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 End

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 plot, and a set of characters in his head, writing nothing down, until he has the whole in mind. Then he writes the final paragraph. Then and only then does he start actually putting words down on paper going from beginning to end. His description of the writing process is a fascinating view into the creative act, most fascinating for me because I do it so differently.

I come up with an idea, often in the quiet mind time of the morning shower or the last thoughts as I slow my mind on the way to sleep. It is usually a blurb of an idea, often captured in a few words or a sentence or two. Never more than that. I repeat it over and over again to myself so that I will remember it, because my memory is notoriously terrible. I sometimes work on that idea for a few days, coming back to it, testing whether I still like it, adding a few connections to it, but rarely carrying it much further. I basically write that sentence of two on my brain and hold it there until I have the inclination or the time to actually develop it, compose it. For I am most fascinated not with the original idea but with what will become of it, where it will go, what it will develop into when I start keying it in for real. To me, the thrill is in discovery. It is in running the experiment and finding the result. It is in seeing the working invention. It is in printing the beautiful picture that I have tweaked and messed with. So I find writing not a painful demanding activity but a creative thrilling one that I take joy in. For I never quite know where it will go or what it will produce. I suppose it is the reason I so love asking “What if…” in our spreadsheets. What does your creative process look like? I just learned more about mine!

Personalized Learning

These two words have caught the imagination of educators and parents. They were designed to be the frames for talking about the value of digital learning. They were to replace the bland “individualized learning.” They were meant to symbolize a focus on the student, student-centered, and on that great American tradition, individual freedom. What surprises me is how we can attach so importance to this idea of personalization of learning and at the same time accept a common core curriculum, so dominating that it today takes up most of the school day.

The core of an apple is maybe 1/5th of its width, and if we square it to get its area 1/25th or cube it to get its volume, 1/125th of the whole. So if there is core knowledge, which it is argued, has to be at the foundation of what every student should know, and if we believe that learning should be individualized, then shouldn’t that core knowledge be a very small ratio to the whole? Shouldn’t core learning make up only a tiny portion of the school day? Shouldn’t we redefine core curriculum if we have any hope of making learning a personalized affair?

Because personalized means that a student has choices. It means that what, as well as how, a student learns and certainly why a student learns, must be the student’s choice. It must fit their interests as well as their abilities. We have always known that students have to be motivated to learn, they have to care to pay attention, pay attention to concentrate, and concentrate to learn. So, in fact, learning can’t be forced or required. It can’t be mandated. Learning has to be wanted which is the reason, the fundamental reason, it has to be personalized.

So let’s go back to work and define a core curriculum that represents the true core of the learning apple. The core curriculum need not follow the apple 1/125th model, that would most certainly be too stringent. But we should expect it to be reasonable. Core knowledge in the 21st century is changing every day and is easily searched for. Core skills on the other hand, 21st century skills, are sure to be necessary for as far into the future as we can see. Shouldn’t our curriculum reflect that? Shouldn’t the Math Common Core flip the importance and thus the time and priority between the Standards of Practice and the Standards of Content. For only then will we engage our students, personalize this their dreams, and really prepare them for 21st century work and life.

Function Machines

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 2^nd graders and used by STEAM professionals. It is called a function machine, and it represents the way we think about change, cause and effect, and technology as well as mathematical functions. For since the dawn of the industrial age we have pictured our world as a machine, as a “rule” that converts (connects) an input into an output.

This image of James Watt’s early steam engine shows a variety of inputs, outputs, and connections between them. On the left side, the steam from heating water provides the input to the rule, the big piston outputs the steam into the vertical motion of the piston. That vertical motion, through the rod connecting the piston to the lever, is now a new input. The lever is a rule changing the direction of the motion connecting it to a wheel on the right side. This rule converts vertical motion to circular motion. The lights lines are belts to link the circular motion, yes a link is a rule to drive some other outputs, one of which is the governor. The governor, that diamond shaped object with two balls attached in the middle of the diagram controls the speed of the engine spreading as it speeds off to reduce the steam output slowing the engine or narrowing to let more steam speed it up. Feedback enables a rule to modify the input based on the output.

