time around that the piecemeal approach doesn't create the interesting context for learning".

Thanks!
Kathy (Kathy has been working with her daughter on infinite series (Ch.1 in his calculus books)

Sarah, age 7, said to Don, unsolicited, after working on an infinite series in Ch. 1: "At school when we do math we use different methods that I am not used to. And they are hard. But if I used my own methods it would be easy." -The wisdom of young people!  

Don thinks his students' works are important for others to see; that's what his books, website, and mathroom show.

 One overriding motivation in Don's teaching comes from this quote:

"In his first paper on the Calculus (1669), Newton proudly introduced the use of infinite series to expedite the processes of the calculus...

As Newton , Leibnitz, the several Bernoullis, Euler, d'Alembert, Lagrange, and other 18th-century men struggled with the strange problem of infinite series and employed them in analysis, they perpetuated all sorts of blunders, made false proofs, and drew incorrect conclusions; they even gave arguments that now with hindsight we are obliged to call ludicrous."

   -from 'MATHEMATICS THE LOSS OF CERTAINTY' by Morris Kline (Don had his grandson as a student!)

Don makes lots of mistakes, so it's alright if his students make mistakes; that's why starting young people working on important mathematics is necessary.

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."

Don would also add :
-visualization-make graphs, diagrams..
-look for patterns,
-learn to learn,
-every student is different,
-teach one student at a time,
-have a student do the same problem different ways, 
-guessing is important,
-have students make up problems; if you let the student make up the problem, it will be much harder than the teacher makes up!
-give praise when a student figures out new things, solves a problem correctly
-the important thing about doing most math is that we really want more than just the answer, we want to generalize the answer, to find the answer for any problem like we're working on.
-listen carefully to the question a student asks, and to what they are doing
-have a good time- we all need to smile, and laugh!         

2 September 2012After the Summer of '12, Jackie working with Don, he received this email from Jackie's Mom:
"I have been passing your name around like candy. I am so delighted with the work you've done with Jackie. :)  [Jackie is continuing with Don in the Fall].:

 

3 May 2012 In an email: "Hi, Don,
I just watched the YouTube video of your honorary James Scholar Award of 21 April 2012[from the College of Education, U IL]. 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

19 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!" (on receipt of the honorary James Scholar award from the College of Education, U IL)- from Lori Johnson Morse, a great friend and great math tutor in K.C., MO

 

12 May, 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)

 

3 April, 2012 , 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

 

Natalie's Mom wrote in an email to Don after they returned to CA (he worked for a week with Natalie, ages 7 & 8, in 2 summers): 

"I personally believe that you are one of the rarest teachers on earth. Thank you for being."

Natalie wrote Don: "Dear Donald Cohen, What I liked about your class most is your creativity. I had lots of fun because it was hard. (Are there any tornados?) I think kids in my old school would be amazed at what you do. I had a fabulous time with you. I hope every thing is going well. Are you having a good time? I hope you are !! Your student, Natalie"

 

An email Don received after working with Johann (age 4) for a week  from CA:

 '..I am still in awe at how much Johann learned while visiting with you.  He seems to have grown a lot in his understanding of many different concepts.  I wasn't quite sure how much a little guy like him could absorb in such a short amount of time, but he continues to surprise me.  I myself learned a lot about patience from you and although not able to apply it all the time, I am trying.  Don, you are truly a great and unique teacher''- Johann's Mom from CA

An email Don received July 27, 2011, after working with Zachary (age 8) for 5 days from IN:
               

                     "Dear Mr. Cohen,

                          Thank you for 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 on one teaching challenged him, made him go just a little bit further

                      and made him excited about math. Again my hat is off to you.

                                          Sincerely,

                                           David K." (Zachary's Dad)

26 March 2004: Don was asked to be the facilitator of an online Young Scholar Colloquium March 22-26, for The Davidson Institute for Talent Development. Don's topic was "Iteration to infinite sequences in solving quadratic equations, and obtaining infinite continued fractions". His work with the 14 students was enjoyable, challenging and a memorable experience!

