Founds this entertaining and well-written
essay by Peter Taylor via my twitter feed recently. I first want to say that I agree almost entirely with what Peter Taylor has to say, especially the call for doing more "artistic" math and letting go of doing it all for the students. It's a good read and I recommend it.
There are two points in Peter Taylor's essay, however, that I find incomplete, which ultimately affects how we go about transforming our educational system. I'd like to expand on those here and encourage others to think about these two points further.
Is teaching = art? It's been debated, but in my opinion the answer is no. Effective teaching has aspects of art (more artisan like) that require creativity, but teaching is teaching. It is its own thing, and making analogies to other disciplines can help us make sense of it, but taken too far diminishes the unique activities and mindset required in the teaching profession. While teaching is a creative endeavor, it also requires mentoring, organization, managing young learners, learning outcomes, learning goals, assessment, etc.
Style matters to an extent in teaching, but learning outcomes matter more. Much more. I can't just teach my style and not think about the impact on my students. I'm not saying Peter Taylor says this. He doesn't. But that's the way "teaching is art" gets interpreted by some people. Artists have a freedom of expression and freedom of intention. Their work can be interpreted in many ways by viewers, who see things through their own lenses and experiences. Teaching on the other hand is very intentional work with real outcomes that matter to young people.
Math is beautiful to mathematicians, but math is not art, just because it is beautiful. Yes it requires similar kinds of dedication, creativity, and expressing our ideas in clever ways. But that doesn't make math an art form, unless we really relax the definition of art.
Teaching $\neq$ art.
Now this all sounds like academic banter. I bring this issue up, because I think it matters in the real world. The danger in thinking that teaching is art is that some people mistakenly take that to mean it's primarily about personal teaching style, which can disconnect the act of teaching from learning.
Teaching as a profession is more akin to medical practice. Medicine uses science and problem solving in creative ways with the goal of improving health. Likewise, teaching can be studied, it relies on knowledge of the academic disciplines, with the goal of improving learning and thinking. We can study teaching, find better ways to teach through scientific research, and so on. It's better to then to think of teaching as a unique profession.
Teaching is also fundamentally a system and a cultural activity, which brings us to the next point regarding curricula and reform. Many reformers in the past have been tempted by the Sirens of "Reform = Curriculum Change." Many reform efforts have crashed on the rocks of model courses and innovative curricula as complete solutions to reform. I emphasize that good curricula is absolutely necessary for authentic reform. Updated curricula alone, however, is not sufficient. If all it took was good curricula to make our teaching system change, then reformed would have occurred already decades ago. So why is curricula insufficient?
Math classes have their own distinct culture and history. When students and teachers walk into math class, there is an expectation of what is going to happen and what math is. The teacher shows. Students mimic. Students practice quietly to get the same answer as the teacher in the same way as the teacher. Then it's on to the next topic. That's the standard culture, where the assumptions for our (K-12) system have roots back in the industrial revolution, when the focus was on learning algorithms and facts for the factory workers, and a few elite would rise up to run the empire (by attending college). The challenge is to shift this culture to a new model, and that has been a challenge that has resisted change for centuries. The entire culture of teaching and learning that has to be shifted, and that is why changing curricula is insufficient. Necessary, yes. But insufficient.
What we somehow need to figure out is to change our teaching culture and teaching system. It's a big, complex problem, where the core subproblem is implementation of active, student-centered teaching on a broad scale.
Do we have full answers to the big problem? No, not yet.
Can we do this? Yes. But my guess is that it's going to take creative problem solving, coordinated efforts by large, organized groups of people, and about a generation of time. Hopefully we can bet on exponential growth, and see changes sooner.
I have had the fortune of seeing Picasso's Guernica in person that Peter Taylor mentions. It's absolutely a great work of art with meaning and power that transcends time and culture. All subjects should inspire people to equivalent stature. Picasso once said that all children artists, and that the problem is to remain an artist when one grows up. Likewise I believe all children are mathematicians. The problem is to remain a mathematician when one grows up!
Upward and onward!
