It takes 43 gallons of maple sap to produce one gallon of syrup in the sugaring-off process*.  In all of the education news I see, a small fraction has something compelling, or at least challenging, to say about learning and teaching mathematics.  This blog is my attempt to keep track of the sweet stuff — and maybe some of the steam — as well as some of my responses.  I don’t claim to be exhaustive, and I will stray off-topic sometimes.  Your contributions are welcome (as long as you’re willing to identify yourself).

How do people learn mathematics?  What does effective math teaching look like?  It fascinates me that we have only partial answers to these questions, and that what is known is not widely known.  I’m interested in math learning and teaching at all levels.  I’ve been teaching at the college level since I was a peer tutor, and as a full-time instructor since 1983.  More recently, I have been working with K-8 teachers in the Vermont Mathematics Initiative (VMI) professional development program.  Several of my former Middlebury College students, I’m happy to say, are now mathematics teachers.

In my own teaching, I’ve been moving toward an active learning model wherever possible.  I’ve largely abandoned the lecture format in Abstract Algebra, in favor of small-group work on carefully constructed worksheets.  (Thanks to Bill Barker of Bowdoin College, whose presentation in 1992 gave me the courage to try this.)  In Number Theory, I now use Number Theory Through Inquiry, which requires students to provide most of the proofs; I have mine work together to produce a solutions manual. I’m working with colleagues at Middlebury to redesign our calculus curriculum in light of consequences of the growth in the AP Calculus program.

My not-so-secret hope is to foster more communication among mathematics instructors at all levels.  Having  gotten to know school teachers at VMI in Vermont and in Cincinnati, and having spent time in school classrooms as a volunteer, guest speaker, observer, and mentor to student teachers, I now realize how little I knew at the start of my career about the challenges of teaching elementary and secondary school math.  At the same time, there is plenty that we all have in common, which I intend to explore here.

*About the photos above:  I’ve ridden my bike past George Crane’s sugar house on River Road in New Haven (VT) dozens of times, always intending to stop in sometime when he was boiling.  I finally did this spring, and he was happy to show me around.  From left to right:  the sugar house, with wood smoke coming out of the metal smokestack and steam escaping from under the small roof; the boiler itself; syrup coming out of the tap; the grader (at my house we prefer the darker Grade B); and finally taps from various points in history, from the indigenous American wooden version on the left, through pewter and steel and finally plastic in the middle column.  On the right is an old mercury sap thermometer.

More photos:  The fire box, steam rising out of the roof, the perfect sugar maple (according to George), George’s horse.

The fire box under the steamerSteam rising out of the roofThe perfect sugar maple, according to George  George's horse


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