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.

From a former student: Received May 1993, with Kohler's photo and  H.S. graduation announcement.

"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" (see Kohler's work to get Pi, on the MAP)

 

17 May 2010 in an email to Don from a former student: 

"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" 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.

 

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.

       2nd email after Don's response about her work on the MAP:

Hello again Mr. Cohen, 
 
I do remember doing that work with you! I showed that to my parents this morning and spent awhile trying to figure it out for themselves. Both my parents and my brother and sister say "hi" and I attached a picture from college graduation of the whole family so you can see how much everyone has changed.

I am so happy to hear that you and your wife are doing well. I will definitely keep in touch and please, you do the same. Tell everyone I say "hello". 

Have a great Sunday, 
Maggie

Subject: Thanks

Mr. Cohen!
Hi, it's Caitlin R., I took math lessons from you for years. Maybe you remember me. 
I just finished my Masters in Public Health at Columbia University. I thought about you after my final in applied regression for biostatistics last year. My calculator died 5 minutes into the exam. I had to take the whole test by hand! I got a 94% despite it and I thought, "Thanks Mr. Cohen." I am now working at Oxford University as a research assistant while I apply for my PhD. I just wanted to tell you that I might not have been here without you. I hope you are well.
Thank you for teaching me,
Caitlin

 

Saturday, February 6, 2010
The Mathman (taken from Don Cohen's website)

9 March 2008 Homeschooling mom emails Don: "Dear Don, ..I teach an enrichment math class to 6th and 7th grade students. I also tutor between 8-10 children a week separately from my work in the classroom. I am excited by your philosophy and methods. I am not a certified teacher. I just happen to be a homeschooling mom who was passionate about preventing innumeracy in my children. I read Marilyn Burns and used Miquon Math. From there I discovered Harold Jacobs' books and The Number Devil. I hate timed tests for times tables. I always want my students to find the pattern and connections between math topics. I especially want them to get excited and see the beauty of mathematics.

Would it be possible for me to come to learn from you how to better serve/teach my students. I took Calculus in high school and college, but I have had no use for it in my life. I would like to learn Calculus the way I try to teach my classes so that I can make the connection for my students". Elizabeth came to work with Don in May. She said one of the things she really liked on Don's site, was the pictures of his mathroom!

Don Cohen is my math hero. His site is not flashy, but his methods are nothing short of wondrous. I had the privilege of spending two days with him and his lovely wife, Marilyn. Watching him in action with his students is what I imagine it is like for people who claim to gain a spiritual benefit by being in the presence of their guru. Don's presence and manner with his students inspired me as much as his work, Calculus By and For Young People.
Posted by Mathknotter at 2/06/2010

17 June 2008 Don received this 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"As of this writing in 2010, Paul is a junior in college.

From the 2008 Excellence in Education award brochure, given by the Alumni of The SUNY Albany, which Don was a recipient:

Dr. Ezra Black (NYC), whose daughter has studied with Cohen via email, said: "He has succeeded in teaching Emily many mathematical skills which she has tried unsuccessfully to learn in other ways and with other instructors. Perhaps most importantly, Emily's work with Don has reinforced her fascination with mathematics and her ability to perceive the elegance (or, as she would put it, the "coolness") of mathematical argumentation. It is no exaggeration to say that Don Cohen has come to constitute a force unto himself, a powerful force helping to cultivate and nurture one of the things which our country stands most in need of: a generation of pupils with a passion for mathematics and science."  

From the 2008 Excellence in Education award brochure, given by the Alumni of The SUNY Albany, which Don was a recipient:

"Mr. Cohen's scholarship in mathematical pedagogy demonstrates his leadership and ability to take steps beyond just interacting with students," said Janet Dubinsky, professor of neuroscience at the University of Minnesota and a former seventh-grade student of Cohen's. "His groundbreaking publications constitute a legacy for math teachers to come."

