A Plug for PCMI

Hey, are you looking for a great mathy thing to do this summer? Try applying to PCMI. It's awesome, and Park City, Utah, is a fantastic place to be for three weeks of the summer. When you go there, you feel like the sky is bigger/cleaner and the days are way longer somehow. And there are some great math teachers who are passionate about teaching and doing math. Although you can find last year's problem sets here, it's hard to imagine the level of energy and camaraderie unless you've been to PCMI.

It's magic for three weeks, and you'll miss it when it's gone. There is also a generous stipend that covers most of your expenses.

Apply today! Deadline is the end of January, so you had better hurry.

PS. If you do go to Park City, bring your yoga mat if you've got one. It's utterly beautiful there to do yoga outdoors. Also bring your hiking shoes, your best karaoke persona, your fine dining belly, and your thinking cap. Just sayin'.

Resources on Implementing 8 Mathematical Practices

Hey awesome web community,

1.) Here are the Common Core resources I mentioned that our group developed/collected during our time at PCMI: Rubric and Supplemental Doc. Even if you work outside of the country or in a private school, I think these docs would be helpful, because you would probably still want to implement similar mathematical habits of mind.

2.) If you do use it to evaluate your own task/teaching, can you please give us specific feedback on how to improve it? :)

Thanks!

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?

Meta-cognition: More than a Buzzword?

Some things I gleaned* out of our recent PCMI discussion on meta-cognition:

* Research shows that when kids are encouraged to continuously reflect on their own thinking/learning, they actually become better at the process of learning to solve problems.

* We don't care if kids leave our classrooms knowing necessarily all the content, but it is uber-important that they know how to learn effectively and efficiently in the future. So, in a way, meta-cognition isn't only a means to an end, but it's the end itself.

* Meta-cognition is personal. Kids who are given the same task, who arrive at the same results, may have very different evaluations of their thinking processes used. Conversely, even if two kids arrive at two different solutions (either both correct or both incorrect), their meta-cognitive reflections may not be so different. Content mastery needs not dictate how we think about our own thinking.

* Sometimes being more "meta" isn't better. There are different levels of meta-cognition, and some are more closely tied to skills -- such as "Hey, I notice that I keep messing up the signs when I do algebra!" -- and others are more abstract or removed from the content and are, instead, more closely tied to processes or Habits of Mind -- such as "When I encountered problems of great complexity, I persevered and also turned to my peers in order to gain new insights/perspectives." A proficient meta-thinker should be able to move fluidly up and down that spectrum of abstraction, and use their own awareness of their thinking to modify their strategies to be more reasonable or more efficient, in real time!

* We can encourage kids to think meta-cognitively by pairing two kids to work together in pairs on a challenging problem, and assign a third student to only observe and ask probing (but not leading) questions and to take notes on observed evidences of meta-cognition. I believe that meta-cognition happens naturally and implicitly when two kids collaborate productively and "equally" on a task, and a debrief afterwards can help all students realize the benefit of thinking out loud and asking/answering clarifying questions. Teacher needs to circulate during such exercises, however, to make sure that no one group is dominating in voice volume or trying to "give answers" to other groups.

* Meta-cognition is closely tied with kids taking responsibility for their own learning. If a child is successful at one of them, it feeds into their success in the other realm.

* If a kid cannot answer a question posed by the teacher during class, they need to turn and pose a specific question to the rest of the class about where they are confused. This helps kids self-diagnose trouble spots and helps all kids remain actively engaged during class. It also helps the teacher to set the tone that content achievement is not the only thing that matters during class, and that successful meta-cognition is a different form of success. (ie. Teacher can explicitly praise students who are able to pinpoint nuances within concepts that are troubling them.)

I think this has been the most productive discussion yet! :)

*Well, maybe "gleaned" isn't a good word. Some of this is not new, but I thought I'd put them all in one place. Maybe "distilled" would have been better...

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!! :)