What if you made a series of unit fractions with the odd numbers as their denominator, added the first two together, subtracted the next one, added the next one and so on. And finally multiplied that number by 4? What number would you get?
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.
Math as a Laboratory Science
Math is not only the last letter in STEM or STEAM, it is the only one that we do not picture as experimental. We don’t imagine students learning science without doing experiments. We don’t imagine them learning technology without writing code, or learning engineering without building models, or learning art without messing with paint, clay, or paper. Yet, we easily imagine learning math without experimenting. In fact, it is rare that students ever do a math experiment or think about math that does not have a “right” answer.
I learned to experiment from one of my great teachers, Walt Hunter. I even had the great good fortune to also being his chemistry lab assistant my senior year in high school. That I did not fall in love with chemistry was not his fault; I had just loved physics since I was 7 years old. But I did fall in love with experimentation, and like Walt I gained a deep belief that learning to experiment should be an essential aspect of every student’s education. I brought that belief to my physics classes replacing teacher demonstration with student experimentation. I took it to my Jr. High math classes, where I made my students worksheets that let them play with numbers and mathematical patterns. I carried it to my focus on manipulatives as a math coordinator, and I bring it to What if Math.
Using spreadsheets as basic learning tools for math has many advantages, but I think the most important one is that it turns math into a laboratory science. It enables students to experiment, to build and iterate models, to test those models, and to apply them to real-world data, complex rich data. It lets them ask and answer what if… questions. And it turns them into explorers who love to use math and who gain Walt’s experimental habits of mind, the thrill of discovery. It is this, I now know, that Lynn Steen saw when he described mathematics as the “Science of Patterns,” for math does belong to STEM/STEAM after all. So, when you plan your math classes, imagine your chemistry teacher, and the twice weekly labs where you learned to act like a scientist, to explore, to discover, to ask, “What if…”
Art
*Portrait of Antoine-Laurent Lavoisier and his wife by Jacques-Louis David, ca. 1788, Wikipedia
Framingham What If Workshop
This is Why I Love Graphs!
This graph appeared on one of my favorite websites – Statista.
Given the “breaking news” of the day, that the President wants to impose new tariffs on steel imports, it is fascinating to see from this graph the countries most affected, certainly not the ones we might have thought. It is a perfect example of the power of visualization, of graphs, to tell a story, and the reason we consider them fundamental to our What if Math Labs. Take the Tour to see more.
Art
Revolutionary Math
Cape Cod in the winter is one of those marvelous places filled with interesting shops and people waiting in the quiet winter time for the soon to come crowds. It was on one of those pretend spring is here days in February that we went to visit a dear friend on the Cape and then take a lovely drive to empty beaches, delicious lobster rolls, and of course a bookstore or two. It was on that last stop, just before the bridge, that I came upon a hidden treasure, a math textbook from 1788. The author Nicolas Pike entitled it, A New and Complete System of Arithmetic: Composed for the Use of the Citizens of the United States. Pike, proud of his brand new nation so recently created, says that it needed a book to educate its newly minted citizens in mathematics.
It is however the opinion of not a few, who are conspicuous for their knowledge in the mathematics, that the books, now in use among us, are generally deficient in illustration and application of the rules; of the truth of which, the general complaint among schoolmasters is a strong confirmation….as the United States are now an independent nation, it was judged that a system might be calculated more suitable to our meridian, than those heretofore published.
Pikes Arithmetic, Nicholas Pike, 1788, Preface.
The book follows, for the most part, the sequence and topics laid out by Leonardo of Pisa in Liber abbaci. Though it lacks pictures, it is full of contemporary problems, problems faced by farmers, shopkeepers, traders, surveyors, sailors, and even militia. It is full of such real-world problems and full of tables to help the users to calculate the answers to those problems. It was a reference book as well as a textbook. It was designed for this new country, “suitable to our meridian” including decimal currency.
Over the past 230 we have desiccated this work, taking out its focus on problem solving in the real world, both in the problems given and in the tools for solving them. I love the thought that in What if Math we are returning to Nicholas Pike’s 1788 vision, to focus school learning on the kinds of problems students will need to solve and giving them training in the tools and skills they will need to use. Yes, this was a revolutionary vision then and it is a revolutionary vision today. But it is a vision for a nation whose promise has been: to enable all of its citizens to thrive. I would love to have been able to take Nicholas Pike on our Tour. I think he would have liked it.
Art