My Story and the Making of Making Math

I’m going to start off this blog about me since I think it’s important to get it over with and lay it out there in the beginning so I can just move on to ranting about math education.   I’d like to share my personal history with Mathematics, Education, and Business which should explain my interest in blogging about these things. This is a re-post and continuation of a blog series I wrote for the O’Reilly School of Technology where I am currently employed. 

From Math hater to Math lover in an instant

I went to high school in south eastern Ohio. This area lies geographically in that region of the country called “Appalachia”. Wikipedia says this about Appalachia:

” Early 20th-century writers focused on sensationalistic aspects of the region’s culture, such as moonshining and clan feuding, and often portrayed the region’s inhabitants as uneducated…”

The community I lived in didn’t seem to place much of a premium on getting a good education. With all that moonshining and clan feuding, who has time for school? But it wasn’t just because they were drinking moonshine and clan feuding; it was more that in general the people there weren’t all that ambitious. They were generally accepting of their station in life, no matter what that may be. They were actually quite content, and as long as they had their family, friends, moonshine, and clan feuding they were happy to just sit on their porches and swap stories. In fact, highly educated people tended to be less popular and were regarded with a bit more suspicion than the more common and less educated blue collar workers that dominated the area.

Don’t get me wrong; it was a great place to grow up, but the school system I was in would not be confused with a bastion of academic prowess. Even so, and even among a student population in which only a few were intended to go to college, I managed to finish ranked a lowly 35th in a class of 80 in High School. I was mediocre student, at a mediocre school, in a mediocre region of the country.

The subject I was absolutely worst at was Math. In fact, in order to pass math, and even graduate from High School, I bet the particularly horrible Math teacher that I could take 3 whacks of a paddle to my back side in front of the class. If I won, I passed; if not, I failed. I won the bet, albeit with a lot of pain and embarrassment, but I passed Math, and I graduated from High School.

Without much else to do, I decided to give college a try. At that time, if you lived in Ohio and applied to Ohio State University, it was state law that they had to accept you. Given my high school grades, and the scores I had on the college entrance exams, that was the only hope I had to get into college. I had a rich great uncle offer to pay for it, so I off I went to college.

When I got to Ohio State, it was really like grade 13 to me. It was the same old path, but a different location. I was just going through the motions, and not doing it well. I was majoring in Geology at the time, but had always been more interested in Oceanography. However, the Math requirements intimidated me, and so I chose my major based more on the lack of math requirements than on genuine career interest (something I’ve seen all too often with college students).

Early on, I took my first math class – Algebra I. I failed it. The next term, I took it again, and somehow just managed to get a D.

The next math class I took, Algebra II, I failed. I took it again, and again got a D.

By time I finished my first year of college, and I had a .067 grade point average, and was on my way out. However, Ohio state had a program called “Freshman Forgiveness”, which allowed you to drop15 credit hours of classes that you had either failed, or had received a grade that you didn’t want to be seen on your transcripts.

By the end of my second year of college, I had used up the Freshman Forgiveness, and still had a terrible grade point average. Somehow, because of these forgiving policies at Ohio State, I was still in the game — but losing horribly.

By the beginning of my third year, I took my first calculus class. I can still remember the first day of this class like it was yesterday. The instructor was late. In fact, he was so late that the students in the class were discussing the rule for tardy instructors. No one knew the rule so we decided to stay a bit longer.

He finally arrived, and he did so magnificently. He sprinted in the room sliding up to the front desk. He was in 20′s, had black curly hair, and a full beard to match. He was disheveled, seemingly un-showered, and his clothes were completely wrinkled. Soon, someone in the class pointed out that his v-neck sweater was on backwards. He looked surprised, and took it off in order to put it on correctly. Once he got it off, it became apparent that he also had a white oxford shirt on backwards — and somehow it was buttoned-up.

Eventually, he got his clothes on correctly, and he started solving problems for the class on the chalk board. The board was filling up with chalk faster than I could write. Math symbols everywhere; it was a foreign language to me. As he was vigorously writing along, he suddenly stopped, stepped back slowly, put two fingers to his lips, and stared at the board. He was motionless and silent. The class stopped as well, put their pencils down and sat back. We were all looking at him, waiting for the next line of chalk, but he just stood there staring in uncomfortable silence for what seemed like 15 minutes. I couldn’t take the silence and suspense so I asked, “So, what’s up?” To which he said, “There is a mistake somewhere.” and he went back to staring and holding his fingers to lips.

