I Really Love Maths

 Tomorrow night I'll be giving the key-note presentation at the VMLC (Vermont Math Leadership Council)  annual meeting in Randolph, Vermont. The title of the presentation is I Really Love Maths. I plan to present a sequence of examples of things that have caused me to love the subject I teach to prospective and practicing teachers in three main areas; the theories that have influenced my thinking, the people who have influenced the way I teach, and the life experiences that have caused me to develop a lifelong passion for teaching maths.
  

Perhaps the two most influential theories that I was lucky enough to encounter early in my career were Skemp's idea of instrumental (fragile) versus relational (robust) understanding, and Shulman's conceptual and procedural knowledge. Being able to look at preK-6 maths through these incredible lenses has allowed me to clearly see what matters more and what matters less, as well as the flaws of some of the traditional instructional practices we have had to endure in years past, and sadly still do in some places today.

Two of the people that have most influenced my thinking are smiling at you right now. At least Sir Ken Robinson is. I looked long and hard but could not find a picture of John Dewey smiling. Sir Ken gave me permission to be creative while Mr. Dewey impressed upon me the value of experience in the educational process. To these names I would add Jo Boaler of Standford  whose work in teacher education in math has been completely illuminating in so far as it has shone the light squarely on the need for teachers to help  children  understand the math they are learning. I would also include Vi Hart who's videos on irreverence in math class are so inspiring. And finally I would add Carol Dweck who gave us Mindset theory with the unbelievable idea that everyone can learn math if they have a Growth Mindset.

And finally my experiences working with English Learners has taught me the humility that comes with standing back  and listening to the way people from other countries do math and think mathematically. The diversity  in the ways we count and communicate mathematically are one of the hidden riches of global thinking. I also think of all the students with disabilities I have worked with some of whom think very differently in terms of the maths in their lives. Some function, and very well too, with an almost exclusively  understanding of nominal number as opposed to cardinal number while others can seemingly compute in milliseconds..

I have been lucky indeed to embrace such diversity of thought, experience and practice during the past 50 or so years.   

John Dewey; a Vermont Legend

There was a wonderful article on John Dewey in the Burlington Free Press this weekend. Dewey is a native son of Vermont and was born and raised in Burlington where he taught at the University of Vermont for some years. His greatest gifts to the field of Education were probably his steadfast beliefs that students should be taught to think for themselves and to learn through discovering the true meaning of knowledge. Labeled a progressive and a pragmatist, he wrote many books about education and was a strong advocate of education for democracy and the role of discovery learning.

He also developed theories about thinking focused on the ideas of deductive and inductive logic. In How We Think, he relates two stories about the ferries that ply Lake Champlain between Burlington and New York State 13 miles away. In one story he describes how, standing on the car deck of the ferry, he notices what looks like a crane derrick, a 20 foot pole,  jutting out from the wheelhouse at a 45 degree angle. He notices that is had no rope attached to it so it couldn't be a crane. He then notices that it has a ball on the end and is the same height as the pilot in the wheelhouse. Being a ferry, there is no pointed bow, just a flat place where the cars drive on and off. From all these observations he deduces that the pole is in fact a false bow that allows the pilot some accuracy when steering the ferry across the lake. The ferry captain can line up the ball with something on the shore. I remember standing in the identical spot on the same ferry when I first moved to Vermont and looking at the pole in the same way Dewey had done..

In the second story he describes a strange sight of sparrows flying down and landing in front of cars parked waiting to board the ferry. As soon as the birds land they disappear up inside the engines of the cars only to reappear moments later with something in their beaks. Knowing that cars have radiators at the front and that all kinds of bugs get caught in the radiators as the car is moving he deduces that the sparrows have somehow learned that there is a veritable cooked feast waiting for them in every car that shows up at the ferry dock.
I have seen sparrows doing this too at the ferry dock. I wonder what they would do with an old VW Beetle with the engine in the back and no radiator.

Dewey's ideas are alive and well in the Teacher Education Programs at St. Michael's. His ideas of "Inspired Vision" and "Executive Means" are illustrated and exemplified in senior student licensure portfolios where they share their philosophical beliefs about teaching, their inspired visions,  and the teaching skills they craft in classrooms in local area schools, their executive means.