Dialogue vs. Content

One of the things that's been circulating in my head is the idea that dialogue has more value in terms of developing teachers than giving teachers already well-developed content. During KSI, we read some article that talked about different forms of lesson studies, and the surprising takeaway for me was that after these teachers had worked so hard to craft their lessons and to try them out and then to reflect on them, they decided not to publish their final revised lessons, because they felt that the product was not the most valuable part of the entire experience. Instead, they placed the greatest value on the dialogue that had led to that development of the improved lesson.

Immediately upon reading this, I reflected on my own tendency to share content from lessons or activities that I have tried and liked, without stepping back and thinking about the fact that that's not helping other teachers learn the process of creating similar activities from scratch.

During PCMI, in our "working groups" we had to develop projects that we think are worthy of being published by the Institute of Advanced Studies in the future. On Day 1 of the program, our group leader had us look at some example projects from the past, and then gave an open-ended challenge that we were to create something that is not necessarily content-heavy, but something that can be used to facilitate the development of the mathematics teaching community at large.

We spent a day just brainstorming. It was stalemated at some point. I felt pretty strongly that the "lesson" content we create should not be as important as the framework we create to facilitate teacher dialogue, and some other teachers felt equally strongly about making the Common Core our primary focus, while other teachers felt that we should still be putting our energy toward making a GREAT, collaboratively designed lesson. We all compromised by deciding that in order for teachers to have effective dialogue about pedagogy, they need to be looking at something specific and concrete -- such as a lesson plan. In the end, our group split up into four sub-groups: 1. One group to develop a PD session that brings teachers from a school community to examine the differences between their existing state standards and the Common Core; 2. another group to develop an exemplary lesson based on some of the Common Core features; 3. another group to develop a rubric (and supplemental document of resources) for assessing how well a task or a teacher is facilitating the mathematical practices as outlined by the Common Core; 4. a group mapping the content topics of the Common Core as threaded throughout the various grade levels. The products from all the four sub-projects can either stand alone, or work in conjunction to open up the space for teacher dialogue about where they currently stand and where they wish to go.

After 3 weeks of hard work, we're done with the projects!! --For now, anyway. :) My group was responsible for the rubric project, and (if I may say so myself) it's looking pretty fabulous. My partners are pretty much both rock stars. We pulled together a 25-page document supplementing the goals of the mathematical practices, clarifying expectations and giving ideas for how to implement those goals. I am very proud of what we've accomplished, both as a sub-group and as a collective working group! yay. I hope our stuff gets reviewed and published, sooner rather than later, so that they can be made publicly available and serve the purpose that we had hoped to achieve.

And, not to go too "meta", but in creating the rubric, our group had some GREAT dialogue about teaching and learning. It ties rather nicely together with my belief that the dialogue is more important than the end result.

What do you think? Where in your own experience (besides the web) do you see dialogue about teaching contributing to your professional growth?

Summer in Utah

Time for a little summer update, I guess.

1. I am in beautiful Utah! --Park City, to be exact. After the two intense weeks at KSI, the math program (thus far) in Park City has seemed much more like a vacation. I have not yet had any major "Aha!" moments about teaching since my arrival in Park City, but part of that could be because I was so overwhelmed with "Aha!" moments in Jersey and my plate is now already full of things that I want to try out for next year. In any case, PCMI is a fun math vacation for me, because they have allotted copious amounts of time for us to sit and grapple with superbly scaffolded math problems -- ones that are hard (and thus fun and addicting) for me. :) *doing the mathgeek snort*

In the evenings, there are usually great optional things, like when I went to one kite-building session with one of our fellow math tweeps, Barb! Last weekend, I was busy enjoying the nature and town life around us -- very different from our experience in Jersey during KSI (which was mostly workworkwork, even on the weekends)!

2. On the teaching front, I found out that I'll be teaching grades 7, 8, 9, 11, and 12 next year at my new school!!!!! I am pretty sure that actually means 5 preps (definitely 1 class per grade), and I'm terrified and SUPER EXCITED at the same time. (My certification is grades 7 through 12, so this will fill in all the holes in my resume if I can pull it off.) I have plans to sit down and to make a GIANT matrix of Big Ideas vs. grade levels and to brainstorm concrete projects or activities within each topic, so that I won't feel zapped of energy to be creative next year when I'm in the thick of it.

3. I move to Germany SO SOON! I am keeping my fingers crossed that we'll get the apartment we want. It's next to a high-demand, very happening neighborhood and is just under an hour of commute to work for me. If this doesn't work, I'll have less than 10 days when we arrive in Germany to find another place. That can get stressful very fast.

I've already subscribed to all the Berlin swing dance emails; never mind that they're in a language I don't understand. I can't wait to begin our life anew!! :)

On Being a Multi-Faceted Educator

I've noticed that as time passes at the Klingenstein Summer Institute, each day I more fully develop a sense of how much I suck as a teacher.