The class got restless waiting for this guy to figure out the problem. However, he didn’t budge, he just stood there. Since I didn’t have anything better to do, and since I felt like helping him, I started looking at what he’d written. I went through each step, having to go back through several times, but to my surprise I actually found the mistake in this gigantic calculation. It was just a sign error. He had a minus sign where he should have had plus sign. Sheepishly, I pointed out what I thought the problem was. He sighed, pointed at me, thanked me, and then continued.

That term, this scene repeated itself again and again. He kept making mistakes, and I’d correct them. It got to be so that when he’d step back into his perplexed ‘there’s a mistake’ look, the class would look over at me, and wait for the answer.

That term I got an “A” in Calculus. In fact, I got the highest score in the class.

Something amazing had happened to me. I became a mathematician, that suddenly, and that fast. Without any previous knowledge of mathematics, I learned to think like a mathematician, and it suddenly all made sense to me.

I took many more Math courses, and I got many more “A”s. I felt empowered, and I felt ownership, and even decided I wanted to know what the heck Einstein was so famous for doing. So, I took every course on Relativity available, until not only did I understand it, but could use it to make simple predictions and observations.

I went on to graduate school, pursued a Ph.D. in mathematics, and did research in Applied Mathematics, namely geometric classical mechanics and control theory.

In order to pay for graduate school, I had teaching assistantships in the math department, and taught college Math courses. I discovered that if I’ve ever been really good at something, it was teaching — and I fell in love with it.

How I became a Constructionist

Because of my own “ah ha” learning experience in mathematics, I was convinced that everyone could learn math well. l if they had a passionate teacher with the communication skills to get them there. I certainly had the passion, so I set out to transform students into mathematicians.

By all the standard measurements and expectations, I became a great teacher. At least my students thought I was great;nothing feeds the ego like teaching. My night time math review sessions had become so popular that I had to hold them in the largest auditoriums on campus. One of my classes even presented me with a large engraved trophy to thank me for my teaching . They did well on exams, and they were very happy. All was well.

But despite all of this positive reinforcement, my point of view (confidence?) and self-esteem began to suffer a bit after a visit in 1993 to Moscow. I visited the mathematics department at Moscow State University, and stayed with a couple who were both professors there. They had two wonderful daughters, the younger of whom was still in high school. At one point during my stay, she asked me to help her with homework in mathematical mechanics. Of course, I was proud to help, since Mechanics was my research (specialty?). Her homework seemed to me to be rather difficult (advanced) for high school; I had a bit of trouble with it myself. Suspecting that this high level of work might be a strange exceptionin the Russian educational system, I asked her parents if she was in a school for gifted students or some other advanced learning program. They told me that, no, she was actually an average student in an average school. This confused me.?Mathematical mechanics is historically a major focus in Russian Academics, but that didn’t explain how their students could be so much more advanced than the students in the United States at this level. After a lot of probing questions, I eventually found out that all of the math exams in Russia are oral exams. Students in Russia have to be able to explain mathematical problems and their solutions out loud.

Intrigued and inspired, I came back to the states, and started giving my students oral exams after their written exams. This was a long and arduous process, because I had to schedule an hour for testing for each student. However, I discovered something that depressed the hell out of me. None of my students knew what they were talking about. Even students who got perfect scores on my written exams didn’t really understand what it was that they were doing.
It became clear that students were simply emulating calculation techniques, without understanding where those techniques came from, or how to create them themselves. Then it became clear to me why my review sessions were so popular. In those sessions, students would ask me to solve every type of problem they could find in the text book. Even though I’d have them try the problems before showing them the solution, they were really preparing a decision matrix for a matching game. If the problem was like this, then they would do this; if it was like that then they’d do that, and so on. I also realized that the problems I was asking them to do, were designed with this system in mind. It seemed that most of the calculation techniques were designed to help students pass tests, but did not illuminate the true nature of the mathematical structures .

In the American system of teaching mathematics, we are actually teaching algorithms for getting answers from synthetically designed problems,but not teaching students the art and science of mathematics. Sure, some students get through school, and become great mathematicians despite this system, but we are losing most students through attrition. Ask your friends and neighbors about their experiences with math education, and most will say they hated math in school. Others might say they were good at it, but hated word problems, which I always thought was a curious thing to say (what those people are really saying is that they were better at the matching game when the thing to match was given in a simple form).

