The End Is Nigh

So, I was planning to retire at the end of this academic year but a bit of a serious heart attack got in the way just before the end of last year and I'm forced to take medical leave this semester. I had planned to really enjoy the last semester of my working life but sometimes things just don't work out the way we want them to; just  like some maths problems I have encountered over the years. No matter what you do, they seem to defy resolution. And so it is with my last semester. I was to have eased into retirement tidying up all the loose ends, making  sure my courses were complete and ready for my replacement to take over and make them hers or his.

The remarkable thing about teaching, something maybe only teachers know and understand, is that the courses one develops and teaches become incredibly, unbelievably, and almost inexplicably personal. The three maths education  courses I have taught in the Education Department at St. Mike's for the last several years are each unique and exclusively my own creations. Yes, of course there are curriculum standards and teaching standards that have to be addressed but my courses are my personal interpretations of those standards. I use the philosophical theories that I have experienced and developed over the past forty something years to operationalize those standards for my students. I use the experiences I have had teaching maths to children to illustrate and exemplify those theories and ideas with inspiring stories.

Each course I teach is characterized by an emotional set regarding the content I teach. I choose to focus more on those things that I truly believe work and cause my students to think. I minimize the time I spend discussing and exploring things that I know create negative feelings or are just "tricks of the trade" so to speak. I believe that to teach maths one must intellectualize the process, base ones practices on well reasoned theory or, as John Dewey said, we must use our "executive means" to get as close as we can to our "inspired vision". One must listen to children speaking mathematically and get to know what they think mathematically. One must know, understand, and love the maths intimately. My students were always actively involved in their learning by doing, talking, thinking and reflecting.

I cannot believe how difficult this is;quitting cold turkey, the sense of being shut out, stopping teaching, not meeting my students each week, not reading papers, not standing in front of the class, not telling stories, not conferencing  with students about their dreams and aspirations, not talking with colleagues, not helping students over their maths anxiety, not lighting up students' eyes about the joys and wonders of learning and teaching mathematics.

I hope there's a way I can continue to be a part of the maths education community and make a positive contribution in some way.

Teaching Teachers to Teach Math

There's an old saying that goes "Those who can, do,  those who can't, teach, and those who can't teach, teach teachers. This is patently untrue since most teachers can do, and most teacher teachers have reached that position by becoming good practicing teachers and then choosing to get into teacher education because they don't want to get into educational administration. At least that's what I did.

One of the uphill battles I have faced most of my professional career is the oft-spoken sentiment that really anyone can teach elementary school math since it is so elementary and the math cannot possibly be that  difficult. Perhaps this is the primary reason why the US has never truly embraced reform in math education. Perhaps this is a more plausible reason than the oft blamed "new math" of the seventies as to why there is constantly such a strident call for "back to basics" math education. Sometimes my professional life seems like one of failure and futility!

The unbelievably sad thing is that we now know so much about how children and students of all ages learn math much of which is, sadly, not applied in schools or in classrooms where children need it the most. We now know that learning to count, for example, is an extremely complex activity in which children pass through several stages using different forms of number before, if they are lucky, they have developed a secure sense of numeracy by the end of first grade. It takes a skilled, knowledgeable teacher to provide students with activities, guidance and practice with this pedagogical content knowledge. It also takes a skilled, knowledgeable teacher educator to teach teachers the many diverse aspects of teaching elementary school math. For example, do you realize that when you count ,say five objects, with a young child, your voice goes down automatically when you say the number "five" while it goes up with 1,2,3 and 4. If you know this is how we develop the sense of cardinality in children you are a much better parent or teacher than if you do it without realizing what you are doing.

There is so much to know about math education and the way children think mathemtically.