Author: Art Bardige

I am a digital learning pioneer who believes that technology can play a great role in enabling every child to learn efficiently, effectively, and economically. What if Math is my latest work and the most exciting I have ever been involved with. I hope you will give it a try.

The Bit

The key to the digital age is also the key to learning algebra.

Despite what many of us may believe, our digital age did not began with the microprocessor, or the personal computer, or even the iPhone; it began with a single amazingly simple idea by a quiet man who few of us would today recognize. Claude Shannon grew up in Minnesota when radio was becoming the means of communication to all, broad cast. It was the age when sound was added to movies, when phonographs and records storing sound became a must in every home, when the first facsimile machines were used to transmit photographs and text, and when everyone could take their own pictures with the Kodak Brownie camera.

Each of these transforming inventions used a different analog means of storing or transmitting data. Analog data is continuous; on a graph it is a line, sometimes smooth, sometimes jagged. All of these inventions had to deal with the problem of noisy data and of separating the noise from the data. This was the problem Claude chose to work on. Before him the common way of dealing with noisy data was to turn up the volume. If the radio static was bad, make it louder. If the picture was muddy, increase its contrast. If the telephone call was hard to understand, yell.

To solve this problem of noisy data both in storage and in transmission, Claude came up with a truly brilliant, surprising, and original idea. Think about all data as digital. Think about it as being broken down into discrete bits, a collection of just 1’s and 0’s. No longer would data be stored or transmitted as a wave like the grooves in a phonograph record, a continuous quantity. In Claude’s new world it would be like atoms, discrete, separate, objects. Bits, the word he chose, came from binary digits; where his “atoms” took two and only two forms. It was transmitted in bits, stored in bits, and processed in the same bits. He then figured out how to find corrupted noisy data, how to minimize it, and how to replace it. When he died at the turn of this century, his vision for data was just becoming an overwhelming reality. Because today, we have the bandwidth, the storage, and the processing power to handle all data digitally, and the processes that make noise no longer a problem we concern ourselves with.

Isn’t it time our schools deal with its noise problem by becoming digital and focusing on discrete data? Today’s “analog” continuous variable algebra makes the concept of variable abstract and difficult for many students to understand. It requires students to learn a complex set of special cases to solve abstract equations. It turns algebra into collection of mechanical processes focused on cases that are easy to solve. What if we were to follow Claude Shannon’s lead and treat variables as discrete, digital quantities? Spreadsheets make this easy. Variables become concrete, easy to understand, iterate, build into functions, and use those functions to build models. They give us the means to focus on real, messy, interesting data to solve fascinating problems.

Try this new way of thinking for yourself. Go to our Tour to see apply the digital world to algebra. Try it with your students. Tell us what you think.

Art

Exhausted

Teaching done right has always been a hard job, but it is now substantially harder. Talk to any teacher and they will tell you that they are overwhelmed. Blame it on kids more distracted, on parents more demanding, on the misery of an over reliance on testing that saps creativity and judges teachers on things they cannot control, on a lack of money, on cell phones. The list is endless, personal, and the results exhausting.

If we seek not blame but instead deep cause, we will see that much of the pain teachers are now rightly feeling is due to the new digital technology, technology that has had a positive affect on most other aspects of our lives. Digital technology in the form of cell phones not only distracts students, it invades teachers’ lives, for they feel the need to answer students queries 24/7. Email which has become a primary form of communication opens the door to parent-teacher and student-teacher dialog again extending the school day and adding burdensome demands. Powerful computers now enable standardized testers to analyze data and grade teachers on student progress. Shared syllabi on common instructional platforms rigidly sequence and control teacher lessons removing any opportunity for creativity and innovation. The scope and sequence that used to weight down teacher desks collecting dust in the bottom right hand drawer are now online controlling the day.

Word processors, while making it easier for teachers to read written work, also make it easier for students to write more and to demand that teachers immediately read, respond to, and grade it. PowerPoint presentations of content are not as easily erased as chalkboards, saving class time but demanding more preparation time. And like doctors today, teachers too, feel the need to be up on the latest info available on the Web. Last year’s lecture notes just won’t do any more.