I wanted to quit teaching. The whole thing seemed a bit hopeless. I could certainly try to change how I was doing things, but how? I didn’t know. I thought back to my own “ah ha” experience and realized that the reason it had happened was because the instructor actually didn’t show me how to solve or understand problems directly, but because I wanted to help him figure it out. I was given space and motivation to explore and figure things out for myself. I suppose I could have tried to apply that teaching technique in my class, but I realized in that particular class, I was the only one who was having that special learning experience. The rest were simply waiting on ME to explain the math. Helping just one or two students reach their potential out of fifty wasn’t very appealing to me.

After discussing this with my colleague, Lee Wayand at Ohio State, he told me he’d started working with Jerry Uhl and Bill Davis and their Calculus & Mathematica math reform project. He told me it was a completely different paradigm, where students were really learning the math, and not just learning computational tricks. I was suspicious of using technology to teach. I’d tried some Calculator driven courses that were complete failures, but Lee assured me that this was different. I talked to Bill, and after some coaching, I started teaching Calculus & Mathematica at the Ohio State University in 1993.

These courses were clearly different from their traditional counterparts. Bill asked me not to lecture to the class, but instead to participate as their coach and their peer. This was possible because the course materials were written in Mathematica software files and housed on computers in the computer lab. When I’d walk into the room, the students were already working on the material. When I left, they’d still be there, working on math. I’d never seen anything like it. Students were working, engaged, and talking about math with each other without me leading them. They’d call me over, and ask me questions, but instead of answering the questions directly, I’d ask them leading questions, and give them ideas to explore. Bill once told me that to answer a student’s question outright, is to steal from them the opportunity and thrill of discovering the solution themselves. He was right!

Mathematica is an extraordinary piece of software that is a bit like combining the text editing capabilities of Microsoft Word with the most powerful scientific calculator in the world. The language of Mathematica is, of course, very mathematical and natural, and as you learn that languauge, you are actually learning mathematics, and visa versa. In these courses, Mathematica is never taught directly, but it is learned indirectly, as a consequence of learning Mathematical concepts and combing though patterns.

Suddenly, by going through these materials, and interacting with their instructor in this new way, the students were not only learning, but gaining ownership of mathematical concepts. For the first time , they were seeing Mathematics as a science. They were looking for patterns, finding them, and explaining them. That’s what mathematics is all about. When I gave oral exams to the students in these classes, a lot of them were able to explain the concepts and structures of Calculus.

That first term of teaching Calculus & Mathematica changed my life. I became a disciple and evangelist for this new teaching paradigm, and began a quest to understand more about why it worked, and how to extend and expand this paradigm to change education.

 History of Computers in Education at the University of Illinois

First, let me give you a short synopsis of the world of technology in education. The University of Illinois at Urbana-Champaign (UIUC) has a long history of using technology as an instructional aid. As early as 1960, U of I began experimenting with computers in education in a project called Plato. Many of today’s social networking technologies have roots than can be traced to the Plato Project. In fact, this year marked the 50th anniversary of the Plato Project. At UIUC, Plato was expanded upon and used throughout the 1970s and 1980s. It was eventually commercialized by the Control Data Corporation and was in use through 2009.

Meanwhile, in the 1980s, a successor to Plato called novaNET was being developed at the UIUC. It was a satellite-based system that allowed automated question generation. novaNET was eventually bought by Pearson and is still in use today.

In the early 1990s, the University of Illinois developed Mosaic, the world’s first web browser. Naturally, Mallard, the world’s first web based Learning Management System (LMS), was developed at the U of I as well, in its physics department.

Valuable lessons were learned from these experiments with computers in education at UIUC, mostly with negative results. It turns out that simply using technology does not guarantee improved learning outcomes. In hindsight, it’s clear that these technologies weren’t offering any real change in pedagogy, because the technology was just being applied to traditional teaching techniques. They were being used as another way to deliver information and quizzes. They didn’t change the learning behavior of students. They didn’t change the roles and relationships between the instructors and students.

In other words, they didn’t put the computer to work as a mechanism of student exploration with instructor coaching.

