Category: Blog

A Book or a Course?

I 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 equations are beautiful and even familiar, very few people understand them. So, when I came across this paper by the great physicist Freeman Dyson called “Why is Maxwell’s Theory too hard to understand?” I could not resist reading it. His telling of the Maxwell Equations’ story led me in a new direction not just in thinking not about physics but about education in the digital age. It led me to ask: “What’s the difference between a book and a course today?” and to further ask, “What will they look like in the future?” Before you help me tackle those questions, I suggest you look at the story Dyson tells about Maxwell’s great work.

In the year 1865, James Clerk Maxwell published his paper “A dynamical theory of the electromagnetic field” in the Philosophical Transactions of the Royal Society. He was then thirty-four years old. We, with the advantage of hindsight, can see clearly that Maxwell’s paper was the most important event of the nineteenth century in the history of the physical sciences. If we include the biological sciences as well as the physical sciences, Maxwell’s paper was second only to Darwin’s “Origin of Species”. But the importance of Maxwell’s work was not obvious to his contemporaries. For more than twenty years, his theory of electromagnetism was largely ignored. Physicists found it hard to understand because the equations were complicated. Mathematicians found it hard to understand because Maxwell used physical language to explain it. It was regarded as an obscure speculation without much experimental evidence to support it. The physicist Michael Pupin in his autobiography “From Immigrant to Inventor” describes how he travelled from America to Europe in 1883 in search of somebody who understood Maxwell. He set out to learn the Maxwell theory like a knight in quest of the Holy Grail.

Maxwell’s Equations in the elegant form found on college student tee shirts and physics classroom posters were not the the way Maxwell wrote them down in 1865. He did not have the benefit of the power or the simplicity of vector calculus. And the idea of fields as environments was then brand new and hard to grasp. But of greater interest to me, beyond the significance and power of symbol systems which have been well known, was Dyson’s recognition that for many, maybe most new ideas, just the process of writing them down for someone to read in paper or book form is not enough. We have to be taught. We have to learn them. Dyson continues.

Pupin went first to Cambridge and enrolled as a student, hoping to learn the theory from Maxwell himself. He did not know that Maxwell had died four years earlier. After learning that Maxwell was dead, he stayed on in Cambridge and was assigned to a college tutor. But his tutor knew less about the Maxwell theory than he did, and was only interested in training him to solve mathematical tripos problems. He was amazed to discover, as he says, “how few were the physicists who had caught the meaning of the theory, even twenty years after it was stated by Maxwell in 1865”. Finally he escaped from Cambridge to Berlin and enrolled as a student with Hermann von Helmholtz. Helmholtz understood the theory and taught Pupin what he knew. Pupin returned to New York, became a professor at Columbia University, and taught the successive generations of students who subsequently spread the gospel of Maxwell all over America.

I highly recommend you read the rest of Dyson’s paper, but for now, I want to consider the question it has prompted. As books have become more interactive, as textbooks become linked to fancy interactive websites, as courses become MOOCs wrested from the tyranny of a 15 week calendar the physical classroom and the format of live teacher; we now see both methods of education in a wide variety of shapes and sizes. So, today, “What is the difference?” “Are we trying to write and publish (perhaps self-publish) a book, or are we trying to teach an online course?”

For me, these questions are not philosophical; they are real. I am in the process of putting together a book/course on the future of education. Since it is about education in this new digital age, the form and format are just as important as the ideas. So I ask your help.

As we learn from the Maxwell’s Equations story, courses help people digest and learn new ideas that simply reading them in a traditional paper or book form does not. The ideas in my vision of the future of education are radical and no doubt in need of something that looks more like a course, but certainly not a 20th century course and even less like a 19th century book. “So what does it look like, I wonder?” “What does the merger of books and courses make?”

Touching the Sun

The Parker Solar Probe was launched yesterday to study the sun. Sixty years ago, Eugene Parker launched my scientific career. A young physics research scientist at the University of Chicago, Parker volunteered to be a mentor to encourage science-promise high school students to develop their own science projects. I had the awesome fortune to be his mentee. My project, to develop a fuel cell, may have been outside of his focus on solar wind, and I may have not understood his fascinating story, but I remember both his kindness and scientific attitude that so excited me then and animates me to this day. Of all the things I did in high school, this project stands out in my memory. It did not even work, indeed it was a complete failure, I never got any current from that battery, but with this project I began to learn the “scientific attitude” that remains the core of my work and life.

That was the first time I did real science, not a high school subject, not copying something out of a book. I was doing something new, seeking to discover, to explore, to invent. Parker was patient with this very young and immature scientist, procuring sintered graphite and other materials, asking questions, suggesting things to read, and probing, always probing. I had always wanted to be a scientist, so I do not credit Eugene Parker for putting me on that path, but I do believe that his gentle nudges introduced me to the scientific habits of mind I carry with me today, the spirit of discovery, the thrill of invention.

He is remembered in this spacecraft and in the scientific community for his discovery of the solar wind. He is remembered by me for making science and scientific problem solving — real. I thank you Mr. Parker for giving me your time and your gift. In my work I seek to bring it to all students bathed by our great sun, and by it make problem solving real for them too. Hopefully they will look at the video and fall in love as I did.

Is the Textbook Dead?

It 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 obviously thought would be an attention grabbing, contentious, and controversial topic. Their conclusion: NO!