New technologies can be insidious. While as teachers we may worry about big tech issues like flipped classrooms, online assignments and tests, personalization, and the need to ensure our students have equitable tech treatment; we must also prepare for the future of blended classrooms and online courses. Digital technology has made our lives harder, much harder.

Technology is always like that. It starts out by making us work harder. It requires us to follow a learning curve. It demands we learn new ways to do old things that do not make them easier or save us time. And it is invasive, causing us to add new problems like student security to all the old problems. This is where most teachers at both K-12 and college find themselves, fighting digital technology instead of enjoying its benefits. For powerful new technologies, technologies that change our lives, require us to not just adapt our old forms, methods, and content but to rethink them. It requires us to learn to fully use technology and integrate it with what we are doing. And it requires us to imagine our role in a new way.

What can you do to make technology work for you and for your students? What can you do to make your job easier instead of harder? What can you do to prepare your students for a world you were not prepared for? Stay tuned!

Learning to Swim

The 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 had to take and pass a swimming test. Despite my parent’s best efforts, I had never learned to swim, and thus had to take a required quarter of swimming classes. Now, unfortunately, I am a slow learner, particularly on the physical side, and I failed my final swim exam that first quarter. I had to take the course again the next quarter.

I went into my first class in the old Bartlett Gymnasium pool that
cold winter day and dutifully lined up at the edge of the pool like my swim coach told me to do, the edge of the pool at the deep end And I patiently waited instructions. None came. He, instead, moved in back of me and pushed me in. “Sink or swim,” he said. I started to swim. I had been taught the strokes, I had been taught to float, I had been taught to kick and to breathe before. Now I just needed to be pushed off into the deep end where I had to use those skills, conquer my fears, and swim. I am still here today, so though I am not a world class swimmer, I do know how to survive in the water and even enjoy swimming.

I think about my swimming lesson when I talk to students, teachers, and others who fear spreadsheets. I want them to get a couple of simple skills under their belt and just jump into the deep end. No practice dogpaddling in the shallow end of the pool, no kicking exercise holding on to the edge of the pool, no holding your breadth and swimming underwater across the pool are going to turn you into a swimmer. If you want to learn to swim, practice breathing in the water, kicking, and using your arms in a crawl stroke then jump into the deep end of the pool, jump in and swim.

The same holds true for spreadsheets, arguably the most important and most feared business technology we have. Practice using a rule on an input cell to put its output into another cell thus creating a function. Use relative and absolute addressing to copy those functions and build models combining them. And start with a parameter table to enable you to ask, “What if…” of those models.

Go to whatifmath.org and click on Tour to see how simple models can enable you to build and do math across the curriculum. So, I say to teachers and students, “Jump in! The water is fine. You won’t drown. And I promise you will learn how to swim in the spreadsheet ocean and come to really enjoy learning math with spreadsheets in this Happy New Year.”

Real Feedback vs Artificial Feedback

Math 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 before your eyes when you solved a simple math question. It thus gave you immediate feedback and like pinball, it kept score. My friend Jan Davidson designed and built this first in a lineage of educational products.

Today, most of our digital learning programs pretend to be more sophisticated. They deal with multistep problems and less rote practice. Their feedback is less shoot ‘em up, and their interactions are no longer pure gamey response. Yet they remain wedded to the same kind of “artificial” feedback where the computer knows the answer and students guess it. Students may look like they are doing authentic problem solving, but they expect their computers to check each step they take, and with the same artificial feedback keep them on track to solve the problem. The computer now knows not only the answer, the product, it knows a particular process as well, and it tries to ensure that students get the problem right by following that process.

