A Response To Brewer & Daane

After reading the Brewer and Daane texts, I find myself somewhat torn. On one hand, I know from personal experience that learning from my mistakes and failings has yielded insights and valuable knowledge (often as much about myself as about technique, that is, how to do something.) However, the formation of the knowledge gained from these experiences has rarely, if ever, occurred within an educational vacuum. That is, that often, my knowledge gained has often been as a result of the informed opinion of a mentor, friend or teacher, rather than a sort of ex nihilo creation of knowledge.

Brewer and Daane's observation of the math teachers who consider themselves to be Constructivists, while yielding some insights about how this school can be applied to mathematics, is still a very small sample and anecdotal at best in my opinion. The kernel of truth at the heart of Constructivist theory is that the 'error' in a 'trial and error' model can create conditions where more knowledge may be gained than through a series of effortless successes. In my own experience, the more spectacular my failing has been, the more knowledge I have gained. Yet, if it were not for the guidance of a mentor with great experience to guide and help me see the value in the experience, it would have amounted to nothing more than another painful failure.

A case in point: During my first year of teaching, many years ago, I was assigned as the teacher and editor of the student newspaper. The paper had been in abysmal shape prior to my arrival; issues were released rarely, if ever, the issues released were filled with inaccurate stories of dubious journalistic value, even from a learning perspective.

Upon taking the helm I spent 3 weeks with the students at the beginning of the year going over proper journalistic writing style, marketing, editing, photographic style, etc., etc. I appointed students in positions of leadership and off we went for the rest of the year. It was a spectacular year, we won 3 major awards for the paper that year. All the credit for these strides belonged to the students I had appointed as editors, in my opinion. I merely had final authority over what we produced.

The next year, however, was a nearly unmitigated disaster. Having lost much of my key staff, I re-trained and re-appointed students in editorial roles. The really fatal blow, however, was that, due to our success the previous year, the class was over-subscribed and, where I had set a ceiling of 18 students, I had 25. Just too many people for the amount of work we could produce. As a class and as a group, we struggled desperately, rarely turning out issues. The crisis came to a head when I had to relieve several of my editors over misconduct regarding distributing an issue of the paper that I had said was unacceptable for publication. The students involved were the few remaining bright lights from my 'championship year.'

I still remember sitting in the Headmaster's office following the dismissal of these students from the paper, for many of them, this had been their raison-d'etre, and I felt terrible about how everything had played out. The Head, who to this day is a good friend and mentor, sat down across from me after the students had left and said to me: "Jack, you have to know when to ask for help. You need to know when you are getting in over your head and you just can't go it alone." Coming at another moment, from another person, I would never have been able to hear these words as the kindness and hope for my learning that they were meant as. It was by accompanying me in a moment that looked like failure that was a watershed of self-insight, growth and learning. If that wisdom-figure had not been there to shepherd me through it, that moment may well have turned in to one of scarring defeat and belittlement, rather than one that made me a better teacher.

This is an extreme example and one far-removed from the maths classroom. And yet, is it not possible, on a smaller scale, to feel these sorts of defeats even on something more mundane such as a maths problem? Left to the Constructivist device of forging and hanging my own meaning on my experience with the paper, I believe I would have turned it in to an experience of self-flagellation and excoriation that may well have driven me from teaching altogether. So ultimately while we appropriate and possess knowledge for ourselves and seek to understand the meaning of our experience on our own, it is often in the act of being accompanied in that knowledge by someone, ideally someone who cares about us as a person and desires to see us grow, that true and lasting learning can occur.

This is ultimately my critique of Constructivist theory, that we need to be allowed the freedom to make our own mistakes but we need be in an environment of educational relationship where we are safe to make those mistakes accompanied by people who care for us and will not allow those mistakes to be catastrophic to us as persons.