This remains the biggest problem with instructional designs that use the computer and internet today. Most educational technologies still simply replicate the same old teaching and learning patterns onto a new medium–and it doesn’t work.

But we can fix this problem. And I’m confident that history will eventually show that the most significant thing ever to happen in Educational Technology since the invention of the printing press, happened at the University of Illinois, Department of Mathematics, in 1989. Several events coincided perfectly in the late 1980s in Champaign, Illinois that led to creation of the Calculus&Mathematica Project. First, in 1987 Stephen Wolfram, who was then part of the mathematics department at the U of I, launched the Computer Algebra System (CAS) called Mathematica. This is a powerful program that supports mathematical editing, computation, and symbolic mathematics. Second, in 1988, the National Science Foundation (NSF) began offering grants to institutions for the purpose of Calculus reform. Third, Jerry Uhl and Horacio Porta, both of the University of Illinois, and Bill Davis of The Ohio State University, wondered collectively whether the new Mathematica software could be used to teach Calculus. (Jerry had been disappointed by past efforts to use the computer in education, and despised Plato and novaNet.)

After receiving a grant from NSF, the three of them created calculus lessons in Mathematica files called notebooks. They also built computer labs specifically designed for the project, where students could work on these lessons using Mathematica. There wasn’t a separate textbook. The content was integrated into Mathematica by virtue of being written in Mathematica notebooks. This turned out to be very important to the effectiveness of the paradigm.

The first Calculus&Mathematica courses at the University of Illinois were offered in 1989. Almost immediately, something unexpected happened to the structure of the courses. At first, the courses were taught during three lectures and two lab hours per week. Jerry noticed that his once popular lectures had barely any students present attending them now. He asked some students who happened to be in the lecture one day where the other students were; they took him to the computer lab, where the rest of the students were all working on their math lessons using Mathematica. Jerry, being very adaptable and open minded, decided right then that he would no longer lecture to teach mathematics (read Jerry’s Why (and how) I teach without long lectures).

(Aside: Please don’t get the impression that using this technology is the complete recipe for success. It’s not. The instructor is STILL the most important part of these courses. What changes is their responsibility and relationship to students. This is very important to understand and I will be discussing it in more detail in future posts.)

A year after they began teaching using Calculus&Mathematica on campus at the U of I, they started Netmath, a distance-education project that used the Calculus&Mathematica model to teach mathematics to high school students who lived in remote rural areas. Both of these projects are still alive today which speaks to the effectiveness of the methodology, as well as the passion of the people implementing the programs.

Other NSF funded reform projects haven’t done so well. Between 1988 and 1994, the NSF supported some 127 Calculus Reform projects. Of those projects the only ones that I know are still being used today are the Calculus&Mathematica(C&M) and Netmath projects at the University of Illinois.

The creation of Useractive, Inc.

As I mentioned in the previous blogs, I became passionate about this new paradigm, and was doing everything I could to spread the gospel of this new approach in math education. I went to conferences, and I met with teachers, professors, and administrators. But by 1996, I realized that this project wasn’t going to spread across the land to other schools and change education like I hoped. There were too many barriers, some of which were inherent in the technology, and some of which had to do with the structure of educational institutions themselves (I wouldn’t fully understand this until years later).

I did realize that if there wasn’t some sort of business supporting this paradigm and keeping it going, that it would eventually wither and die in the University system. There is no bureaucracy or budget within university math departments to start such a program, let alone maintain it. C&M only got off the ground at the U of I because the project received elusive NSF funding and benefited from the heroic work of its founders. I knew that when Jerry Uhl and Bill Davis retired, there wouldn’t be any of that kind of support left in their respective departments to maintain and grow these projects. And in fact, these courses ended at Ohio State shortly after Bill retired because no faculty remained to take the reigns.

In 1994, while working on the C&M project, I became interested in the internet, and specifically the new “World Wide Web”. At one point I picked up a copy of Learning Perl by O’Reilly, because I wanted to use Perl to build some CGI programs to make my web pages more functional. I became an immediate fan and follower of O’Reilly books. Randall Schwartz wrote a lot like Jerry Uhl and Bill Davis. “Learning Perl” was very conversational, funny, and used simple, well thought out examples to explain concepts.