These are just a few of the functions that make up this function machine, converting heat to steam to drive a piston, to turn a wheel, to add more water, to… The function machines we build on spreadsheets work in the same ways, sometimes just multiplying a quantity, sometimes changing one form of data, or sometimes using the output to control the input. Though we may think about different things today than people did 300 years ago, we still build our ideas in much the same ways. We still build models as collections of functions.

Stand and Deliver

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 be for our physical classrooms today, it is even more of a problem for digital learning classrooms. It is the reason that the most common refrains we hear about teaching online is how much harder it is, how much more time it takes, how difficult it is to keep connected with students. For we have taken the stand and deliver classroom model and transmogrified it into the online model.

Stand and deliver teaching puts the educational burden on the teacher. Students are the recipients of the knowledge in the head of the teacher. I am reminded of this old Egyptian image of Akhenaten’s god. In the paper classroom the teacher’s ability to motivate, to tell a story, to organize, and to simplify the textbook’s knowledge was nearly all of the content available to students. Stand and deliver was a reasonably efficient way to bring the content to the student. Eye contact, proximity, raised hand signals, and easy verbal interaction made this model sufficiently flexible, engaging, and rewarding.

But stand and deliver in the digital classroom without eye contact, proximity, or easily recognized hand signals requires us to rely on other means to hold the engagement of students or to recognize their learning signals. A number of tweaks have been tried to make the model work. MOOCs make their video lectures less than 7 minutes long and separate them with student activities. Teachers make themselves available 24/7 to talk online with individual students. New communication and presentation formats have been tried to enable students to engage with each other as well as with the teacher. Teachers have to provide a wide variety of additional materials and different formats to accommodate student needs. But if technology is to enable a more valuable and efficient learning experience then we must think anew about its use and let go of the thousand-year-old stand and deliver model.

Balance

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. They, like their students, had to learn to balance these new contraptions, just as most of our children do today. They took that core skill to their work on flight. For they were not the first to try to solve the problem of mechanical flight, but they were the first to be successful at it.

That success was built on many things, on a sense of design, on an understanding of both the physics and the engineering of lift, torque, control, and material science, on observation of birds, and even on the design and manufacture of the then very new gasoline engine. But if we had to ask, “What singular idea enabled them to be the first flyers?” The answer would have to be balance. They would have taken that from their bicycle business for it is also the secret to riding a bike. The small wing sticking out in front of the main wings had a reverse curvature to balance the lift of the big wings. The wing warping mechanisms enabled them to balance the chaos of wind and air currents and use a tail as a rudder to turn. They balanced weight, size, and structure to make it possible to carry a pilot and a passenger. And they even had to balance success and failure, secrecy and publicity, business and invention.

Education today is off balance, and like the Wrights we too have to make balance not just a priority but our central driving force. The balance between the arts and the sciences, so long a key aspect of our educational system is now gone. The practical arts are no longer part of our school day. The fine arts are for all intents and purposes missing in action. And the design arts, so critical to business today are not found in our schools. The sciences which includes math, for math is the “science of patterns,” have taken over our curriculum. English Language Arts, is not artistic but scientific with word counts, difficulty formulas, and non-fiction governing that subject.

We try. We add an A to STEM and make it STEAM, but we don’t seem to have a clue about how to integrate those subjects. We talk about the importance of the need to bring the arts back, but we are so nervous about those tests that we cannot find the time in the school day to do that. And while private schools flaunt their wonderful studios, their darkrooms, their theaters, and so many of the people demanding charter schools seek to emulate the privates, the measure of a good high school remains its SAT and AP scores.

As we invent an education system for the future and not the past, we, like the Wright brothers must make balance our central design principle. Just as balance enabled the Wrights to create a new form of transportation, so too must balance, by infusing our classrooms with the creativity of the arts, enable our students to fly.