Holiday break began yesterday and I find myself with time to breathe and (hopefully) get some real writing done. Before thinking about work for January, I want to take some time to pause and reflect on some of the great stuff my kids were doing before the break.
I found this problem on twitter and shared it with colleagues and classes last week:
It took me a minute or two to notice what was happening. I showed it to a colleague who started chuckling instantly. He has a faster mind than mine!
So I showed it to my classes, they all eventually noticed that the digits 1 through 9 were all used in this equation. My challenge to them was to write an equation using the digits 0 through 9, once each, that was also true. I urged them to not simply add a zero to one side of that equation above.
The kids dove into this challenge and came up with some great solutions. I have a photo I took on my iPad with some of their solutions superimposed on the image of the original problem.
Fun, right? Even better is the fact that some kids were still working a couple of hours later coming up with ever creative solutions. My favorites were both cooked up by a student who had a sub in his Health class (me!) and he was tinkering with this problem at that time.
This one won my heart, I must admit.
I hope to do some more writing in the next two weeks. Some will be public, some will be piles of problem sets for my kiddos.
Not too long ago according to my calendar, but a long time ago now according to how the pace of school life moves, I finished an online workshop run by Robert Kaplinsky. The workshop, in six modules, was called Empowered Problem Solving. The modules were released on a weekly basis and were centered on videos of a workshop that Robert ran. These videos were accompanied by some outside reading in the form of blogposts and some PDFs. There were question prompts to encourage lively conversations on a message board, and there was quick support through emails from Robert and others working with him in the one or two cases early in the course when questions popped up about navigating the interface that they had set up. I did not recognize the names of folks on the message board there but I came to develop a sense of kinship through our conversations over the course of almost two months. Several themes emerged, of course, and it was interesting to go back through message boards from earlier lessons to see how my thinking was moving/growing and how the conversations deepened over that time. Looking back now, a few weeks after the course ‘ended’ [we still have access online for at least another month to revisit ideas and to help deepen our understanding/comfort with the ideas of the course] at a folder I created with documents that Robert organized for us, I realize that it will probably be out extended Christmas break when I can really digest and inject some of the habits of mind that are encouraged in the course. It made me think of my journey in grappling with/enacting/understanding the principles of inquiry and open-ended problem based lessons in the math classroom. I was forutunate to have had a Master’s Degree class in 1987 (before my teaching career began) called Mathematical Problem Solving. My grad school advisor, Prof Mary Grace Kantowski earned her Ph.D. in 1974 and her dissertation was Processes Involved in Mathematical Problem Solving, so I got a dose of this working with her and taking her class. I entered the high school classroom in the fall of 1987 and I have been honing, adapting, striving, to really figure out how to incorporate something more meaningful than practice exercises with my students. I was further energized by my first visit to the Anja Greer Conference at Phillips Exeter (I know it was between 2001 and 2005 but I cannot remember for sure what year it was) when I met Carmel Schettino and learned from her about problem solving in the math classroom and I am certain that this was my first exposure to the Exeter problem sets . The conference was mind-blowing and I was fortunate enough to attend one other time since then. Carmel’s work and advice energized me further and I started writing my own modest problem sets. Later, I wrote my own Geometry text that our school used for five years and in the process of that, I wrote HW for the course in the form of smaller problem sets. I have been fortunate enough to attend a summer think tank styled workshop that Carmel ran. I went with three colleagues to a workshop run by some folks from Packer Collegiate Institute in Brooklyn last year. I visited the Peddie School in New Jersey with three colleagues and we saw what they had done with their curriculum. Our school was visited by a member of the math department from Saint Andrew’s School in Delaware and he shared what they have done with their curriculum. All of these experiences led me to want to enroll in Robert’s online classroom and it was well worth my time and energy and the school’s investment of professional development funding. Conversations are happening in our school about the direction we want to go for our students and the visits and workshops last year helped prompt these conversations. The ideas and resources from Robert Kaplinsky’s workshop will be immensely helpful in moving this conversations forward.
All of this is a long winded way of me saying thank you to Robert, to Carmel, to the folks at Peddie who welcomed us, to Eric Finch from St. Andrew’s in Delaware, to my advisor Prof Kantowski. All of these voices throughout my career seem to be pointing the way to a more meaningful way of teaching and learning mathematics. Robert will be running his workshop again in February and March and I encourage you to take part. Whether you are just beginning to grapple with the ideas of running your classroom as a place of open inquiry and driven by problems (rather than exercises – a distinction that Prof Kantowski often discussed) or if you have been working with these ideas for years and are looking to be re-energized or more organized, this will be a great experience for you.