All I can say is: “You have got to be kidding!”

Now, I know that textbooks continue to play a central role in most of our schools across the grade levels. I know they have done so for centuries, I collect antique math textbooks. And I know that both the textbook publishing community as well as the school community believes that paper textbooks will slowly morph into online interactive versions. Textbooks are so ubiquitous, so standardized, so traditional that most of us cannot imagine school without them. So is it any wonder the panel came to its conclusion: the textbook, designed for print on paper (text is derived from the Latin for tissue) will always be with us. And while many expect paper to morph into tablets, few imagine fundamental change in form. So, I continue to ask: “You have got to be kidding!”

In 1962 by Thomas Kuhn published a revolutionary work called The Structure of Scientific Revolutions introducing the term paradigm into our lexicon. Kuhn argued that science changes for the most part continuously “normal science”, but the history of science is punctuated (to use Stephen Jay Gould’s term) with “revolutionary science.” We need only note the Copernican Revolution, the Newtonian Revolution, Maxwell’s Field Theory, Einstein’s Relativity, and Quantum Mechanics in the world of physics. These scientific revolutions introduce new paradigms, fundamentally new ways of thinking that change the focus and direction of a scientific field.

I would argue that technology, like science, grows in the same way. Most of the time it normally grows by small incremental changes, improvements, but every once-in-a-while its history is punctuated by revolutionary changes. The iPhone was not a mere smaller version of a corded or a better cord-free phone. It was a fundamentally new experience, a transformative experience that changed the ways we communicate. The integrated circuit changed the way we work. The Web revolutionized the way we learn.

So, the textbook, as we know it, an invention enabled by cheap printing in the middle of the 19th century, provided a way for large numbers of students to “take a teacher home.” Its lack of interactivity meant it did not replace a teacher, but for perhaps half of the student population it provided an effective supplement of class time with additional practice and information. It was not so much a tool for learning as a tool for practicing what you hopefully learned in class.

Digital technology with its amazing interactivity, its dynamic communication capacity, and its opportunities for collaboration, gives students powerful tools for learning. What if… we could use digital age technology to enable students to learn on their own without the direct instruction of a live teacher? What if… the new paradigm for the student’s learning tools was not dependent on text or repetitive mind-numbing practice? What if… we placed, into every student’s hands, the interactive power of the Web to imagine all learning as a science experiment.

At What if Math, over the past several years, we have been reimagining a math education, indeed a STEM education, designed for the digital age. Over the past several months we have made substantial changes to our content and our website as we have come to understand learning in the digital age. Over the next several weeks we will be rolling out the last of these changes.

This is not a new textbook for the digital age. The textbook is dead. This is a new way for students to learn. It is the way we believe, someday in the not too distant future, all students will learn. We look forward to your thoughts.

Art

The Problem with MOOCs

When MOOCs were the rage in higher education, I asked my friend David Kaiser, a physicist and professor of the history of science at MIT, when he was going to do a MOOC. Dave has won teaching awards at MIT and writes brilliant books on the history of physics. Who better to do a MOOC or two bringing his wonderful style of teaching and presentation of important physical ideas to more people. But he was not at all interested, and as far as I can tell several years later has not done any.

“Why” I asked. “Because you can’t change them.” he replied. As he explained, one of the most wonderful aspects of teaching a course year after year for a great teacher is the opportunity, indeed the necessity, to change and adapt the courses in general and the presentations in particular. His reaction brought back a vivid memory of my first couple of years of teaching high school physics. I usually carefully prepared my lectures which were the standard fare for most of my classes. Occasionally too busy, too tired, or too lazy to develop a new one, I would grab my lecture notes from the previous year which I thought pretty good. The class usually started all right, but I soon got into trouble. The coherence was gone, the presentation no longer seemed to make sense to me. I don’t know if my students realized that I was stumbling, they were too busy taking notes, but I did. So, I would stop lecturing, told my class what I had done, apologized, would come back the next day with a fresh lecture and gave them time to work on their assignments. One of the things that makes teaching such a great job is the year-to-year, day-to-day, and even student to student opportunity for improvement, for growth, for learning. This has not been true of curriculum.

MOOCs like textbooks are expensive to produce. They are linear, moving from topic to topic in a standard form, a continuous line of lesson following lesson. They are thus difficult, often impossible, to update or change. Once created, except for minor revisions they are for all practical purposes, fixed. Yet, the world is constantly changing, and even more importantly students are constantly changing. A fixed curriculum or presentation cannot work. It will no longer work to expect textbooks to have a 7 year lifespan. Nor will MOOCs, made once and used again and again, work either. The analog continuous linear sequence of lessons that represent a course is no longer functional in the digital world.

The digital world is a discrete world. It needs education to be flexible, easy to change, constantly renewing, and growing. The metaphor for the analog age and the MOOC is the book, done once and then published. The metaphor for digital age educational content is the newspaper, renewed and reimagined everyday. One is fixed, unchanging, the other constantly refreshed. One is designed to be the same for all students, the other can be different to suite the needs and interests of every individual student. One is the education of the past, the other is the education of the future.

Functional Thinking

We call our problem-solving process, functional thinking. When we apply functional thinking to digital age problem solving, we find a few fundamental models give us the tools to creatively solve quantitative problems. Think of functions as LEGOs, add columns using new rules, use outputs as new inputs, combine simple functions in new and creative ways.

Functional Thinking