email from Cheyenne Noel Chun, a former student at Miss Hall's School|
I was an MHS student in your 20042005 Honors Precalculus class. I want to thank you for being a wonderful educator. At the time, I found trigonometry far less exciting than the social explorations of high school. I'm sure that was evidenced by in-class sleepiness, giggling, and other teenage behaviors I've thankfully forgotten :)
Nonetheless, you showed up to each and every class with genuine kindness, unapologetic excitement at the wonder of mathematics, and nurturing yet firm leadership. Your class was a diamond among several years of mathematics taught by openly sexist, dispassionate instructors. Though those experiences were enough to dissuade my younger self from the discipline, your influence informed my decision to dabble in Chicago's IBL Mathematics program and to see expressions of gender bias in the sciences as puzzling human foibles rather than as reflections of truth.
Not only did you connect my young mind to the world of mathematics, you served as one of my first and most powerful role models. I didn't understand this at the time, but you were one of the first adult women I saw unflaggingly pursuing her passion, confidently asserting her values while radiating empathy, and completely ignoring our world's myriad pressures to perform stereotypical femininity (by rejecting “unladylike” forms of intelligence/intellectualism, deriving self-worth from material possessions or physical appearance instead of accomplishment, objectifying oneself, expressing self-deprecation rather than confidence, etc).
Because of your influence (and that of other powerful women), I have had the bravery to act authentically and with integrity in many situations where I felt pressure to conform to anti-intellectualism, materialism and sexismto practice “Meus Honor Stat” as I craft my life. I play Khan Academy and Tree of Math over Netflix; I assert my beliefs and values while expressing empathy for other positions; I am weird and wild and wonderful without shame, deprecation or apology; I take life, integrity and education seriously in a culture that mocks those things in favor of immediate gratification. I am that way because educators like you set an example.
Most importantly, I am unafraid to make mistakes and to fail because I understand that's how I learn and grow. That's what mathematics taught me. That's what you taught us when we thought we were learning SOHCAHTOA. I didn't show it at the timeI didn't even notice myself, but you deeply touched my life. And many more, I'm sure.
Thank you for that gift. (Yes, it was a giftI know true educators never get nearly the money or thanks they deserve, and that that's not why they teach.) Thank you for modeling the courage to give not for thanks or compensation, but because the soul has something to share. I've only started on that journey, but I see now that's what it's all about.
email from Trey Brister|
Dear Dr. Burns
I tried Khan and was confused by the lack of a clear path of progress starting from nothing. Just seemed like endless videos.
Then I googled and found your site and have done each level until I can master the exercises sufficiently to answer 20 correctly without thinking too hard.
I am on level 29 of 168 now and I trying to figure out how to solve variables, I just need to practice another week on 29 then I should get it down.
I think that since you are PHd there is a clear instructional path so I can learn algebra and maybe even progress to calculus using your site then I can teach it to my 13 year old son who is struggling with math. He is stuck on level 3 multiplication. We read the page content out loud taking turns by paragraphs then he dictates the answer to me to type on the keyboard in order to help his timing.
I just wanted to let you know how I was using your site to teach math and if I am doing something suboptimally you may let me know if you want.
God Bless You Dr. Carol
email from Ali Ahsan, Maldives|
Hello Dr. Carol JV Fisher Burns,
I am just writing this e-mail to you just to show my appreciation for the great and hard work you have put to make such a easy to comprehend and yet the most useful maths resource I have encountered on the Internet. I am wholeheartedly grateful to you, and so I want to thank you and I hope you will be carrying on with your work.
I am a student from Maldives and I find this website really helpful. Everything is explained in a way that not a single detail is missed. I just wanted to give you my feedback about it. I want to let you know that there are students around the world that value your work. Any future amazon shopping and hopefully any friends I have who shops using amazon I will try my best to convince them to use the link you have provided to assist you in cash, as I believe web-hosting is somewhat costly, and as the website grows it will get a bit out of hand. I am glad a person like you exist. To be honest, If I were the person to give away noble prizes you would be on top of my list. Once Again Thank you for the great work you have done to put all those information available on the Internet for free.