Dubinsky notes that Cohen was ahead of his time in teaching methods, incorporating hands-on activities and active learning strategies at a time when that wasn't typically done. "Our class was a constant buzz of activity as students in one comer explored probability with dice, while another group solved matrices aloud on the board, and others read math puzzle books or played and analyzed chess moves. We were totally engaged. Engaged in the natural beauty and power of math." Dubinsky notes that many of the educational programs she sees and reviews now try to incorporate methods Cohen pioneered years ago. "All the programs I see strive to utilize the same techniques that Don Cohen has pioneered: using structured problem solving and engaged learning to develop higher order thinking skills. In this realm, Don sets a very high standard that few teachers can reach."

25 October 2009 in an email to Don:

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. 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

A teacher who attended sessions as a student with Don, writes:

"Don Cohen's class was superb! Seeing him teach; being taught; and taking this information to my classroom has greatly enriched my students and me. Don's worksheet book has been easy to follow and adapted to my own needs and situations. I actually tore out the worksheet book pages and put them in a spiral notebook, fitting in my work between the appropriate pages. The 'toys' have been great manipulatives for all my students to enjoy and apply to math. His library has been of great value to me. Two thumbs up!" Patricia Plaut, 5th grade teacher.

 

 A Math by Email student's parents:

"Don Cohen's Math by Mail has been a wonderful and fun enrichment for our son Grant, who has learned more about higher math than otherwise possible for his age"--Dr. and Mrs. Stan Kolar, OK
"(I'm too busy to eat right now)"--Grant Kolar, while doing one of Don's problems, and "Don is an alright dude". 

[Grant corresponded with Don for two years, and came to study with him twice during the summer of '90, between the two years. Grant started with Don at age 11, then he skipped 7th grade and as an 8th grader was tops in his algebra 2 class. Some of Grant's work is in Don's worksheet book. In '99 Grant was in medical school].

From a parent who brought her son from Idaho to work with Don for a week:

'Dear Don, Just a note to let you know how helpful I continue to find your book and workbook.  Watching you work with children in person has increased my understanding of how math can be approached in a different and more meaningful way.  The way you interact with kids is truly masterful.  Math is more than just memorizing ways of doing problems and you are living proof of the excitement and stimulation that lies ahead for those who are fortunate enough to have contact with you.'

 

From one of Don's students:

Don had Sheri as a 4-6th grader (see her work on the Map); 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. Today, 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". What a wonderful family- Don had Sheri, her sister, mother, 2 aunts and 2 cousins!

 

Don worked with Grace via email from Chicago on infinite series, infinite repeating decimals and bimals, and area under curves and the integral (see the MAP). Her parents brought her and 2 brothers to Champaign twice on Sundays.Grace, at age 10, writes about teaching-unsolicited:

'There are many teachers who are boring and not original. They do not make learning fun, they do not explain things clearly, and avoid letting youngsters do "challenging" work. However, there are ideal and exceptional teachers who are just the opposite. I believe that a mathematics teacher name Mr. Donald Cohen is one of those ideal and exceptional teachers.

Mr. Donald Cohen is an ideal and exceptional teacher because he is creative and makes learning fun. While other teachers try to bore you down with memorizations of math terms, he encourages students to explore and make mistakes.

He believes that it is not impossible for youngsters to do anything. On the other hand, other teachers think that youngsters cannot do something because it is challenging and new. However, Mr. Donald Cohen actually thinks that youngsters can do more than adults!

He explains things in a way that is very easy to understand. Some teachers tell students to memorize formulas, which can be complicating to understand. On the contrary, Mr. Donald Cohen teaches us by helping us visualize the math terms and figuring it out. He says, "Visualization is key".

To be an ideal teacher, the teacher must be creative, make learning fun, believe that a student can do anything, and explain things in an easy way. Mr. Donald Cohen has those qualities and more. Therefore, he is an ideal and exceptional teacher'.

     July 11, 2003 

"Hi Don!
I'm doing fine. School ended about three weeks ago. I'm going into 8th grade. I am currently attending the U of C Young Scholars Program. We're learning geometry. Right now, I'm working on groups, subgroups, and polyominoes.

