This was a #mathchat topic in July of 2012 that I really wanted to write about but didn't quite get around to at the time. This happened partly because I was busy juggling work and graduate school, but also because I felt a bit overwhelmed by the topic. I've learned so many things through my involvement in #mathchat that the idea of collecting them all was daunting. It also kind of bothered me that my first attempt at a response to this prompt turned into a lengthy list of tips, books, and links. This type of content makes sense on Twitter. It's actually the perfect medium for it. However, to turn this into a blog post I needed some coherency. I felt like there was a pattern to all of these things that #mathchat has taught me but I just couldn't quite put my finger on it.
A year and a half has passed since this topic came up. It's now been 6 months since the last official #mathchat. Despite this, Tweeps from all over the world continue using the hashtag to share their lesson ideas and thoughts about math education. It's inspiring. The weekly chats might have stopped, but the community continues to flourish. Looking back on how things have changed on #mathchat helped put perspective on how #mathchat changed me. I think I'm finally ready to answer this prompt.
What I learned by using #mathchat was that learning requires taking risks.
On the surface, it seems like this assertion might be obvious. Whenever we attempt something new, we run the risk of making a mistake. By making mistakes we have an opportunity to learn from them. The issue is that we go through this routine so many times that it becomes habitual. When learning becomes automatic, it's easy to lose sight of the risks and how central they are to the learning process.
Consider the act of reading a book. For many, like myself, this is the routine method of learning new information. In fact, it's so routine that the risks aren't readily apparent. That doesn't mean they aren't there. Have you ever read a book and found yourself struggling to understand the vocabulary? For me, Roger Penrose's Road to Reality is still sitting on my bookshelf, taunting me, because I can't go more than a couple pages without having to look things up elsewhere. Attempting to read a book like this entails a risk of making myself feel inadequate. It's much easier to read a book that's within one's existing realm of knowledge. By taking the risk out of reading, it becomes a recreational activity. This isn't necessarily a bad thing -- we could all use some relaxation time now and then -- but it's not until we step out of that comfort zone that the real learning begins. Have you ever read a book that made you question your own assumptions about the world? It's not often that this happens because we're naturally drawn to books that reaffirm our own beliefs. When it does happen, the impact can be quite profound. The further a book is from your existing world model the greater the risk of that model being challenged by reading it, but the potential for learning scales in proportion.
I was rather fortunate to have discovered #mathchat when I did. I had signed up for Twitter at approximately the same time I started teaching math. Anyone that's ever been a teacher knows that learning a subject and teaching that subject are two entirely different beasts. I'd been doing math for so long that most of it was automatic. It wasn't until I started teaching that I realized I had forgotten what it was like to learn math. As a result, I was struggling to see things from the perspective of my students. I needed to step out of my own comfort zone and remember what it was like to learn something new. It's through complete coincidence that my wife stumbled upon Twitter at this time and said, "Hey, I found this new website that you might find interesting".
I didn't join Twitter looking for professional development. In fact, for a while at the start I didn't even know what "PD" stood for. I joined Twitter purely out curiosity. I was never really comfortable interacting socially with new people, and it seemed that this was an opportunity for me to work on this skill. I called it "my experiment". I didn't even use my full name on Twitter for the longest time because I was afraid of "my experiment" going wrong. I started simply by looking for topics I was interested in, following people that sounded interesting, and speaking up when I felt I had something to say. One of my saved searches was "#math" and I started trying to answer questions that people were asking on Twitter. This lead to making some of my first friends on Twitter. I noticed that some of those people that regularly tweeted on #math also frequently tweeted with the hashtag #edchat. I started to observe these people would often post multiple #edchat Tweets within a short period of time and had inadvertently stumbled upon my first real time Twitter chat. Once I started participating in #edchat my network grew rapidly. From there, it was only a matter of time before I discovered #mathchat.
My social anxiety was still quite strong at this time. With each Tweet, I was afraid that I would say something stupid and wake up the next day to find that all my followers had vanished. However, #mathchat provided a welcoming atmosphere and discussion topics that were relevant to my work environment. This provided me with an opportunity to engage in discussion while mitigating some of the risks. I knew that each topic would be close to my area of expertise and the community was composed of people who were also there to learn. There was a certain comfort in seeing how people interacted on #mathchat. People would respond critically to the content of Tweets, but always treated each participant with dignity and respect. I was experiencing first hand what a real learning community could be like.
A frequent motif in these #mathchat discussions was Lev Vygotski's model of learning. With my background in psychology, I was already familiar with the concepts and vocabulary. However, #mathchat helped me link this theory with practice. I became more and more comfortable with a social perspective on learning because I was learning through my social interactions. While I had known the definition of terms like "zone of proximal development", I wasn't quite to the point where I could see the line separating what I could learn on my own and what I could learn with assistance. I had always been a self-driven learner, but in order to be successful in learning I needed to limit myself to areas that were close to my existing skills and knowledge. I needed to minimize the risks when learning on my own. Learning in a social environment was different. I needed to become comfortable taking larger risks with the reassurance that the people I was learning with would help me pick myself up when I fell.
