Who am I?

featured on the front pages of the Philadelphia Inquirer and Monterey Herald. In 2009, I was one of two Pennsylvania charter school teachers chosen for the ACE (Appreciating Charter Educators) award, which recognizes teachers who improve student achievement, use innovative and creative instructional strategies, and make a difference in the lives of students.

In 2010, I taught a continuing education course for teachers at Neumann College in Aston, Pennsylvania – Mathematics and Visualization Across the Disciplines:  Applying the Singapore Method.  From 2012-14, I worked as a fluency writer for the EngageNY/Eureka Math curriculum.  In November of 2016, I completed my second major collection of Sprint Books.

Throughout the 2025-26 school year, I will regularly work with schools across the country.

For the past 19 years, I’ve been fortunate to learn under the tutelage of several brilliant educators.  During the summer of 2006, Dr. Yoram Sagher, professor of Mathematics at Florida Atlantic University, trained me in elementary Math teaching methods.  He has been the most influential mentor in my teaching career.

Madge Goldman, the late president of the Gabriella & Paul Rosenbaum Foundation, introduced me to Dr. Sagher and also Robin Ramos, the founder of The Ramos Group.  Robin is a wonderful mentor and has been instrumental in expanding my understanding of elementary mathematics.  She also introduced me to Louisiana State University Mathematics professor, Scott Baldridge, who mentored me in his A Story of Units project.

My Beliefs

"Emphasizing effort gives a child a rare variable they can control...emphasizing natural intelligence takes it out of a child’s control, and it provides no good recipe for responding to a failure."

- Carol Dweck

I believe that the role of a teacher can be defined as one who maximizes the social, emotional, and academic potential of every student they teach.  This definition, of course, sets all teachers up for failure.  Still, I’m at my most inspired when working towards this lofty ideal with colleagues who know the impossibility of the task, but strive to accomplish it anyway.

Growing up, I often heard people in my hometown use variations of the saying It’s not the size of the bucket a person carries, but how well they fill the bucket they have.

When I was a kid, my favorite athletes tended to not be those who possessed the greatest talent, but instead the ones who did the most with the talent they were given.  As a teacher, the students who have made the most lasting impact on me are those who – regardless of aptitude – exceeded what I thought they were capable of accomplishing.

Students like Thinh, Nasir, Jermaine, Michelle, Jane, and En-hui are not the same age, came from very different homes, went to different schools, and scored drastically different results on standardized tests.  However, bound by a relentless determination, they all belong to the same phylum of student – Potential Realized.

I believe that very few students realize more than ten percent of their academic potential.  I state this with humility, knowing that I graduated from high school functioning on a middle school reading level, but five years later graduated from college with a language arts degree.

I also feel that most teachers only realize a fraction of their professional potential.  I state this admitting that I spent my first five years of teaching categorizing students into those who could and could not, and believing that the bell curve was inevitable.

My philosophy changed during the 2006-07 school year when Dr. Yoram Sagher trained me in elementary mathematics teaching methods. Through his guidance, I learned that it was realistic (not to mention a lot of fun) for every child to feel successful in Math and in turn make drastic improvements during the course of a school year.  I realized that the reality of the bell curve had previously been magnified by me, not my students’ aptitude.

Dr. Sagher helped me understand that if I was able to master the content I was teaching, and willing to focus on clearly sequencing its delivery, then it was within me to arouse the latent mathematician laying dormant in many of my struggling students.

My experiences of working as an elementary Math teacher and consultant have forced me to change not only my definition of good teaching, but also my notion of what children are capable of achieving.

The Myth of Ability by John Mighton is a book that Dr. Sagher encouraged me to read.  It has helped shape many of my beliefs.  For a list of other books that have positively influenced my education career see:

Further Reading

Teaching

• Teach Like a Champion by Doug Lemov

• Practice Perfect by Doug Lemov

• Teacher Man by Frank McCourt

• How the Other Half Learns by Robert Pondiscio

• The Truth About Teaching by Greg Ashman

Math Education

• Elementary Mathematics for Teachers by Thomas Parker and Scott Baldridge

• Elementary Geometry for Teachers by Thomas Parker and Scott Baldridge

• The Myth of Ability by John Mighton

• The End of Ignorance by John Mighton

• Mathematical Mindsets by Jo Boaler

Learning, Schools, & Social Justice

• How the Other Half Learns by Robert Pondiscio

• The Teacher Wars by Dana Goldstein

• Amazing Grace by Jonathan Kozol

• Death at an Early Age by Jonathan Kozol

• Fire in the Ashes by Jonathan Kozol

• Ordinary Resurrections by Jonathan Kozol

• Rachel and Her Children by Jonathan Kozol

• Savage Inequalities by Jonathan Kozol

• The Shame of a Nation by Jonathan Kozol

• The Smartest Kids in the World by Amanda Ripley

• Little Soldiers by Lenora Chu

• Grit by Angela Duckworth

• Make it Stick by Peter Brown

Why Learn Math?

“...throughout the city, artists sharpen pencils and dip brushes and tune guitars.  Others (mathematicians), with their theorems and equations revel just as much in the world’s possibilities. / The world needs artists.  Into words and pictures, notes and numbers each transforms their portion of the night.  A mathematician at his desk glimpses something hitherto invisible.  He is about to turn darkness into light.”

- Daniel Tammet, Thinking in Numbers

“The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done.” 

- R. Askey, The American Mathematics Monthly

“No branch of education is considered so valuable a preparation for household management and politics, and all arts and crafts, sciences and professions, as arithmetic; best of all by some divine art it arouses the dull and sleepy brain, and makes it studious, mindful and sharp.”

- Plato, on why the understanding of mathematics was critical to entering the Academy

“If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.”

- Galileo Galilei

“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”

- Charles Celeb Cotton

“One of the most amazing things about mathematics is the people who do math aren’t usually interested in application, because mathematics itself is truly a beautiful art form.  It’s structures and patterns, and that’s what we love, and that’s what we get off on.”

- Danica McKellar

“A lot of music is mathematics.  It’s balance.”

- Mel Brooks

“The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.”

- Gottfried Wilhelm Leibniz

“Mathematics is the door and key to the sciences.”

- Roger Bacon 

“Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.”

- Roger Bacon

“As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.”

- Joseph Louis Lagrange

“This, therefore, is Mathematics: 
She reminds you of the invisible forms of the soul;
she gives life to her own discoveries; 
she awakens the mind and purifies the intellect; 
she brings to light our intrinsic ideas; 
she abolishes oblivion and ignorance which are ours by birth…”

- Diadochus Proclus

“The understanding of mathematics is necessary for a sound grasp of ethics.”

- Socrates

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

- Pierre-Simon Laplace

“Singapore Math® is a registered trademark of Singapore Math Inc. and Marshall Cavendish Pte Ltd. All rights reserved.”

**EngageNY is the common law trademark of the state of New York

**Eureka Math is the registered trademark of Great Minds Corporation, D.C.

Presently, The Davidson Group utilizes educational materials created and owned 100% by Bill Davidson