“Just try it on!”
July 14, 2017Spanglish is one of those movies that grows on you. A coming to America story filled with themes that move us: a dedicated and resourceful… Read more
“Algebra before Acne”
June 14, 2017As I was again reading the Common Core Standards, I was struck by their introduction of variables in grade 6. Jim, I could not help… Read more
209 to 7
February 10, 2015If a mathematician were asked what these two numbers had in common, she might wonder if they were both primes. They are not. A gambler… Read more
A Book or a Course?
September 13, 2018I have long loved Maxwell’s Equations as the epitome of beauty in physics and as the source of inspiration for my teaching. But though the… Read more
A Maker of Patterns
April 25, 2016G.H. Hardy, one of the greatest mathematicians of the 20th century wrote this: A mathematician, like a painter or a poet, is a maker of patterns.… Read more
Another Sunday Ritual Soon Gone
June 1, 2015When I was a kid, Sundays in the summer were car washing days. The stores were closed. The roads were generally quiet. And we took… Read more
Back- to-School – add 10%
September 8, 2016It was forty years ago this September that I started my career as a high school mathematics teacher, a career that spanned 36+ continuous years.… Read more
Balance
June 16, 2016As I watched a young woman the other day learning to ride her bike, zigzagging down the street, desperately trying to keep her balance, I… Read more
Baseball and Math
October 29, 2018If you are a Bostonian by address, birth, or just a connection, you can’t help but be full of pride this morning for your baseball… Read more
Change
October 26, 2016“Today, it seems as if nearly everyone agrees that high school mathematics needs to change. For far too long high school mathematics has not worked… Read more
Cloisters
June 15, 2017I like to hang out in the Harvard Graduate School of Education library. It has a good vibe, is usually full of students focused on… Read more
Collaboration is Cheating?
June 29, 2017One of the four C’s, perhaps for many the most important 21st century skill, is considered in our schools, cheating. Students caught talking to each… Read more
Curiosity
June 11, 2018The words curious and curiosity do not appear in the Mathematics Common Core Standards document, yet they are arguably the most important words in mathematics… Read more
Empathy
June 6, 2017Empathy is an odd idea to discuss in math or even in STEM/STEAM education. It is usually thought of as an issue in psychology or… Read more
Exhausted
February 12, 2018Teaching done right has always been a hard job, but it is now substantially harder. Talk to any teacher and they will tell you that… Read more
Function Machines
June 29, 2016I do not know who, when, or where this iconic mathematical representation was developed. It is, however, one of the most powerful and ubiquitous of… Read more
Functional Thinking
April 11, 2017We call our problem solving process, functional thinking. When we apply functional thinking to problem solving in the digital age, we find that a few… Read more
Headmath vs. Handmath
February 9, 2015There are really two kinds of mathematics we do every day. I like to call one headmath and the other handmath, one is the mental… Read more
Is the Textbook Dead?
July 24, 2018It caught my eye, this headline/story posted on EdWeek recently. Seems there was a panel at a conference that was supposed to debate what they… Read more
Learning as a Creative Experience
January 1, 2015We are in a time of dramatic, some would say, revolutionary change in education, “challenging” as Sir Ken Robinson says, “what we take for granted.” His… Read more
Learning Math as a Creative Experience
April 20, 2016As mathematics takes an increasing role in work and life, creativity must become central to its learning, because: 1) creativity and creative problem solving are… Read more
Learning to Swim
January 25, 2018The University of Chicago is not known for its athletics, so when I entered it as a first-year student I was very surprised that I… Read more
Lynn Steen
June 24, 2015My fortune cookie today read, “If you’re happy, you’re successful.” Usually for me that is true, but not today. For during that same lunch my… Read more
Mastery
July 20, 2016The word seems so benign. Yet it has become the goto word in education. School superintendents, even the best and most advanced of them, use… Read more
Math as a Laboratory Science
April 17, 2018Math is not only the last letter in STEM or STEAM, it is the only one that we do not picture as experimental. We don’t… Read more
Minkowski’s Connections
June 23, 2017I still feel it months later, the thrill and awe I knew from finding an answer to a question I have long been troubled by.… Read more
Opportunity for Creativity
June 3, 2015I just looked at a wonderful short video by Sir Ken Robinson on creativity at https://youtu.be/63NTB7oObtw in which he describes creativity as a process that… Read more
Over the Rainbow
June 13, 2016Over the Rainbow by Harold Arlen and E. Y. Harburg is considered the greatest song of the century and the greatest song in a movie… Read more
Personalized Learning
July 7, 2016These two words have caught the imagination of educators and parents. They were designed to be the frames for talking about the value of digital… Read more