At home, I'm learning Advanced Algebra. I come across many problems that are related to the questions in your worksheet book so I use the book as a reference tool.

Bye, Grace" (about 2 years after Don started working with Grace!)

 

From the mother of 3 of Don's students (2008):

"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 [see daughter Katy's work on infinite series on the MAP, now at college]. Thank you! Bernadette"

 

                     

Above photo is from the back cover of Don's worksheet book: Don, with Khaki at age 17, used the computer program Derive  to "zoom in" on a curve to find the slope of the tangent at a point on the curve, leading to the derivative. She was preparing for her Fall calculus class (see ch. 14).

 

On 8 April 2005 Don led a monthly meeting of the UI Physics Education Research Seminar. A member of the Physics Dept., Dr. Inga Karliner, and mother of a former student of Don's, had invited him. Don has always had a lot of respect for people in physics because they need to know the mathematics as well as the physics!

13 April 2005: Don received this email from Dr. Karliner:

"Dear Don,

Many thanks for your visit. I know that you warned us that you never gave a talk exactly like this, but the people who came to it told me it was very interesting to them and they enjoyed it. Some of them will probably visit your program when their kids are a little older. The kids who come to your program are so fortunate, you are forever interested in seeing how their minds work.

Best regards and many thanks from us all,

Inga Karliner

on behalf of the Physics Education Research group at the Physics Department at UIUC"

 

"Hi Mr. Cohen, How are you and Mrs. Cohen doing? I hope you are both well.. I have just finished my first year of graduate school in physics at the University of _. I am working with _.. to explore the physics of particles containing charm quarks (particularly D mesons) more thoroughly. Currently I am looking for irregularities in the detector's magnetic field and unusual properties of the detector's momentum resolution..

 I still fondly remember the summer work I did with you so long ago now. It is great that you are so busy teaching and encouraging more students in mathematics. My brother and parents join me in sending fond regards.  Best, Jonathan"

(Jonathan was the first student who came from afar to study Don's calculus program and, with his Mom, the student who started Don doing his Math by Mail/EMail program. Jonathan's Dad brought him from CT for a week, two summers in a row, when he was 7 and 8 yo. Don is thrilled that his students are smarter than he is and are doing so well. Some of Jonathan's work is in Don's worksheet book and in Don's two videotapes.

 

In an email Don received from Kodansha Ltd. about 3 years after his book Calculus By and For Young People (ages 7, yes 7 and up) was published in Japanese:  "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". 

After Don's naturalmath google group talk online, Math 2.0, August 4, 2010, from Peter Horn's blog at http://peterhorn33.wordpress.com/2010/08/08/4-7-don-the-mathman-cohen/

Don 'The Mathman' Cohen

August 8, 2010

Calculus for 7yo
Don Cohen 'The Mathman' guides students along a path to deeper understanding of patterns that lead to infinite series. during the Live event, we got to see the true joy that Don still gets from seeing his students succeed. Don has put together, with the help of one of his former students a wonderful 'map' of calculus. The map has all sorts of examples of the work his students have done through the years. Some of the more notable work has been done by 2nd ' 4th graders wherein they discovered infinite series while working on problems such as ' how can you divide 6 cookies among 7 people?' While he does not introduce any formal calculus terminology into his teaching of young children he is able to bring out the important concepts that they will need later in their schooling, all while helping to take away the 'fear' of math.

 

Peter,

That was an excellent webinar. You hit on some of the highlights. However, there were a couple of items that were staggering. Don, 'The Mathman' Cohen has earned such a place of trust with his students that he is now teaching their children. And in one case, he mentioned that he is teaching a third generation of children from the same family. Regardless of the subtlety with which Don guides his young learners, I don't think there is a laurel leaf quite so powerful as bringing one's children to him because you loved him so.

The map also has depth and breadth. He, along with his former and current students, capture the two essential elements of calculus. And he relates them to infinite series and infinite sequences. I was priveleged to participate.

     by prmarcadia August 13, 2010 at 12:59 am

When students are asked to make up problems & are encouraged to ask questions, good things happen.

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".

