Walt Hunter was a quiet man, slight and balding with a Great Plains accent. You might mark him as a teacher, but likely not the dynamic personality with a certain brashness that you would think of as a “favorite” teacher. He did not convince me to change my major from physics to chemistry even though he made me his chemistry lab assistant and spent untold hours talking with me about chemistry and teaching in his small office off my high school Chem lab. He did not convince me even though I learned to blow glass and enough chemistry to place out of two quarters of the first course at the University of Chicago. He did not convince me to become a teacher.
I came across his name recently while searching my house for old letters, pictures, and documents. He had sent me a letter, while I was then a new teacher at our old high school, inviting me to come to Missouri to see him at Meramec Community College where he had become a dean of instruction. I never went. Instead I headed to Fort Lauderdale to stay in high school teaching and to my great good fortune to meet the woman who I would spend most of my life with.

So as our digital world calls us to do, I looked him up and found an article he published in 1971 called Self-Directed Learning at Meramec Community College. It was a short report on a program he had initiated. It was written in his plain style and tells an amazing story, for this program he developed some 50 years ago reverberates in our time. He argues for Universal Higher Education and for a system of education under the heading Modern Challenge in which:

<em>“…college departments need to develop more learning modes, leading to individualized achievement of well defined objectives. Thus, the student can, with guidance, select objectives which are appropriate to his needs and learning modes which fit his learning style.”

He calls for “A New Kind of College” </em>

<em>“a college based on a new philosophy of student learning and achievement.” “…colleges will be able to make significant gains in the efficient and effective utilization of available talents, spaces and facilities. Students would be freed to pursue learning individually via the most appropriate pathway…colleges would become learning centers…”</em>

You can see why I now think him my favorite teacher. Teach as he taught. I learned so much from him including the vision of learning as a laboratory science. I wonder what he would have imagined if he had the technology we have today. I wish I could tell him that his student is continuing to carry on his mission.

In a magazine published for college trustees, a recent short article captured the latest statistics from the ACT and SAT tests. The downward trend was notable especially in math. For example, “Forty-nine percent of the class of 2018 that took the SAT (2 million students) showed a strong chance of getting at least a C grade in a college-level math test, much lower than the 70 percent who reached the same benchmark for reading and writing, according to the Washington Post.” Math is preventing our kids from getting a college degree.

But what really broke my heart was this number: “The share of ACT test takers who showed readiness for college math fell to 40 percent–the lowest level in 14 years.” They go on “‘The negative trend in math readiness is a red flag for our country, given the growing importance of math and science skills in the increasingly tech-driven U.S. and global job market,’ said Marten Roorda, ACT chief executive officer. ‘It is vital that we turn this trend around for the next generation and make sure students are learning the math skills they need for success in college and career.’”

This is a great ad for What if Math, where math for the digital age is not hard.

Art

I feel most fortunate when I have a year I get to work on a new great idea in it. This past year has thus been one of good fortune. Some great ideas can appear huge from the start, covering wide swaths of life, and some, at first, can seem small, almost insignificant initially, but on reflection turn out to be consequential and central. This year the great idea was the latter, an idea that appeared tiny and obvious at first glance, but that grows and grows, becoming more valuable with each passing day. Some great ideas seem to be wonderful creative inventions, unique and very, very different, while others are quiet, seemingly so common that we easily miss them. This year’s great idea was again the latter. I would never have expected it to grab hold of our minds and continue to pull us in new directions. And some great ideas seem to spring whole formed, exploding like the Big Bang connecting all sorts of wonderful things together. While others, like this one, play hopscotch in our minds, jumping to and fro with little recognizable pattern to see at first, but eventually linking all sorts of ideas together.

This year’s great idea germinated late last spring as Peter and I were working on what we came to call Classic Story Problems, in particular, the familiar motion, work, and mixture problems found in middle school and high school math textbooks. These problems are painful, that is the only way to describe them, painful to learn and painful to teach. You know the type, “George leaves New York and Martha leave Washington at the same time going at different speeds, where or when will they meet?” Students fight hard to figure them out and many, I would argue most, finally succumb and memorize a formula. Then, of course, when the wording changes, even by a small amount, they are lost again.

In the process of building simple tables in Excel with time in hours in the first (input) column and distance in miles (output) connected by the rule that multiplies time by speed to get distance, we realized that we did not need to fix the input values. Originally, as I was starting to develop spreadsheet lessons, I would let Excel create my input column by putting the first and second input values into the column and then dragging the + to create the column of values. As we got more sophisticated we began to use a rule to create the column, add 1 to the previous number. Well it finally occurred to us that it would be very nice if we could enable students to easily change the input values. Why not make a parameter table with an initial value for the input and an incremental value, and build the input table using a formula and those values? This way we could easily change the start value and the increment value.

Seems such a simple change. But what power. We could enable students to easily solve story problems using a table with discrete values by letting them choose the level of accuracy they needed, developing an understanding of accuracy along with problem solving ability. We could enable them to easily change the domain of any function they choose to graph and quickly and easily control their graphs. We could enable them to zoom in on a particular aspect of a function to study it, or zoom out to picture its form. We could enable them to easily ask “What if…” in a myriad of new ways.

