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 Democratization of Knowledge

On this 10th anniversary of the iPhone it is worth remembering that this invention, as world-changing as it was, will not be deemed the most important one of that decade. It will, in the long thrust of history, take second place to an event that truly and profoundly changes the course of human thought. For in this first decade of the second millennium we will be most affected by the democratization* of knowledge. Before this decade, knowledge was rare, a scarce and valuable commodity to be bought, sold, and transferred in schools, workplaces, and books. It was owned by the few and sold to the many. Our schools sold knowledge to students in the form of teacher presentations and textbook descriptions. Our workplaces sold it as apprenticeships, training, and professional development. And our encyclopedias, sold these compilations of all knowledge door-to-door, and libraries were handsomely constructed to give all the opportunity to acquire it in printed form.

During the first decade of our new century, knowledge ceased to be owned by the elite, ceased to be rare, ceased to be precious. It is now owned by all, ubiquitous, and, for all intents-and-purposes, free. Wikipedia, a tiny but highly significant reflection of this revolution, began in 2001. Its rate of growth, as we can see from this fascinating graph, inflated around mid-decade and is even now slowing down as it has filled up with much of the past knowledge. And Wikipedia is but one of billions of posts and sites that today freely contribute knowledge in every sphere of human endeavor. For knowledge continues to expand at, what to most of us seems like an accelerating pace. Knowledge for the first time in human history, and for as far as we can see in the future, is now democratically produced and distributed.

From an educator’s perspective, this revolution profoundly changes our job. We can no longer be paid to carefully dole out the precious knowledge, mainly in text form that we acquired from our sweat and treasure, for it is now freely available on the Web. As painful as this may be to those of us who are or have taught, we will no longer be valued for what we know and show, but instead for how we help our students find what they want or need to know.

Applying this to problem solving demands we change our role from telling to asking, from answering to encouraging, from giving to wondering. Our job is now to encourage our students to use the Web to find things out, to learn how to solve a problem, to search for conceptual understanding, to explore possibilities, and perhaps most of important of all, to choose problems of interest to them to practice and build their skills. While students likely know Khan Academy and YouTube videos, most still need to be invited and yes encouraged to use all the tools available on the Internet to solve problems (in our case to learn to use spreadsheets to solve problems). In the digital age, they and their collaborators need to learn to aggressively find and use the digital opportunities to work on and solve problems. They need to learn to separate good from bad, valuable from worthless, helpful from wasteful. They need to be encouraged to find things out for themselves, to try again, to try harder, to keep trying. And they need to be told to get help from their peers and from experts if they need it. They may, of course, at times need some direction, need us to bend their path a bit, but we will have to remember it is their path and not ours!

*I borrow this term, as it applies to education, from my dear friend Jim Kaput.

National Numeracy Network Conference

November 17-19, 2017, Barnard College, NY.

Scientific Reasoning and QR in the Digital Age

Introducing our new Tour of mathematics and problem solving in the digital age.

ATMNE Conference 2017, Nov 2, 2017

New Marlboro, MA, Nov 2, 2017, Session #11 10:45 – 11:45 Sudbury Grades 6 – 12
Peter Mili & Art Bardige

Problem Solving in the Digital Age

Problem Solving

Known as Word problems, Story Problems, or Application Problems, making sense of and solving these problems is challenge for many students and teachers. We bring you a unique, spreadsheet based problem solving strategy. You will leave with lessons presented in a spreadsheet lab format to take back to your classroom, along with an engaging pedagogy to help all your students become better problem solvers. Participants should plan to bring their laptops to this session.

Inverse Variation

The variables in most of the functions we are used to working with vary directly, as one goes up the other goes up. What do functions that vary inversely, when one variable goes up the other goes down, look and act like?

Google Sheets

Microsoft Excel

“Just try it on!”

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, highest on my list, is when Flor, who has just started as a housekeeper at the Clasky home, comes back to her own house after witnessing the mother embarrassing her daughter over her weight by buying her clothes a size too small. Flor, who had never learned English, asks, no she demands, that her daughter teach her how to say, “Just try it on!” They repeat it in synchrony over and over again. Flor arrives at the Clasky house before dawn to let out the new clothes, then she wakes Bernice up and holding up the clothes, she speaks English for the first time. “Just try it on!” “Just try it on!” she demands again and again until Bernice finally succumbs and the smile returns to her face.

I think of that poignant scene when I contemplate students and teachers in math classes today, for in conversations with teachers, parents, administrators, and yes students, I hear story after story about classrooms filled with kids who have given up on their ability to learn math, are just plain bored, or who see no reason to learn the math they are being taught. Teachers, who are themselves bored with a curriculum so heavily structured and predetermined it leaves no opportunity for creativity or even fun, try to pretend they are not. It is clear that teachers, students, parents, and administrators are dealing with a subject that no longer fits, a subject which has shrunken beyond recognition, a subject no longer relevant, no longer meaningful. Though, it claims to be conceptual, to enable students to learn to think and to solve problems, in reality it is mechanical in an age where machines have taken over most of those functions. It is too small for our digital age students and teachers who are wanting more, more relevance, more creativity, more fun, more learning. And it is too small for our classrooms where teachers want more discretion and more opportunities to engage.

In What if Math we have done more than just let out the old curriculum. We have started from scratch to build a digital age curriculum. Did we get it right? Do your students enjoy it more, learn more, feel better about their math ability? Are you having more fun? There is only one way to know, so I ask you, “What have you got to lose?”, and as Flor coaxed Bernice, “Just try it on!”, “Just try it on!”