The #mathchat discussions themselves were not without risks of their own. Colin took a risk himself by creating #mathchat. It was entirely possible that he could have set this chat up only to have no one show up to participate. Indeed, many a #mathchat started with an awkward period of silence where people seemed hesitant to make the first move. There's much lower risk in joining a discussion in progress than starting one from scratch. The risk is lower still by simply "lurking" and only reading what others have said. As time went on, there was a growing risk that #mathchat would run out of topics for discussion. This risk has since manifested itself and #mathchat has entered a state of hiatus.
I'm aware of these risks only in hindsight. At the time, I wasn't really conscious of the shift occurring in my own model of learning. What started to make me realize this change was the adoption of my two cats. This provided my another opportunity to put learning theory into practice by training them (although it's arguable that they're the ones training me instead). The smaller one, an orange tabby named Edward, responded quickly to classical and operant conditioning with cat treats. The larger one, a brown tabby named Alphonse, didn't seem to care about treats. It quickly became obvious that I was using the wrong reinforcer for him. With his larger body mass and regular feeding schedule, there was no motivation for him to consume any additional food. It's easy to forget that in the experiments that these concepts developed from, the animals involved were bordering on starvation. The risk of not eating is a powerful motivator for these animals to learn in the experimental setting. My cat Alphonse was under no such risk. He was going to be fed whether he played along with my games or not. I've since learned that Alphonse responds much better to training when there's catnip involved.
The key to successful training is very much dependent on being able to identify a suitable reinforcer. What functions as a reinforcer varies widely from subject to subject. With animal studies, survival makes for an universal reinforcer as the reward of living to procreate is (almost) always worth the risk. However, humans follow a slightly different set of rules because our survival is seldom in question. We're also unique in the animal kingdom because we can communicate and learn from others' experiences. In a typical classroom situation, the ratio between the risk and reward takes on greater significance. We're faced with such an overabundance of information about the world that we can't possibly learn it all. Instead of maximizing performance on a test, the desired outcome, a common alternative is for students to minimize the risk of disappointment. It's often much easier for a student to declare "I'm bad at math" than to go through the effort of actually trying to learn a new skill. Rather than taking the high-risk choice of studying for the test with only a moderate payoff (a grade), these students opt for a low-risk low-payoff option by simply choosing not to care about the exam. When looked at from a risk/reward perspective, maybe these students are better at math than they're willing to admit.
The solution, as I discovered through #mathchat, is to lower the risks and adjust the rewards. I've started working on making my courses more forgiving to mistakes and acknowledging them as an integral part of the learning process. I've started working on increasing the amount of social interaction I have with students and trying to be a better coach during the learning process. There's no denying that I still have much to learn as a teacher, but thanks to #mathchat I have a clearer idea of how to move forward. For me to progress as a teacher, I need to more comfortable taking risks. It's far too easy to fall into habit teaching the same class the same way, over and over. I need to do a better job of adapting to different audiences and trying new things in my classes. Fortunately, there's a never ending stream of new ideas on Twitter that I'm exposed to on a regular basis thanks to my "Personal Learning Network".
I feel it's a crucial time for me to be sharing this perspective on the role of risk in learning. There seems to be a rapidly growing gap between teachers and politicians on the direction of educational policies. There's a political culture in the US that is obsessed with assessment. Policies like Race-to-the-Top and No Child Left Behind emphasize standardized testing and value-added measures over the quality of interpersonal relations. The problem with these assessment methods is that they don't take the inherent risks of learning into consideration. Risk is notoriously difficult to measure and it doesn't fit nicely into the kinds of equations being used to distribute funding to schools.
There was recently a backlash of (Badass) teachers on Twitter using the #EvaluateThat to post stories of how our assessment methods fail to capture the impact teachers make in the lives of their students. Teachers are the ones that witness the risks faced by students up close. It's our job as teachers to identify those risks and take steps to manage them so that the student can learn in a safe environment. As the stories on #EvaluateThat show, many teachers go above and beyond expectations to help at-risk students.
While teachers struggle to reduce risks, policy makers continue to increase them through more high-stakes exams. At times it almost seems like politicians are deliberately trying to undermine teachers. Maybe what we need in education policy is a shift in the vocabulary. Lets stop worrying so much about "increasing performance outcomes" and instead focus on "decreasing risk factors". Doing so would encourage a more comprehensive approach to empowering students. For example, there's strong statistical evidence that poverty severely hinders student success. By addressing the risks outside of the classroom, we can enable students to take more risks inside the classroom.