Sunday, July 31, 2011

Call for Submission: Math Teachers at Play!

In case you have not seen the latest edition of the fabulous Math Teachers At Play blog carnival, you should head over to Math Mama Writes... to scope out her plethora of interesting links for July.

The next issue of MTaP will be hosted right here on my blog, to be published on August 19, 2011! If you have recently written a blog post that you would like to be published to a wider audience, or if you have come across something that you think is very interesting, you can submit it via the web form here or directly to me at . We have been having some trouble with the web form recently, so if you don't hear back from me within a couple of days, please do send me a follow-up email.

Thanks! Hope you are all having a lovely summer. :)

Wednesday, July 27, 2011

IB MYP Brainstorm

Last summer, I did some summer brainstorming/researching for all the math topics of the upcoming school year, and it was super helpful as a reference guide as I moved through the year, because even during the dreary months when I felt zapped of creative energy, I could still go back to my summer list and tap into that list of ideas.

Now, as I move into a year of craziness -- with 5 preps (grades 7, 8, 9, 11, and 12) and a brand new IB curriculum to tackle, it is even more important for me to brainstorm some ideas before I get slammed with the realities of day-to-day school.

So, I started a rough list of activities, projects, and very rough organization of topics around themes for at least the IB Middle Year Programme (which starts in middle school and lasts through grade 10). I did my brainstorm in Prezi because I am a fan of being able to add things and toggle things as I brainstorm, and I don't really know what other platform would allow me to do that. Prezi also lets you import PDF files page by page, which is nice, because then you can seamlessly integrate just the parts of the PDF file that you want to retain.

Check it out -- it's a very rough draft -- and please give me additional ideas that are missing! Here is my brain dump; it's wordy because it's not meant to be viewed in a presentation context. (If the font is too small, there's a blue tab that will appear on the right edge of the presentation screen if you hover there, that allows you to zoom in and out on a slide...) I will work on my organization of thoughts around the IB Standard Level (grades 11, 12) classes soon... That will no doubt impact how I view the depth of these "middle year" topics.

I'm nervous and excited, all at the same time. :) I've gathered a lot of new ideas from the summer and I hope they will enrich my teaching for the coming year!

Addendum Aug 10, 2011: I took a hiatus but I came back and finished a first run-through draft of the implementation of IB Standard Levels topics here. Some of the things overlap because the kids need to take a test at the end of Grade 12 on the cumulative content, and so a fair bit of review is in order. Other things I have to assume that teachers before them have taught something similar to the IB MYP program I outlined and that they are proficient with the basic skill set.

On a technical note, I also noticed that you can hover over the "More" button in Prezi and it'll allow you to view the slideshow in a full-screen mode. That's definitely more user-friendly than my suggestion before of using the + and - zoom. Suggestions on the outlined content and/or implementation?? I've pulled some good stuff from Sam's filing cabinet, but I'm sure I am still missing tons of good stuff.

Friday, July 22, 2011

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? :)


Thursday, July 21, 2011

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...

Monday, July 11, 2011

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!! :)

Tuesday, July 5, 2011

A Good Read on Racial Identity

For some reason, I was very intrigued by the discussions of racial identity at the Klingenstein Summer Institute. The discussions helped me reflect on my own lack of a coherent understanding of my racial identity and how it helps me fit or not fit into the larger society. As a teacher, I feel that I could become a more effective facilitator if I can reach a higher level of self-awareness, so I picked up a book that's supposed to be a classic on the topic of racial-identity development, called Why Are All the Black Kids Sitting Together in the Cafeteria?

Surprisingly, it was a thrilling read. Here are some choice quotes I picked out of the book (I wasn't doing a good job highlighting as I went through, so I just went back and randomly picked some quotes out). I hope the way they're strung together helps you see why this book was so powerful... I highly recommend it; even though we had some great conversations around the topic of diversity at KSI, I really felt like this book helped me solidify my basic understanding of various issues involved in racial identity.

"Stereotypes, omissions [in curricula], and distortions all contribute to the development of prejudice."

"Even a member of the stereotyped group may internalize the stereotypical categories about his or her own group to some degree. In fact, this process happens so frequently that it has a name, internalized oppression."