This tiny idea, a parameter control table that enables students to change constants as well as variables has great power. Make the increment smaller and smaller on a quadratic function and you can see that segment of the graph becoming straighter and straighter. Change the initial value and you can watch that straight line change slope as it moves around the parabola. It is almost magical. We don’t need to try to get students to understand limits or secants to picture derivatives, or find a common way to solve story problems. And we are giving them the tools to be flexible problem solving thinkers and explorers.

So as Frank Sinatra sang, “It was a very good year.”

Motion Problems

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 produce something original that has value. Isn’t that the essence of what learning is or at least should be. Can all learning be a creative experience? Can it be problem-based with interesting problems that can appeal to a wide variety of students? Can it provide powerful tools for students to experiment with and to stretch their imaginations enabling them to produce something original and of value? We believe most, if not all, of it can!

The spreadsheet math problems and experiments in What if Math are designed to enable every student to be creative and to experience creative learning. We hope you will encourage your students to learn and use the wonderful power of spreadsheets to be a creative problem solver. And we hope you will help us create new Labs by sending us problems to develop or Labs you would like us to publish. I look forward to hearing from you.

Art

When I was a kid, Sundays in the summer were car washing days. The stores were closed. The roads were generally quiet. And we took out the hose and the pail, filled them with water and dishwashing soap then rubbed, scrubbed, and waxed the family car…or later our own car…beautiful again. Sundays have already substantially changed and now in an article a recent Economist magazine, one of the last of the great suburban Sunday rituals will soon be going away too. For a scientist has found a pattern made by an obscure but available laser that sheds water and dirt with it. One day in the not too distant future we should be able to buy a car that not only no longer needs waxing but will never get dirty and need washing. Perhaps, about the same time, we will no longer even own cars but instead will ask for one on our cell phone, and an Uber Self-Driving car will pull up to our house to pick us up and drop us off wherever we want to go.

Crazy ideas, great changes. Yes, this is just a tiny example of the new world our students need to be preparing for. We are all linear thinkers. We think the world will continue in much the same way it has been going, with changes that take place slowly and methodically, changes that we can get used to, changes we can plan and prepare for. But change is not linear at all. It is, like the word used by the wonderful writer and biologist Stephen Jay Gould to describe evolution, “punctuated”. Sometimes change accelerates quickly and sometimes it moves at a constant speed. This has always been the nature of change and it is evermore so true today. For things that shed water don’t get dirty and don’t need cleaning — cars, windows, even clothes. And cars that don’t need drivers don’t need parking spaces on streets, driveways, or shopping centers. Our world could, and likely will, change dramatically.

How do we prepare children for work and life in this future world? What should they learn in their school years to make them ready for a lifetime punctuated with change they cannot predict? We cannot base it on the Sunday rituals of our past like counting the cash my dad brought home from his dental practice so that he could put it into the bank on Monday morning. We cannot base it on the paper and pencil calculating rituals we spent innumerable hours on, the paper algorithms that define most of the math our students practice. We cannot base it on “What is____?” habits of thought of the past, when the answer can almost always be easily Googled. We must base it on “What if…” thinking, functional thinking, the basis of science, technology, engineering, and math, the heart of business planning and quantitative reasoning, the question the future depends on.

Sunday rituals will come and go. Technology will sometimes change rapidly and sometimes slowly. But we can prepare our children for their future by making their education about “What if…”, their practice and mastery not off paper-based algorithms but off open-ended problem solving, their focus not on facts in today’s data-rich world but on thinking, their vision directed not on finding the right answer but on seeing outside the box.

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 teachers, words are our currency, and with few exceptions they are the main way we have always communicated skills and ideas. We come from a very long “stand and deliver” tradition. We seek to replicate Socrates talking to his disciples. When that oral tradition was turned into a printed one, teachers used words, even more words, to communicate ideas. Surely, in some cases, we draw pictures, knowing a picture is worth a thousand words, particularly in mathematics. But we rarely let images stand alone, but embed them in a sea of words, for words have remained our currency and our tradition for 2500 years.

Today, as we turn into the digital age using screens instead of dead trees, we continue to find it so very difficult to get past our tradition. We make videos, draw and animate images on screens, but still we fill them with words. Even when we create content with dynamic, interactive images, we still embed them in a sea of words to either be read or listened to. We, it seems, cannot leave our long tradition of making words our learning currency. Even when our visionaries preach teaching in the tradition of the great Socrates by asking questions, having conversations, seeking roots of concepts, we continue to apply his words based pedagogy to build 21^st century skills.

We have yet to learn the lessons of this new digital medium, the lessons of PowerPoint slide shows, Twitter and Facebook, emails and especially messaging. We have not applied the “less is more” use of words to digital learning. It is not easy to make lessons with just few words that do not have to tell, show, or direct. It is not easy to ask simple questions that suggest. It is not easy to picture concepts in visual representations as tables or graphs or animations. It is not easy to change tradition. But just as in Fiddler, we must!