Personalizing Learning
June 14, 2018Envisioning technology that reinvents our schools not automates them should, I believe, be our goal and our dream for personalizing learning. Read more
Real Feedback vs Artificial Feedback
January 8, 2018Math Blaster was the biggest hit educational product in the 1980’s, the first decade of the personal computer age. Flying saucer like objects would vaporize… Read more
Revolutionary Math
March 1, 2018Cape Cod in the winter is one of those marvelous places filled with interesting shops and people waiting in the quiet winter time for the… Read more
Rows and Columns
May 24, 2018This picture from a recent blog post sends shivers down my spine. It is our picture of a “modern” classroom with the desks lined up… Read more
Rule of 72
June 19, 2017The Genius Behind Accounting Shortcut? It Wasn’t Einstein The Rule of 72 is a nifty shortcut for estimating investment returns; first published mention was in… Read more
Small Changes
October 7, 2014Small changes, seemingly inconsequential acts, can have momentous repercussions. Dead birds set off the environmental movement. An assassin’s bullet protesting an exhausted empire started a… Read more
Spreadsheets and the Rule of Four
October 29, 2014A little over 20 years ago the Harvard Calculus Consortium sought to remake the calculus curriculum. “We believe that the calculus curriculum needs to be… Read more
Stand and Deliver
June 20, 2016It was an appropriate title for the movie about Jaime Escalante and it is an appropriate title for the role that teachers continue to play.… Read more
The Bit
February 21, 2018The key to the digital age is also the key to learning algebra. Despite what many of us may believe, our digital age did not… Read more
The Challenge of New
December 21, 2017One hundred years ago my father at age 9 entered America. He had traveled from his birthplace in a town in what is now Ukraine… Read more
The Democratization of Knowledge
December 13, 2017On this 10th anniversary of the iPhone it is worth remembering that this invention, as world-changing as it was, will not be deemed the most… Read more
The End
July 18, 2016Despite the many attempts to codify the creative process, it is as surprisingly individualistic as it is human. John Irving, author of iconic works like… Read more
The First Graph
April 5, 2017This picture was first published in 1638! It is from Galileo’s great work Two New Sciences, that he smuggled out of his home imprisonment in… Read more
The Great American Probability Machine
October 22, 2015This program started my career in digital learning. I bought my first computer, an Apple II in February 1978 on their first anniversary. I talked… Read more
The Hardest Question
June 28, 2018What is the hardest question a teacher has to answer? As teachers, especially math teachers, we face this most painful question all too often, rarely… Read more
The Hawthorne Effect
June 16, 2015To make its workers more productive, the Western Electric Company, makers of phones and other parts for the Bell Telephone System, conducted one of the… Read more
The Los Alamos Primer
June 5, 2018Or how to build an atomic bomb. One of the best curriculum ideas I ever had was to use this book as the text for… Read more
The Magic Wand
April 8, 2015What if I could give you a magic wand to wave over our educational system and make it fulfill our dreams for our children? What… Read more
The Problem with MOOCs
July 9, 2018When MOOCs were the rage in higher education, I asked my friend David Kaiser, a physicist and professor of the history of science at MIT,… Read more
The Summer Challenge Problem of the Week
May 1, 2016“How do you keep students engaged in math while they are having fun?” We think we have come up with the perfect solution for teachers… Read more
This is Why I Love Graphs!
March 2, 2018This graph appeared on one of my favorite websites – Statista. Given the “breaking news” of the day, that the President wants to impose new… Read more
Touching the Sun
August 13, 2018The Parker Solar Probe was launched yesterday to study the sun. Sixty years ago, Eugene Parker launched my scientific career. A young physics research scientist… Read more
Tradition, Tradition
May 20, 2015Today, I attended an ancient ceremony. It is called “Hooding”. An elaborate and beautiful hood is given to students who have completed their scholarship and… Read more
Tradition, Tradition
October 28, 2016As part of the process of designing and developing new Labs, I visit math content sites all the time to help me think about the… Read more
Welcome to What if Math
January 19, 2015Three years ago I read a wonderful book by Keith Devlin called The Man of Numbers. It told the story of Leonardo of Pisa who was… Read more
What Algebra?
August 10, 2016Each summer, as schools get ready for a new school year, the question returns, “Should we be teaching algebra to our children?” it seems to… Read more
What if Math 2.0
May 31, 2017Over the past year, we have been working to combine our spreadsheet math lessons (downloaded more than 20,000 times) into digital age problem solving Courses… Read more
What if…
March 16, 2016“Rather than ask why our students fail to measure up, this film asks us to reconsider the greater purpose of education. What if our education… Read more