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.