In the documentary “Most Likely to Succeed,” which was screened to Unquowa teachers at the end of October, education author and speaker Sir Ken Robinson used a metaphor that I truly think will stick with me for the rest of my life, as it beautifully captures the overlap of my two passions: he compared an effective teacher to a farmer. “Every farmer and gardener knows that you cannot make a plant grow;…the plant grows itself. What [the farmer does] is provide[s] the conditions for growth. Good famers know what those conditions are, and bad ones don’t.” I find this powerful. What are the conditions that allow for student growth? How do we recognize these systems and implement them in our classrooms?
I have spent much of my time thus far in the PEL program contemplating progressive math education. I have seen much inspiring work in teaching science, humanities, and the arts—hands-on, student-centered learning, brought to life by the careful design of teachers and the genuine interest and drive of the students. Yet, I have seen very little of this sort of work being done in math education—that is, I am not sure the conditions that allow for student growth in math are well understood, and if they are, something is preventing those conditions from being set in many of our classrooms.
In my contemplating, I came across a paper written by Paul Lockhart, a former research mathematician turned private school math teacher, titled “A Mathematicians Lament”* (2009). I strongly recommend reading at least the first five pages, but I’d like to pull from it yet another powerful metaphor from his opening pages that, as a singer and songwriter, rings true to me.
Lockhart imagines that a musician wakes from a terrible nightmare, in which music education has been reduced to the study of the “curious black dots and lines” that state officials decide “must constitute the ‘language of music,’ and which “…students [must] become fluent in…if they are to attain any degree of musical competence.” The thought of students singing songs or playing instruments without this background is considered “ludicrous,” and “[p]laying and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.”
The musician wakes up, relieved, and says to himself, “Of course!…No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression.”
Lockhart then goes on to argue (or lament, if you will) that this is precisely what has been done to the art of mathematics in our schools. About the current system of math education, he goes on to say that “[e]veryone knows that something is wrong. The politicians say, ‘we need higher standards.’ The schools say, ‘we need more money and equipment.’ Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, ‘math class is stupid and boring,’ and they are right.”
I know that many teachers, parents, and students can relate to feeling at least bored, if not anxious, confused, and overwhelmed by math at some point in their lives. As for those students who enjoy and succeed at math under direct instruction (though they are certainly not the majority), many of them will be shocked as they progress in math and find that the tools they were taught in their middle and high school classrooms are useless in college classrooms and beyond. I am speaking from experience.
My argument is that this overwhelming aversion to math is the result of a poor set of conditions in math classrooms across the Western world. This is certainly not to say that everyone will all of a sudden love math. But, in relying heavily on direct instruction, math classrooms rob students of the chance to experience the true pleasure of mathematics: exploring shapes and numbers, finding patterns, asking why those patterns occur, and using logic and creativity to explain them convincingly and beautifully. I believe that this approaches the sort of conditions for a math classroom that will result in real growth for our students.
This topic inevitably raises the question of curriculum, but Lockhart argues that, if kids end up forgetting the stuff anyway, then what does it matter? Furthermore, I would argue that much of that content would likely come up anyway if kids were presented with open problems, and discover all of a sudden that it’d be really helpful to know how to calculate the measures of the angles of a triangle.
As educators, then, we are presented with the challenge to step back, let go of the direct instruction-based conditions that are familiar to us, and to ask how we might go about creating a different set of conditions–ones that will allow student to grow themselves. To be sure, this will be challenging, as many of us have never seen those conditions ourselves, and may not have any clue what they look like or where to start. Lockhart suggests starting with problems like the following.
How much of the box does the triangle take up?
*Also see these videos and other works by Jo Boaler, Professor of Mathematics Education at Stanford.
ProgressiveEducationLab 