Unfortunately, in the real world outside of schools, we seldom get artificial feedback to help us solve problems. We must learn to use real feedback to keep us on the right track, to help us solve real problems, especially those requiring creative solutions. We need to learn to build real feedback into spreadsheets to catch selection and rule mistakes, so we learn to build in redundant calculations as checks. We make graphs to give us feedback, to see whether all our numbers fit the pattern. Though spreadsheets may seem intelligent, we have to constantly find ways of assuring that we have not made mistakes in the models we build, so if we are good spreadsheet developers we us headmath to check whether our algorithms make sense.

Students need to be learning to build feedback skills into their problem-solving processes and strategies. Artificial intelligence may be an interesting arena today, but our kids need to learn to create and use real feedback and not rely on any program’s artificial feedback if they are to become good problem solvers.

The Challenge of New

One hundred years ago my father at age 9 entered America. He had traveled from his birthplace in a town in what is now Ukraine across the vast expanse of Siberia on the Trans-Siberian railroad to its eastern extreme at Vladivostok, from there by ship to Kyoto, Japan and then 6 weeks on a tramp steamer across the whole of the Pacific Ocean to Seattle to meet the father he had not known, who brought him and his mother to Chicago to settle in a new land. This immense voyage in space and in time must have been, disorienting, yet that is far too weak a word for the changes he had to confront. He left a town shattered by war, likely without electricity, telephones, or motor driven transport, an agrarian country where farming, as it had been done for centuries, was the main industry and where industrialization had virtually no impact. Transported into a new world by steam railroad and ship to an industrialized world with electric lights, indoor plumbing, central heating, electric streetcars, telephones, and an abundance of food; he would soon see know air travel, radio, refrigeration, skyscrapers, and of course automobiles. During his all too short lifetime of 45 more years, he would travel on a jet plane, use the modern air powered tools of dentistry to save people from the pain of tooth decay, watch television, buy a house in the suburbs, and travel comfortably throughout much of the United States.

To my lasting regret, I never thought to ask him how he navigated such profound changes, changes in technology, in community, in governance, and in economics. He was just 20 years-old when the Great Depression started. He was 33 years-old when, as a brand-new father, he went into the army. And he was 43 years-old when he left the dirty crowded big city to join the suburban green migration. I often think about the profound and yes unprecedented changes he lived through as I consider what we are going through today. Like him, I am, and actually all of us are, experiencing changes we could never have even imagined in our best science fiction, changes in the nature of work, in the technology we use and the capabilities and comforts it brings, in our political systems, our communications, our personal interactions, in who we marry and what we spend our time on. I wonder often how he felt about those last generation changes, how disorienting they were to him and to others, and how that concerned him. I wonder, as I talk with family, friends, and associates, how our disorienting profound and unprecedented changes compare to his. I wonder if the first Americans, who invaded virgin land, faced with unseen animals, unfamiliar plants, and unknown geological challenges. I wonder if we are, after all, so very different, and if as humans we are most fortunate to have the gift of a flexible mind to enable us to change, to meet the challenges of the new.

My father was by most standards an incredibly successful human being. He was happily married, had three boys who have all had their own families and made useful contributions to their communities. Despite coming here with no English and likely little formal educational experience he learned, becoming a dentist, a community leader and in his later years started a second career as a teacher building a revolutionary new program to educate dental assistants. He not only served his new country and his various communities, he played a key role in their growth and transformations. I can only hope his grandchildren and great grandchildren should be so successful.

He managed to do all of this during a time of change in every area of his life. I have, therefore, hope that in our time of amazing change, when our world, our jobs, our technologies, our communities are so profoundly transforming, we take comfort that our generation is not alone. Our forefathers too have, from time to time, succeeded in navigating such amazing periods. For, I am sure my father would agree, these times of tumult are also times of great energy, these times that look so scary are also times of promise, these times when we cannot see the future are ones we can instinctually navigate. I picture my dad riding on a wobbly rail car across the great stretches of Russia comforting his very frightened mother and believing in a better future. This was his gift to me, and it is the gift I pass on to my children, grandchildren, and all my students. It is why I am so deeply sure that technology not only shakes up our world, it gives us the power to reinvent it. It will give us the power to reimagine education and enable all our children to thrive in their new world.