What If Spreadsheet Math

Spanglish is one of those movies that grows on you. A coming to America story filled with themes that move us: a dedicated and resourceful woman, a dysfunctional but caring family, a highly successful artist, and of course love. It has many scenes that touch us deeply. One of those,… Read more

One 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 other during exams are either yelled at or disciplined for cheating. Homework is supposed to be an individual activity and students are punished for cheating… Read more

I still feel it months later, the thrill and awe I knew from finding an answer to a question I have long been troubled by. I was reading a delightful book on physics by Richard Muller called, Now, in which mixing physics and history, he explained time and in that… Read more

I like to hang out in the Harvard Graduate School of Education library. It has a good vibe, is usually full of students focused on my favorite topic, and is set up to enable technology as you well might expect. Every student has their own laptop. Lots of tables have… Read more

As I was again reading the Common Core Standards, I was struck by their introduction of variables in grade 6. Jim, I could not help but think of you, my old dear friend, and your wonderful command, “Algebra before acne.” Kaput envisioned algebra and algebraic reasoning as fundamental mathematical ideas… Read more

Empathy 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 sociology, perhaps in the humanities, a topic for English or history classes to consider in school. Yet, it is the first step in the Design… Read more

This 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 Florence, when he was 72 years old and effectively blind. Though famous for his telescope and the first images of the surface of the moon,… Read more

As part of the process of designing and developing new Labs, I visit math content sites all the time to help me think about the kinds of questions to ask and the way to explain or represent a concept. I am constantly struck by how talkative these sites are. As… Read more

“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 for far too many students: too many students leave high school unprepared for college or a career, particularly a STEM career; too many students do… Read more

Each summer, as schools get ready for a new school year, the question returns, “Should we be teaching algebra to our children?” it seems to have been started by Andrew Hacker who has tried to argue and continues to argue that algebra is both difficult and an unnecessary burden for… Read more

The word seems so benign. Yet it has become the goto word in education. School superintendents, even the best and most advanced of them, use it all the time. “We want each of our students to reach mastery in each of the standards.” To master something is to be in… Read more

Despite the many attempts to codify the creative process, it is as surprisingly individualistic as it is human. John Irving, author of iconic works like The Cider House Rules, describes his creative process as writing the conclusion before the beginning. He spends a year or more developing a story, the… Read more

I do not know who, when, or where this iconic mathematical representation was developed. It is, however, one of the most powerful and ubiquitous of all mathematical images, and I think the most important. It is taught to 2nd graders and used by STEAM professionals. It is called a function… Read more

It was an appropriate title for the movie about Jaime Escalante and it is an appropriate title for the role that teachers continue to play. We all too frequently see our role in both K-12 and in college as an actor standing and delivering. As problematic as that vision may… Read more

As I watched a young woman the other day learning to ride her bike, zigzagging down the street, desperately trying to keep her balance, I thought of the Wright brothers. They owned a bicycle shop where they made and taught people to ride the then relatively new form of transportation.… Read more

G.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. The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a… Read more

As mathematics takes an increasing role in work and life, creativity must become central to its learning, because: 1) creativity and creative problem solving are essential 21st century skills, 2) creativity drives engagement and enjoyment, and 3) creativity builds understanding. 1. 21st Century Skills: In survey after survey, business and… Read more

“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 system valued personal growth over test scores? Put inquiry over mimicry? Encouraged passion over rankings? What if we decided that the higher aim of school… Read more

My 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 iPhone told me that Lynn Steen had died. I never had the good fortune to meet him in person or to even talk with him,… Read more

To make its workers more productive, the Western Electric Company, makers of phones and other parts for the Bell Telephone System, conducted one of the great scientific experiments of all time. The researchers increased the brightness of the lighting at a plant in Hawthorne, Illinois just outside of Chicago, incrementally,… Read more

I 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 produces something original that has value. At What if Math we seek to make learning a creative experience, a process that enables every student to… Read more

Today, I attended an ancient ceremony. It is called “Hooding”. An elaborate and beautiful hood is given to students who have completed their scholarship and are ready to receive a doctoral degree. The Hooding Ceremony at Lesley University today with its rich pageant and sweet music took me back to… Read more

What if I could give you a magic wand to wave over our educational system and make it fulfill our dreams for our children? What would you have it do? I find this question stumps most people. We all know education in America is far from what we either want… Read more

If a mathematician were asked what these two numbers had in common, she might wonder if they were both primes. They are not. A gambler might consider them lucky numbers because one of the prime factors of 209 is 11 (as you could find out by asking google) and 11… Read more

Three 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 the first to convert Arabic arithmetic and algebra for European use. Devlin told Leonardo’s story and he described the process by which Leonardo’s book Liber abbaci (The… Read more

We 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 How Schools Kill Creativity, the most watched Ted Talk of all time, shows we hunger for learning as a creative experience. Yet we continue to… Read more

A little over 20 years ago the Harvard Calculus Consortium sought to remake the calculus curriculum. “We believe that the calculus curriculum needs to be completely re-thought,” began the text by Andrew Gleason and Deborah Hughes Hallett, both of Harvard University. They sought to get “our students to think.” In… Read more