October 23, 2012

Teaching as the Practice of Wisdom

Deirdre Bailey

What follows is not a typical teacher learning plan. All my previous attempts have taken the form of New Year’s Resolution type finite lists with a very fixed outline and implied expectation of “pass or fail”. I reluctantly admit I don’t have a great track record with these types of goals. I have a history of making it through about one month of successfully checking my expectations off a list before I inevitably fall off the band wagon and resign myself to a renewed attempt the following year. This year our administration suggested that learning plans could take on personalized formats. For me, this prompted a fairly serious consideration of what has been ineffective for me in previous years and how I might re-direct my focus this time around.

I think the reason that a permanent check list has never worked is that I am not the same person from month to month. If inquiry based learning has taught me anything, it is that ideas, thoughts, environments, and perspectives are impermanent. As writing is one tool that has allowed me to effectively wonder aloud, I decided a while ago that my 2012-2013 teacher learning plan should take the form of a blog...


I want to be able to competently articulate my evolving understanding of effective educational pedagogy and hold myself accountable for actually practicing what I believe in the classroom. While re-figuring my thinking is likely to remain a permanent state, it is important to me that I am able to express my educational philosophy in order to continue to advocate for more thoughtful and relevant learning in the school environment.

My own education has been guided by a learned push to consume. Twitter, blog rolls and other social media exacerbate this tendency. I feel I have overlooked the value of concentration, focus and memory, so vital to real personal development. I am worried that I am losing the ability to distinguish between what I know based on experience and what I think I know based on distractions, media, and a commercial agenda.

My goal is to cultivate comprehension through composure and mindful attention to everyday experiences and ideas both in and outside of the classroom environment. I have learned that at the heart of inquiry are simple considerations of experiential origin and historical wisdom. Discourse and disagreement are openings through which complexities, ambiguities and uncertainties can broaden understanding.

As I refine my ability to articulate what I am coming to understand, the aim is to learn to be suggestive and open with my language and approach, to open a space for consideration with a simple comment or question. I would like to be able to engage in dialogue that fosters respectful and thoughtful conversation around the assumptions and intentions at the heart of educational discourse. The more I understand about teaching and learning, the more I understand that knowing everything is neither a possibility nor an objective. What I can do is learn to effecitvely describe the work that is undertaken in our classroom and hope that the better that work gets, the more it will shine a light.

October 20, 2012

Math is beautiful

It has been a bit of a battle this year to convince our students that mathematics is not disconnected. They seemed to arrive in our classroom at 9 years old with the conviction that the discipline exists sequentially, layered based on varying degrees of difficulty, some of which will remain inaccessible to the more artistically minded for most of their lives. We have been working hard to share that math is in fact a wonderfully complex web of recurring concepts, ideas, and patterns accessible through many different points from a variety of perspectives, and consisting of infinite possibilities awaiting discovery.

Our year began again with conversations about what we call multiples, what it means to be a multiple, and what a multiple of the number one is. We wouldn't let our students dismiss multiples of one as "obvious" or "easy," insisting that they consider what it means to be the number one. For example, how the number one can be manipulated without losing its integrity and how it is a part of other larger numbers. Before the fall break, we had explored multiples of one to nine, discovered patterns, noticed which ones fall into columns on hundreds chart, and noticed which multiples connected to others and how.

On Monday of this week we shared Perry the Platypus' birthday dilemma....

at this point in the year, students were quick to glue the problem in their journals and begin documenting their thinking as they worked through answering Perry's question. Some flipped back through their journals to remind themselves of previous discoveries they had made about multiples. Some organized their work in charts and some in diagrams or bullet points. Each was now familiar with the idea of writing down every thought or "a-ha!" that resulted from their considering the problem. 

Almost all of the students jumped right to identifying that in one year Perry would be a multiple of 2, 4 and 8 because every multiple of 8 is also a multiple of 2 and 4. Many wrote notes to remind themselves that the smallest multiple of any number is that number itself. One cool observation that resulted from this problem was that Perry would be a multiple of every single one of these numbers by the time he was 12 BUT that when he was 11, he would not be a multiple of any of these numbers! One student wrote... 'It seemed important to notice that both 7 and 11 are only multiples of one and themselves...' PRIME! Another student noticed that when Perry was an odd-numbered age, then he was only a multiple of odd numbers and he expanded to state that odd numbers can only have odd factors!

The coolest part of the week however, was the conversations that resulted at the tables who had begun working through an extension to the problem which asked..

How long will Perry have to wait to be a multiple of 2, 3, 4, 5 and 6 all at the same time?

At first the question seemed overwhelming and intimidating to many students. They had been preconditioned to focus on finding a solution. We suggested that they look instead at which numbers on a hundreds chart were definitely NOT a solution. For example, which numbers on a hundreds chart were NOT multiples of 5... Right away we were met with excitement.. 

"WE JUST ELIMINATED 80 NUMBERS! A multiple of 2, 3, 4, 5 and 6 HAS to end in 5 or 0." 
Students excitedly crossed 8 columns of numbers off their list when one double takes again... 
"Wait... the number we're looking for also has to be a multiple of 2.. it CAN'T be odd... FIVES ARE OUT!"
"So we've got ten numbers left and we're looking to see which one of these ten is a multiple of 3, 4 and 6.."
"But if it's a multiple of 3 it HAS to be a multiple of 6.."
"Right so just 4 and 6.."

Looking at multiples of 6 students immediately eliminated everything but 30, 60 and 90. One noticed that multiples of 6 only end in zero if they are multiplied by a multiple of 5. The last step was to eliminate numbers that were not multiples of 4. As 30 and 90 were eliminated, another student noticed that multiples of 4 which end in zero HAVE to have an even number in the tens spot.

As we wrapped things up for the day on Thursday, one student commented as he reluctantly closed his journal; "Mrs. Bailey, I never knew math was so exciting. It twists and turns and loops and connects all over the place and it just seems to go on forever!" 

Math is beautiful.