[a later email]
... Salman Khan from KhanAcademy made videos that were nice and helpful, [but] for people who better understand things by reading on their own, I believe the best web resource out there is your website. I have been like searching for great maths resources for about 45 years now and I wish I had seen yours earlier ...
comments from Robert C. Gordon PhD MBA, London, Ontario, Canada|
I once saw an interview with a well-known fiction writer who had just won a prize. The interviewer asked her how she felt about being “a writer”. She responded with humour and some depth of insight: I don’t think of myself as a writer, but as a re-writer. Your work reads as though it has been very carefully re-written many times. Your writing is consistently simple, clear, neither effusive nor dense, patient, and offered in a spirit of service. There is neither vain enthusiasm (the alternative page numbers are fun), nor contempt, nor hurried impatience.
In 1976, Dr M. Fogiel, editor of The Algebra & Trigonometry Problem Solver said that the top reason students have difficulty with Algebra is that there are “no systematic rules of analysis... which students may follow in a step-by-step manner to solve the usual problems [impossible because it] would involve an enormous number of rules and steps to be searched through... ” Until I began reading your writings, I believed in this impossibility. What Fogiel and I did not take account of is your ingenious ability to relate all these rules in a hierarchy of concepts, so that they are not presented to be remembered as isolated algorithms, but are encountered as integrated into the fabric of a holistic pedagogical theory. Cf. p. 272 “the thought process”
I have just completed reading during two days with great enjoyment both your One Mathematical Cat, Please! and your Algebra I course and my comments relate mainly to the latter. I am accessing only the “Read Text”, nothing outside that text. I am not doing the exercises in the text, although I did a few exercises in the text and found they were well chosen to reinforce both by repetition and gratification and also to continue and link the lessons.
Your explanations are effective. I never feel like I am no better off for having read what you say. Never stuck spinning my wheels, never diffident about going on to the next section.
After new concepts, you reinforce with repetition of examples not ad nauseam but ad intelligendum. Your meticulous labour is worth the reassurance of satisfaction in your students' complete and confident understanding. Your examples are so well chosen that no more are needed than what you provide.
Very effective is your use of shaded rectangles (or blocks on p. 266 ff) to visualize quantities, relationships, and operations.
Your technique of restating things in English and having your readers do the same in exercises is (a) an amazingly powerful way of making mathematical ideas more comprehensible, and (b) isolating ideas precisely for important distinctions that are to be made.
Your unusual ways of expressing mathematical ideas (e.g. minus = opposite of, many “names” of numbers, etc.) cannot displace in my internal dialogues in other idioms (e.g. minus n) after many decades habits, although I have tried in a few cases to force myself to use your language and was convinced that it is pedagogically preferable. They are very lucky who learn first from your courses.
Your boxed Definitions (cf. p. 260 “factors” vs “terms”), often serving as a summary of concepts covered, are pure gold! Do keep working on your Precalculus project (I look forward with delighted anticipation to seeing how you explain the trigonometric ratios) but I bet you could also write an extremely helpful Glossary of Terms with definitions aimed at the level of your courses.
Sometimes (e.g. from p. 262 and Definition p. 263 “to factor an expression means to write the expression as a product.”), your way of putting things is so clear and penetrating and original, but nevertheless apparently inevitable, that one begins to wonder whether mathematicians (or math textbook writers) have really cared to enable math learning. I must mention one particularly powerful example of your genius for disarming simplification that conveys a profound insight in a casual turn of phrase: your remark (cf. p. 187) about a “convenient flip” that turns the intimidating “Rule” for negative exponents into a completely generalized and very helpful “technique”. Stunning enlightenment that leaves a deep understanding of the fundamental nature of numbers.
I found meat, potatoes, and pie on every page. It's all dessert.
email from Todd Stone, Kingston, Washington|
Dr Burns, I want to compliment you on your website and texts on Algebra. I'm turning 50 this year and this past fall decided to go back to school and finish my degree. In the process, I changed majors. I was an English major (from years ago) and now am majoring in Business Admin Accounting. I am having a lot of success preparing for entry into the school of business at the university I'm attending. However, it is time for me to take the placement test for math and I began searching the web for resources that I might use to brush up on knowledge (and/or skills) that I either know I have or that I have forgotten related to math.
I graduated from HS in 1980 and to this day I regret the lack of respect I showed for math. Now, after many different careers which eventually lead to a 25 year career in the high tech industry (very successfully I might add), I find myself needing a basic understanding of algebra so that I can take the placement test. Nearly all the remaining pre-cert classes I have to take at school require business calculus and to get there I have to place well enough to show mastery of algebra I and II, or take non-credit based classes as I work up to it.
