Introducing O’Reilly School of Technology’s new series of math courses delivered through Making Math. Our approach signals a groundbreaking contribution to the evolution of online math education.
A wise math professor once said, “…the problem with introductory lectures is that they are full of words that have not yet taken on meaning and full of answers to questions not yet asked by the students.” That math professor was my mentor, Jerry Uhl, who launched my career in online teaching over twenty years ago.
Back in the early 90s, there was a movement by university professors to reform calculus to meet the needs of the 20th century. From there, new and innovative programs were born. Mathematicians performed exciting experiments in integrating e-technologies such as graphing calculators and computer algebra systems into courses. Most of the programs seemed to diverge from the traditional plug-and-chug, drill, and practice mode that was ingrained in the math education machine, which was a great stride, but over time many of them, through publisher-driven revisions, eventually devolved back into what looked much like the same calculus that has been taught since the 1800s. Since math departments generally choose calculus books by committee, there are always those committee members who are resistant to change. Publishers drive the content that is included in mathematics textbooks, most likely to keep the content standard between universities and to optimize sales.
Probably the most radical of the calculus reform movement texts is the Mathematica-based calculus text, Calculus&Mathematica, written by Bill Davis, Horacio Porta, and Jerry Uhl. This project introduced one of the first “flipped classrooms” for teaching math. Through experimentation with hundreds of students at University of Illinois, the authors found out that students performed better if they engaged in the material first and attended a discussion section with their instructor afterward. Students would go into a computer lab to engage with carefully designed problems that encouraged them to experiment until they learned the concepts. These lab times were filled with a lot of student interaction with the material, with each other, and with their instructor. The authors of “Calculus&Mathematica” realized that students were fully engaged and would go into flow while engaged in their courses.
The main premise of these courses is to define by example and then delve into details. This is a complete flip from traditional education that generally provides definition of a problem, statement of theorems, proof of the theorems, then, once the student has learned all the theory, they work on practical problems. Not only is this backward from how math research is done, it is also backward from how people learn. Ralph Boas in his article Can we make mathematics intelligible? (American Mathematical Monthly 88 (1981)) put it best:
Suppose that you want to each the “cat” concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractable claws, a distinctive sonic output, etc.? I’ll bet not. You probably show the kid a lot of different cats, saying “kitty” each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience.
Paul Lockhart makes a similar point in his famous rant on the state of mathematics education. Allow me to offer an analogy of his general idea. Imagine if music were taught like mathematics. We would start by teaching notes on paper without sound or instruments and only after students mastered music theory would they be able to listen to music, touch an instrument, or try to create music. To me this sounds absurd.
Learning requires getting your hands on real tools and practice. Once it became apparent how well such courses were working at the University of Illinois, the authors and some visiting high school teachers decided to see if they could be as effective in online learning. Under the direction of Jerry Uhl, talented undergraduates at University of Illinois created tools to facilitate their proven approach to learning in the classroom and take it online. Twenty years ago, five years after the first Mathematica-based calculus course was offered at the university, I was able to take these materials to teach calculus to rural high school students in the state of Illinois, and build a program that is now offered to students all over the world. That successful program (NetMath) is still going strong today.
We are currently poised to make the next groundbreaking contribution to the evolution of online math education, delivered through Making Math.
The O’Reilly School of Technology is proud to announce our brand new series of online, hands-on math courses. We have improved and simplified the delivery of this still-innovative math curriculum. The courses are taught within a proprietary web-based learning platform, just like other O’Reilly School of Technology courses. As students progress through assignments, they are invited to experiment with code, graphics, symbolics, and numeric calculations until they fully understand the ideas being presented to them. As they work through assigned problems, students are asked to explain their thought processes and demonstrate to their instructor that they truly understand the concepts they are asked to explore. The instructor will grade each student submission and return guidance and feedback. Students continue to work at a problem and resubmit their results until they’ve gotten it right. Once the student has completed his or her course, they can be sure that they have really learned all of the concepts.
It has been an immense undertaking to get these courses prepared for release. It’s truly a thrill for me personally to have helped bring this spark of a beautiful idea from all those years ago, to fruition today.
With so many data-driven careers out there, today more than ever, it is important to have a strong understanding of key mathematical concepts. Our courses leave out the mindless symbolic exercises typically found in other math courses. Instead, we provide students with a rich blend of problems involving data sets, plotting, and real-world applications. Our software handles the tedious symbolics, leaving you free to focus on learning how to apply higher math in real-world situations. If you need a refresher course to reinforce your math skills, or you want to elevate and expand your math skills, these courses are for you. You’ll have the chance to get creative with your math–O’Reilly School of Technology courses will engage both your left and right brain!
In addition to our new math courses, we are thrilled that Faisal Whelpley is with us to kick off the program. He will serve as your mentor and instructor in O’Reilly School of Technology math courses. Faisal was a student in my courses at University of Illinois. Once he completed his graduate degree in Applied Mathematics, he went on to work at Wolfram Research (the makers of Mathematica) until we brought him to the O’Reilly School of Technology a little over a year ago. Like so many before him, Faisal loves the Mathematica-based math courses that we offer and I’m sure you will too!