Because I was in a university math department, I had a Unix account with Perl installed and I had friends who showed me how to access and use Perl. I wondered how people who didn’t have these tools and friends available, would learn Perl. So I set out to make a web-based tutorial that combined C&M’s technique of integrating content with software, and Randall Schwartz’s approach to Perl. I created a website called the “Web Workshop.” Within few months the site had 20,000 users building websites that used CGI on the server to create form-based interactive websites.

The Web Workshop was completely web-based, but still allowed people to program in Perl and test their CGI programs all from one page. The content and programming tools were located on a single web page. The content was preloaded in one textarea, and directly below it was the textarea and form to write Perl code, which was saved to the server to run. Output was displayed on the web as well. This way of combining content and tools made it possible to mimic the kind of interaction that happened in C&M. But still, something was missing. The site needed to an instructor. I was getting a lot of questions from students, so I designed a web-based feedback mechanism that I could use to test peoples programs and give them feedback, quickly. Because of the way it was designed, I could give feedback to hundreds of people a day all in a couple of hours.

In 1996, I met and fell in love with Tricia Mills who was a young, but very competent programmer and a manager in the C&M project. I moved to Champaign, got a job teaching at the University, and Trish and I got married. It wasn’t long before Trish had improved the work I’d done on the Web Workshop by making a more functional and flexible web based IDE called CodeRunner. In 1997, we started Useractive, Inc. a business dedicated to building and delivering online learning systems with the characteristics of both the C&M courses at UIUC and the Web Workshop courses I’d built.

We partnered with the University of Illinois to offer courses through their Department of Continuing Education, which provided us with enough income and momentum to add more partners and employees (including Kerry Butson, Trent Johnson, and Josh Nutzman). Because we were small and had limited finances, we put most of our efforts into building systems that focused on reducing the customer service overhead associated with getting students to work making things and then giving them instructional feedback. We were also forced to make teaching and administering our courses as efficient and effective as possible, without diminishing the teacher/student relationship. In other words, we had higher production costs than other online course producers, but much lower ongoing costs for the level of educational outcome we were achieving.

In early 2000, we made the decision to accept an investment from a local investment group and the state of Illinois.

Taking investment money turned out to be one the worst and best things we ever did. On the lousy side, the money and the pressure from the investment group compelled us to pursue many lines of business which led us down many dead end paths, which wasted a lot of time and money. On the positive end, by exploring those paths and dead ends, we learned a whole lot about the landscape of education. By trial and many errors, like a blind person might walk around in a new room until the entire room is mapped out and understood forever, we developed a clear sense of where we were.

We see a lot of people stepping into the business of education these days with the same kind of misconceptions we once had. They are making the same kinds of mistakes we did. Whenever I’m given the chance, I try to warn those people, but like me ten years ago, people with misconceptions about education tend to be passionate about their beliefs. I’ve decided that the only way to purge the misconceptions about education is to make mistakes, hopefully survive them, and move on.

I won’t describe the business aspects of the education market in this post; it would take us far afield of what I hope to accomplish with this particular series of posts. I do intend to discuss that topic fully in some future posts, because it’s important for anyone considering the profession of education to take the practical elements into account. But the business of education is a remarkably complex and subtle topic. Education is actually a myriad of markets, each with different set of producers, decision makers, end users, and purchasers. Part of the reason education has been so stagnant and resistant to change is because of the way in which these market forces dampen innovation. I will say for now, that the only hope for change in education is to combine teaching and learning innovation with a solid business plan that not only takes these market forces into account, but uses them as tools that require change. Change in education will only happen when economics and demand force it to do so.

Joining O’Reilly and the creation of the O’Reilly School of Technology

Over the years, I had worked with many different publishing companies. Those experiences completely soured me on those organizations. They were all backwards, traditional thinking, and void of any innovative spirit.

However, somehow I knew that O’Reilly was different. Like most fans of O’Reilly, I became a loyal fan after reading that first O’Reilly book. I followed O’Reilly’s story and movements over the years and saw how open and willing they were to think outside of the publishing box.

Since we were in the business of teaching people programming skills, and since O’Reilly is the most revered computer book publisher in the world, I knew a partnership of some kind could be constructive. On a lark, I sent Tim O’Reilly and Dale Dougherty an email. I was thrilled to learn that they were receptive to a discussion. It turned out that we had something in common; we all wanted to build products focused on the learner. It wasn’t long before we worked together to create an O’Reilly branded product called the O’Reilly Learning Lab. Eventually this O’Reilly-branded channel dominated our business.