When I found your site I was amazed at how well the texts simply explain everything. Exactly what I'm looking for! I know this stuff! But the foundation; the thing that will help my recall is on your website. I so appreciate what you have here and I just wanted to let you know and say thanks for doing something so wonderful as this. We all should have a better understanding of math; perhaps that simple fact would ensure we have a better economy... ?!?!
Anyhow. Thanks so much for such a wonderful site and for the work you've done with it.
Regards, Todd Stone
email from Cynthia Mulit, Santa Rosa Beach, FL|
Hi Dr. Fisher Burns,
I want to express deep appreciation to you for your work.
I let Math fear hold me back for decades from taking the GRE. The fear was so great that I probably wouldn't have entered a Master's program a few years ago but for the fact that my Master's program waived their GRE requirement based upon career experience.
I want to go on for my doctorate. So I can no longer fight the math part of GRE. A few weeks ago I found your site. We have been spending hours together! I am working section 58 today in Algebra I. I still feel fear every time I approach the task but it's getting easier. The exercises are so helpful.
I feel progress! I wonder to myself whether if I keep going, well, could it be that I am really mastering what I am supposed to know to take the GRE?? Not 100% sure but the structure you provide is moving me forward.
Anyway, I just couldn't go another day without saying that I am so appreciative of the work you did on this site!
Best, Cynthia Mulit, Santa Rosa Beach, FL
email from Margaret, Educator and Artist, Massachusetts, USA|
I teach 7th grade Pre-Algebra in an advanced program here in Massachusetts and was searching for good ways to present linear equations to my students. I was thoroughly excited to stumble on your site. I have been writing my own lessons and worksheets for the students because I think the textbook presents this topic very poorly. You understand your audience and present the information in a highly “digestible” way! I will be using some of your lessons because they are very similar to how I present lessons to my studentsand it will save me a lot of time if I don't have to write so many new lessons.
I am a math teacher, but not a mathematician, so your site also helps me when my own understanding needs to be bolstered. The advantage of not being a mathematician is that I relate to how the kids are understanding or not understanding what they need to learn. I like to break everything down for them, make everything explicit, and justify all the steps along the way. No assumptionseven though some students who are mathematically talented can work with that (my son was one of themnow getting his PhD in math at UCLA), most students need good scaffolding and thorough instruction to make progress. And they can all make progress.
Thank you for providing such a wonderful website [...]
email from Carolyn Melo, Subject Area Coordinator, Secondary Math,|
Pennsylvania Leadership Charter School, USA
I am planning to use your book somewhat extensively with our special education students who are well below grade level in an attempt to get them somewhat prepared for our state assessment in March.
I will link to your web exercises pages, and ask them to send me screen shots of their time.
This should be interesting, since many of them are not very computer literate. By the way, we are a cyber charter school, so having something like this is a god-send.
I absolutely love the bookit is the one I would love to have written if I were going to write a math book. I am always sending people to the site to look it over.
[...] Right now I am trying to get Algebra Pinball to work on our serverhopefully the prospect of posting their names and times will inspire the kids to practice!
Thanks again for an amazing book!
email from Jose E. Revelo,|
a father in Southern California, USA:
I love your site...
And wish I would have had a teacher like you!!
My wife told me that a student can learn when they have a good teacher presenting the material. In fact, they should see that as part of their job; find what works when teaching and what doesn't.
You see, I could never get it when I was in school back in the late 70's and college in the early 80's. So I felt, well you know, dumb about math, it was not for me, I am not smart enough, etc. The usual cliches. I found your site through Curriki.org and love it. I have reviewed your first 13 sections of Algebra I and really see the light. So much so, that I am helping my 8th grader see that it is easy. You just have to learn the language and know the rules!! Your presentation is so crystal clear; that everything I should have known way back when is amazingly easy for me to comprehend today. I love doing the exercises, and then helping my son.
Because of you, he will never struggle with any of these concepts, or have the same inadequate feelings I had. When he comes to me, I review your site and then have a GREAT time helping him.
Thanks a bunch for your "Mathematical Energy."