"Math Myths"

 - things that are NOT true - but ideas people, because of ignorance, expedience and/or things they were taught, try to shove down their students'/childrens' throats: 
1. You can't take 7 from 3.   (3 -7= ^-4, you're below 0)
2. When you multiply, the answer is bigger. (6 x 2/3 = 4 )
3. You have to add from right to left. 
4. When you subtract the result is smaller.( 4 - ^-3 = 7)
5. Fractions are small numbers. (1/.01 = 100)
6. There's only one way to do something. 
7. When you add the result is bigger. (5 + ^-4 = 1)
8. When you divide the result is smaller. ( 5 ' ' = 10 )
9. I can't do it unless someone tells me how to do it- result of teachers who are afraid to let the student THINK. 
10. "Math is hard and only a few people can do it"- Usually from teachers who want to keep the class size small. 
11. You have to know everything about whole numbers before you can do fractions, when all you need is to count how many of these pieces make a whole cookie, then you can name the fraction. 
12. You have to know algebra before you can learn about calculus.

If the teacher wants a student to do something one way, and the student does it a different way, and gets the right answer, should the student be marked wrong? OF COURSE NOT !!! But they are...

February 2011 From a parent and son:

From Don's facebook conversation with Barbara, his student from 31 years ago, about the pyramid her daughter Maggie made

Barbara: Mr. Cohen, I felt like I was channelling yesterday when Maggie and I got involved in figuring out how many pieces there were in the huge lego pyramid she had built.  My favorite part was when she realized that there was a quicker but less interesting way to do the calculations, and she said, "Let's do it the longer way!  It's more fun!"

I posted a photo of the pyramid and tagged you in it. I'm not sure if it's readable, but that white piece of paper says "10,404'.

Donald Cohen: your pyramid is a marvel, Maggie! It looks like an Egyptian pyramid. I like the idea of doing something the longer way too, but more fun in the process. Is the pyramid made by the squares of even numbers? Like 2^2=4, 4^2=16, 6^2=36? 

Jennifer Olinger (a friend): Wow! That's impressive! Is that number (10,404) the number of Lego bricks she used?

Barbara: "Not the number of bricks, the number of dots. A spontaneous unschooling math project. I posted it to share with my beloved childhood math teacher".

Barbara: "Mr. C, the bottom square side is 48 dots across, with each layer above being 4 dots shorter. We started by figuring out 48 x 48 (which in and of itself was new, since M. had never done double-digit multiplication), and then 44 x 44, and then 40 x 40 (easy!), and then used those three numbers to predict what the next one (36 x 36) would be without doing the multiplication. I have to run now, but I'll send you an email with the details.. And emailing or skyping with Maggie would be amazing. I was just about her age when you taught me two important things: (1) math isn't just arithmetic, and it can actually be fun and (2) that I'm actually pretty good at math! I can't imagine anything better than Maggie getting to get some Mr. Cohen math magic. I'll email you asap!"

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 one of 3 mothers who were Don's students many years ago. They each now send two of their children to work with Don!)

Math in Nature

Science to math activities

New student discoveries

The non-trivial use of Calculators and Computers in Don's materials

The important mathematics in Don's materials

The importance of guessing

Patterns in Mathematics

On Thinking About and Doing Mathematics

Trig for Young People

Puzzles, Games, & Hands-On Activities Don Uses With Students

Who was that Mathman?

After 56 years of teaching math & parenting..

Don works on math; see these links

Area under curves (see the MAP)

Area of triangle  = limit of a series

A Map to Calculus made clickable by Jonathan Storm, a former student of Dons

 

Fine applets to interact with -you need to download free Java program to view these in GeoGebra and IES:

Applets in GeoGebra (download free)

 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

Applets by IES, Japan

 Changing Shapes With Matrices  applet done by IES in Japan to go with Don's book of this title

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!

The six trig functions in one picture applet done by IES in Japan-  upon Don's recommendation

        

            Mathematica

See Lori Johnson Morse's 4 Wolfram Demonstration Projects, based on Don's book Changing Shapes With Matrices