Because of my accumulated experience, I knew that creating a school was key to achieving my ambition of changing education. I also knew that a school would need a strong brand. Students seeking education, seek to identify a school’s brand first. What better brand than O’Reilly to link to a school? O’Reilly already seemed to fuse an academic integrity to their products and their business.

In 2005, O’Reilly purchased Useractive. A year and half later we launched the O’Reilly School of Technology. We’ve grown slowly and carefully, making sure that we continue to build courses using the paradigm and spirit of those first courses in 1989. Web and internet technologies have evolved with giant steps recently and we are continuously building platforms that utilize these developments as fully as possible to reduce the students overhead of getting tools together to experiment and build things, and to make asynchronous instructor feedback as quick and meaningful as possible. (It turns out that synchronous feedback online is full of potholes that actually reduce educational value while increasing cost).

This historical perspective was the hardest for me to write (which may also account for some of the delay), and probably the least interesting to the reader (no Russian intrigue, no wacky professor descriptions, and a whole lot about early mistakes and failure!), but it’s the only way to get a complete perspective of our experience and motivations.

In next and final section of this blog post,  my ambition for Math education come full circle!

The Coming Release of Make: Mathematics

Based on the success and lessons learned through my experience with Useractive and the O’Reilly School of Technology,  I revisited the issues with the Calculus&Mathematica and Netmath programs which are still going strong at the University of Illinois.  Despite the enormous qualitative success of these programs, they haven’t been widely adopted at other universities and schools.   The problem  is that as currently delivered,  it takes a heroic effort to adopt and run these courses.    Instructors who adopt this system must insure that students have access to Mathematica, they must purchase the content, and then they have to get their administrators to set up some kind of Learning Management System (LMS) to manage hand-in and hand-back of Mathematica notebooks.  Even if by chance they manage to put these disparate resources together, the teaching of these course materials still take the management of FILES being traded between 40-50 students and an instructor at least once a week.   To understand what that’s like, imagine if you had50 students  sending you Excel documents that you have to save, open, grade, save again, and then manage to get back to the right person each time.  It is simply too much work and too confusing to accomplish on a regular basis.

At the O’Reilly School of Technology, we have made all of our systems web based distributed systems with extremely efficient mechanisms for hand-in and hand-back. These mechanisms can only be made that efficient and effective because they are distributed on the web from a central server.  I have thought for over a decade that if we could get a high fidelity web based version of Mathematica from a central server, that we could  mash-up these Mathematica based courses with a custom LMS, and create a system that was easy to adopt and manage for both instructors and students. We could make these courses more effective, more efficient, and more extensible AND enable a community of like minded instructors who can build and share even more content and ideas.

So about three years ago,  O’Reilly bought the Calculus&Mathematica course materials from MathEveryWhere, inc. ( Jerry Uhl and Bill Davis’s company).  I secured special permission and a special license to build a CSS/Javascript front-end to Mathematica and distribute it from a server on a per user basis.  Over the past three years we’ve been building the tools and combining our unique learning management techniques to produce a system we call Make: Mathematics.   The instructional design concept that  combines from the ground up  a development tool like Mathematica,  learning content, and an LMS embedded together is called  Maker Cube. I will describe in more detail the value of Maker Cubes and how to design them in a future post. Suffice to say for now that it’s environment that promotes LEARNING BY MAKING and provides all the mechanisms to flip the traditional classroom so that the instructor becomes a coach and the students become makers and explorers, which is exactly what is needed in Mathematics Education today.

We will be going through the final beta test of this new system at the University of Illinois this fall semester. We expect to be completely open for business in January of 2012. The system will allow instructors and schools to self adopt complete courses and choose parameters normally associated with courses  like course names, course numbers, due dates, teaching assistants, and more.  Instructors will also be able to add their own content and lessons and share them with other instructors.  There will be Mathematica enabled forums not only for students but for instructors as well to promote community support and sharing.

I expect this new system to attract teachers interested in trying something new but very much proven to give students a new and fresh experience with mathematics. It’s my hope that together we can all change Mathematics Education and point it in a direction that it’s needed to go for the past 20 years.  I can’t wait!!