Wednesday, December 11, 2013

Learning from History, Warren Colburn 1830, and the Implementation Challenge

More than 180 years ago Warren Colburn presented his work and ideas to the American Institute of Instruction in Boston, MA, August 1830.  It was published in the proceedings, and has been reprinted with permission, by the University of Chicago Press.  LINK

(Disclaimer: In this blog post Colburn is quoted verbatim, and as was the style at the time the gender of students or scholars is written as "he" or "him." In an effort to be 100% clear, these are Colburn's words and not mine, and there is nothing implied by me or the IBL community about scholars = male. My own opinion and the viewpoint of AIBL is of course 100% for equality in math teaching and opportunity for all groups.   I hope we can instead focus on the ideas presented, and put aside the arcane language in Colburn's address. One hundred and eighty years is a very long time.)
"By the old system the learner was presented with a rule, which told him how to perform certain operations on figures, and when they were done he would have the proper result. But no reason was given for a single step...  And when he had got through and obtained the result, he understood neither what it was nor the use of it.  Neither did he know that it was the proper result, but was obliged to rely wholly on the book, or more frequently on the teacher. As he began in the dark, so he continued; and the results of his calculations seemed to be obtained by some magical operation rather than by the inductions of reason."          
It's a very familiar point.  Through Colburn's experiences teaching math (primarily tutoring) and writing his own arithmetic text, he developed keen insights into learning mathematics.  Many of the points he made nearly two centuries ago are relevant and warrant thought and investigation by instructors today.

1. A curriculum with appropriate problems suited to the learner is necessary.  Problems should start with the easiest problems first and be logically ordered.
"…choose the easiest [problems] first, and then the next easiest, and so on.  And where one things depends on another, make them follow each other as much as possible in the order of dependence."
2. Students should be allowed to come to their own conclusions first, even if they are not wholly right.  Initial attempts are a necessary component of learning.
"The learner should never be told directly how to perform any operation in arithmetic.  Much less should he have the operation performed for him.  I know it is generally much easier for the teacher… either to solve the question for him or tell him directly how to do it…. Now by this generally no effect was produced on the scholar, except admiration of the master's skill in ciphering." 
"Secondly, when the scholar does not understand the question or proposition, he should be allowed to reason upon it in his own way, and agreeably to his own associations…. it is the best way for him at first, and he ought by no means to be interrupted in it or forced out of it."
3. Success breeds confidence.
"Nothing gives a scholar so much confidence in their own powers and stimulates them so much to use their own efforts as to allow them to pursue their own methods and to encourage them in them."
4. Understanding student thinking is a critical component of effective teaching.  Teachers should be able to trace the logic of students so as to inform their teaching.  
"…it is very important that a teacher should be able readily to trace, not only his own associations, but those of all his pupils, when he hears them recite their lessons.  When a proposition or question is made to a scholar, he ought to be able to discover at once whether the scholar understands it or not."
5. Exposition (presentations) should be a regular part of class, and as developing the ability to communicate is highly valuable.
"It is chiefly at recitations that one scholar can compare himself with another; consequently they furnish the most effectual means of promoting emulation.  They are an excellent exercise for the scholar, for forming the habit of expressing his ideas properly and readily.  The scholar will be likely to learn his lesson more thoroughly when he knows he shall be called upon to explain it."
This is enlightened work, especially given that Colburn had other non-educational interests,  and was not primarily an educator.   Moreover, Colburn's words are quite alarming for those of us working in education in 2013.  The presented ideas provide a mile markers to compare against, and indeed we have known for a long, long time about engagement and learning.  Seventy years after Colburn, John Dewey and others proposed ideas to engage students, and efforts continue to this day to update how we teach on a broad level.  Despite all this our mission is not accomplished, and classrooms with deep engagement are still in the minority.  Hence, evidence supports the notion that implementation is one of the foremost issues in education, if not the most important issue in education.

I am one of many instructors, who believes that finding new knowledge, new ways of teaching, new ways of understanding how students learn, and all that we work for in education can be used to make the world a better place.  It is clear that knowing is not enough, and we need to do a better job of informing the public, colleagues, policy makers, and students about what the main issues are and what the balance of opinion is by experts.  Teaching innovation is good and necessary, but not sufficient.  We are good at innovating in the U.S.  We are much less successful at broad implementation of our innovative ideas.  Finland, the darling of PISA and international comparisons, imports much of their teaching innovations from american research universities.  If only we could more widely implement our own ideas!

To paraphrase Bertrand Russell, are we just mote of dust floating in a small insignificant solar system, or are we what we appear to Hamlet?  Or both?  We have both the capacity to develop wonderful ideas and wonderful ways to teach them.  This is education's Hamlet moment.

The Implementation Challenge:  Can we solve the problem of implementing empirically-validated, student-centered teaching methods widely?