"[David Wellman] defines racism as a 'system of advantage based on race' -- a system involving cultural messages and institutional practices and policies as well as the beliefs and actions of individuals."

"I sometimes envision the ongoing cycle of racism as a moving walkway at the airport. Active racist behavior is equivalent to walking fast on the conveyor belt. The person engaged in active racist behavior has identified with the ideology of White supremacy and is moving with it. Passive racist behavior is equivalent to standing still on the walkway. No overt effort is being made, but the conveyor belt moves the bystanders along to the same destination as those who are actively walking. [...] Unless they are walking actively in the opposite direction at a speed faster than the conveyor belt -- unless they are actively antiracist -- they will find themselves carried along with the others."

"When I ask White men and women how racism hurts them, they frequently talk about their fears of people of color, the social incompetence they feel in racially mixed situations, the alienation they have experienced between parents and children when a child marries into a family of color, and the interracial friendships they had as children that were lost in adolescence or young adulthood without their ever understanding why. [...] The dismantling of racism is in the best interests of everyone."

"The terms racial identity and ethnic identity are often used synonymously, though a distinction can be made between the two. [...] Both are socially constructed."

"Who am I? The answer depends in large part on who the world around me says I am. [...] Yet, how one's racial identity is experienced will be mediated by other dimensions of oneself: male or female; young or old; wealthy, middle-class, or poor; gay, lesbian, bisexual, transgender, or heterosexual; able-bodied or with disabilities; Christian, Muslim, Jewish, Buddhism, Hindu, or atheist."

"Erik Erikson, the psychoanalytic theorist who coined the term identity crisis, introduced the notion that the social, cultural, and historical context is the ground in which individual identity is embedded."

"The adolescent capacity for self-reflection (and resulting self-consciousness) allows one to ask, 'Who am I now?' 'Who was I before?' 'Who will I become?' The answers to these questions will influence choices about who one's romantic partners will be, what type of work one will do, where one will live, and what belief system one will embrace. Choices made in adolescence ripple throughout the lifespan."

"Many of us are both dominant and subordinate [parts of the culture, depending on what social indicator you are looking at]."

"Many adults do not know how to respond when children make race-related observations. [...] Perhaps afraid of saying the wrong thing, many parents don't offer an explanation. They stop at 'Ssh,' silencing the child but not responding to the question or the reasoning underlying it. Children who have been silenced often enough learn not to talk about race publicly. Their questions don't go away, they just go unasked."

"What pleased and surprised me as we continued to read was that Jonathan began to spot the gender bias himself. 'Hey Mom,' he interrupted me as I read on, 'there is that stuff again!' Learning to spot 'that stuff' -- whether it is racist, or sexist, or classist -- is an important skill for children to develop. [...] We are better able to resist the negative impact of oppressive messages when we see them coming than when they are invisible to us."

"For children to feel good and confident about themselves, they need to be able to say, 'That's not fair,' or 'I don't like that,' if they are the target of prejudice or discrimination. For children to develop empathy and respect for diversity, they need to be able to say, 'I don't like what you are doing' to a child who is abusing another child."

"The process of racial identity development, often beginning in adolescence and continuing into adulthood, is not so much linear as circular. It's like moving up a spiral staircase: As you proceed up each level, you have a sense that you have passed this way before, but you are not in exactly the same spot."

"I call our task the ABCs: 'A,' affirming identity, refers to the idea that students need to see themselves reflected in the environment around them--in the curriculum, in the faculty and staff, and in the faces of their classmates[...] 'B,' building community, highlights the importance of creating a sense of belonging to a larger, shared campus community. 'C,' cultivating leadership, refers to the fact that leadership in the twenty-first century requires not only the ability to think critically and speak and write effectively but also the ability to interact effectively with others in a pluralistic context."

Thoughts? Personally, I think there are many implications for us as educators. The book does a really great job of going into anecdotal details of what we can do personally and institutionally to address diversity issues with our kids. It also coins a lot of the fuzzy things previously floating around in my head and links a lot of the concepts in a very logical discourse. I highly recommend it!