I am sure you have been told that you have a great gift from God! What a blessing!!
selections from email correspondence (July 11, 2007) with Kara C.,|
a home-schooling mother in Atlanta, Georgia, USA:
I home educate my children and last year I started to use [a text] that was published in 2001. My ten year old son and twelve year old daughter were very excited to use this beautiful book and had no apprehensiveness about learning Algebra. Well, that was until they started into chapter seven! [...] It seemed simple enough, but before I knew what hit me our lesson had turned into a debate session [...] they felt that the real-world situations were too vague and didn't give enough details to allow them to feel confident that they had accurately solved the problems.
At this point, it was January and we were over three-hundred pages into the text. Although I had used teacher's resources for testing and they were scoring well, I really hadn't been confident that either of them had a firm grasp of algebraic concepts.
Thanks to a Google search, I found One Mathematical Cat. Suddenly, math was fun again! The children actually looked forward to the lessons. They were encouraged and I could see the puzzled, dazed look in their eyes fading away.
Carol, I cannot thank you enough for offering this course. These are children that had a 94 average in pre-algebra and at a crucial time, when they were ready to admit their defeat and throw in the towel, your Math Cat saved them. Now [...] these two children are sincere and confident when they offer free tutoring services. I think that speaks for itself.
[...] When I think about A/B averages that proved to be false positives, I'm left shaking my head [...]
[...] I've been piecing together curricula for myself, and others, for a number of years and I've found very few people that offer educational material that is so complete and well formatted [...]
"The Miss Hall's School Student Council established the Pietas Award in 2007 to recognize a faculty member
who has a profound sense of duty to their students, their school, and the community.
Qualities that the Student Council looks for in its nominees for the Pietas Award are willingness to go the
extra mile and to be truly involved in the school community not because it is one's job, but because it is one's passion.|
On a once-a-semester basis, in the months of November and May, members of the Student Council review the nominees who are submitted, and the winner will be announced during Morning Meeting where she/he will receive her/his charm and certificate of recognition."
May 21, 2007: Dr. Fisher was the first recipient of this award, nominated by AP Calculus AB student Masha Jones (Class of 2007). There was a gift of a beautiful, engraved, silver box!
Not only does she know her subject inside and out, but she also goes above and beyond to communicate her knowledge to her students. She does not just rely on a textbook, but uses her own index cards to make material easier to understand. She created an entire math website to help her students and other people throughout the world fill any gaps they have in their knowledge of math. Before having Dr. Fisher as a teacher, I never would have imagined myself taking AP Calc. Math just did not come very easily to me. But Dr. Fisher's style of teaching and enthusiasm transformed my entire outlook on mathematics. She prepared me for AP Calc and got me through the course. Granted, there were times when antidifferentiation and slope fields made me want to scream, but whenever that happened, Dr. Fisher's door was always open and she was happy to help me outside of class. After having Dr. Fisher as a teacher, I feel much more confident as I look ahead to math courses that I will take in college. Moreover, Dr. Fisher illustrates for me the kind of passion and continuing curiosity that I hope I will have in my future career.
a series of emails (April 16, 2007) from Naomi Laeuchli,|
a home-schooled American living in Vienna, Austria:
On your site you say you encourage feedback concerning your material and I am quite pleased to do so after the great help your Algebra course has been for me. I am a fifteen year old Home schooled American living in Vienna Austria and I have never been good at math. Though I am still working through the first Algebra course it has already been a great help. It is understandable and clear, and though I shall never be great at math, your course has already been a great help to me.
I have tried several online Algebra courses for my math and have always been confused after the first few sections, yours is the best I have ever found, remaining clear, even after it gets into some of the harder material.
I am reading through the entire text. I read it on the computer but also print it out in case I need to review something. I do have to confess though that I do not print out the worksheets, I simply practice online and do the exercises given in the text. Also I didn't have any trouble whatsoever in installing MathPlayer, it took less then a minute to download with my internet connection.
Also I always enjoy the links you have to other sites with interesting math facts and such.
It really is a wonderful course that has helped me a great deal. Each lesson is long enough and in-depth enough to make things clear. I used to use Saxon for math and after it got to Algebra their lessons grew harder to understand and less clear. Your course explains everything in-depth and always has everything written out so clearly.
The course is indeed very easy to use without a teacher, I have never had to get help from either my parents or my brother (who actually knows something about math), I've always been able to figure it out, based solely on the lessons.
Thank-you for the course, as I have said, it has been a great, great help.