Fortunately, unlike the grad classes I took before which pointed out some gaps in our teaching practice but did not offer any solutions, at KSI we actually spend a significant amount of time brainstorming small things we can do to address various learning and diversity issues in our classroom and at the school.

One thing I think I can immediately implement at my new school is to initiate a professional development community consisting of teachers who are seeking to actively examine their own teaching practice. I've been talking with other teachers here who have reading groups at their schools, where teachers read and discuss educational articles. In KSI, we've also been practicing a lesson study protocol for allowing teachers to voluntarily share the weaknesses in their teaching, in order to ask for feedback and advice. I think that sounds wonderful, and it is something that is very manageable that I believe I can tackle. (I know that there are teachers who do some of this on Twitter, but I'm more motivated by local communities.)

I've also gone to some great tech sessions that discussed various uses of technology inside/outside the classroom. I don't know if all of those things will be available, or if the use of some of them (such as Edmodo, a social networking site) will fit with the school's technology philosophy. But, I feel like the least I can do is to really investigate those options and to talk to the right people when I arrive at the new school in July. If I can integrate some new modes of tech use into my class, they could enrich my teaching style greatly without being too much additional work for me or the kids and (for these particular methods I am thinking about) without distracting from the content.

Teaching about diversity and bringing about positive changes to the school culture is the hardest piece of all of the Klingenstein lessons to implement. I think that is because as educators, we cannot all necessarily agree that teaching about those topics is 1. pertinent and necessary, 2. feasible given the community culture that surrounds the school. (I personally believe those discussions are necessary, but I believe it would be difficult to convince others on my staff of the same.) I am going to start by doing things like putting up pink triangles around the perimeter of my classroom, to signify to GLBT kids that it is a safe space if they need an adult to talk to. And then, once I build some rapport with the administrators and gain their confidence, I can try to tackle bigger tasks. But, that'd have to wait until I get over the hump of being a brand new, young-looking teacher at the school.

Aiyayay. Teaching is hard, and it seems to get harder by the day.

Klingenstein Summer Institute

A while ago, through Sam Shah's blog I learned about a program called Klingenstein Summer Institute, which is a professional development workshop that runs for a couple of weeks each summer, and is geared towards teachers in independent schools who are still within their first five years of teaching. I researched the program briefly on the web and decided that it was probably unrealistic for me to apply and be accepted, but I went ahead and did it anyway. (I am trying to practice being a more aggressive version of myself -- if that makes any sense.)

So, long story short, here I am sitting in Lawrenceville, NJ, which houses the Klingenstein program. The first few days were pretty hectic, but I think it's calming down. Thought I'd take a few minutes to jot down some of the things I've been learning/thinking about since my arrival at the institute.

1. Math-specific stuff: The old way of organizing topics around content chapters needs to be replaced by organization around themes, to facilitate the development of effective schema in the students' minds (which increases retention and all that good stuff). I am obviously a newbie at this, but I'll try to organize Geometry units to illustrate these. I'm not quite fleshing out everything.

• BIG IDEA: Measurement
  --> Dimensions and quantities
  --> Conversions
  --> Measurement methods
  --> Indirect measurements such as Pyth Theorem and similarity ratios
  --> Trigonometry



• BIG IDEA: Conjecturing
  --> Induction
  --> Deduction
  --> Layered math formalism (definitions --> postulates --> theorems)
  --> Making conjectures about circles and triangles and angles inside parallel lines
  --> Multi-step solving of diagrams using various known pieces of info



• BIG IDEA: Multiple Representations
  --> Coordinate plane concepts and skills



• BIG IDEA: Transformations
  --> Both inside/outside of coordinate plane
  --> On objects as well as "functions"



• BIG IDEA: Proofs
  --> Basic postulates
  --> How do we prioritize info?
  --> Formal Geometric proofs (both algebraic and geometric)
  --> Meta-cognition: How do we assess a proof/argument?



• BIG IDEA: Spatial Visualization
  --> Proportional reasoning
  --> 3-D to 2-D, or 2-D to 3-D
  --> irregular area/perimeter/volume/surface area

Thoughts? That's my first stab at re-organizing the topics of a course based on this idea.

2. Small changes in the classroom can make big impacts on student learning. Things I am going to try this fall: slowing it down (wait time/questioning) and being positive/encouraging/empathetic. I'm going to ask a colleague to observe/evaluate me on my goals and to hold me accountable.

3. We do (individually) have the power to substantially affect school culture. One Klingenstein alum once started the first Gay-Straight Alliance (I forget the name) as his year-long project. Now there are GSAs all over the country, in private and public schools, and they help to foster awareness and compassion. I need to believe in the power I have to change the things that I think are problematic in the school.

Ok - dinner time. :) Ciao!