Thoughts on PD 2

I recently participated in a PD experience where it felt like the presenters facilitated the learning experience for us as if we were their students, and they layered our experience with meta-moments.

It made me realize that I do not design my PD that way. I tend to always design the experience for adults (this doesn’t mean that we’re not doing math problem that our students would do).

I am curious how the learning from these differing styles transfers to the classroom.

Thank You Chicago

I’m writing this post while I’m sitting outside on a breezy, perfectly sunny, 75 degree day. The scene probably matches up with what most people imagined when I told them that I was moving to San Diego this summer.

I’ve spent the entirety of my adulthood in Chicago. I went out there to attend college and stayed to teach. Friends can attest that I pretty much assumed I would live out the rest of my years in the city, so even I’m surprised at how I ended up back in San Diego

The quick version of why we moved is that Michelle and I wanted to be closer to family and teach in the High Tech High network. We’ve been here for one week and there are pieces of this decision that sit well with me. I’ve seen my parents more times this week than I have in the last two years (my kimchi intake is also proportional to this.) We’re also waking up and bouncing project ideas off each other. But other parts of not being in Chicago have been harder to reconcile. There’s experiences in Chicago that feel so unique to the city, that I’m sad to be leaving them behind.

When I first got to college, I signed up for a pre-orientation program where we took trips out to different Chicago neighborhoods each day. On the third day, we were going to the city’s Southside to volunteer at the Auburn-Gresham Renaissance Festival on 79th (that’s 79 blocks south of downtown.) Somewhere along the red line train headed south, someone explained to me that it was “renaissance” like revitalization, not jousting (although those two are not mutually exclusive.) When we arrived at the festival, we came across a vibrant, joyful, Chicago summertime street festival that drew out the entire neighborhood. Truth be told, this was not what I was picturing.

Even though this was my first time in the Southside, my 18-year old San Diegan self already had images and beliefs of what the Southside was. It was ignorant stuff – like neighborhoods overrun with poverty, danger, and dereliction. I had formed a negative image of black neighborhoods based on everything except any real experience. Reflecting on that dissonance was a gateway to some of the deepest learning I have been able to do about my racist biases, messiah-complex (I had come to college wanting to be a teacher in Chicago), identity as an Asian American, and ability/limitations to empathize and understand. I’m thankful for the ways Chicago has molded me in ways that no book smarts could.

Sitting here in sunny San Diego, I want to thank Chicago for being an amazing city. For every negative sound byte you’ll hear about Chicago, there are hundreds of amazing stories about amazing people doing amazing things that we’re not being told. I hope Chicagoans continue to elevate those stories, and I hope everyone challenges the narratives they hear.

Thoughts on PD

I am wrapping up two years as a 9-12 math specialist for Chicago Public Schools. One of my favorite parts of this job has been designing and facilitating PD. My managers have allowed me to learn by doing and my coworkers have been amazing collaborators throughout the process. In this series of posts, I’ll add to the internet some notes on what I have found important.

On Think, Pair, Share

When designing a session, I default to reflecting on an activity by having participants Think > Pair > Share. I started to get the sense that this was getting repetitive. The first cycle of T, P, S would be rich with discussion; we’d transition into the next experience; then when we reflected on that experience, the conversations always felt less robust.

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Those who live by the TPS, die by the TPS.

As I was in the planning phase of an upcoming workshop, I started paying careful attention to the rhythms and patterns of reflection. I would sketch diagrams like the one above (without the red). It would help me analyze if I was being too repetitive and/or too frequent with my reflection prompts.

David Foster from Silicon Valley Math Institute had this to say when I reached out to him for advice:

The most important goal of a workshop is to allow everyone time to talk. The most efficient way to get conversations activated is conducting pair, share and then maybe small group discussions. That is when more people are talking and many of the participants are more comfortable sharing real feelings with one another. Learning psychologists claim one uses more of her/his brain when one is talking, so these periods of conversation are most critical for learning. Sometimes I think whole group sharing is over valued.

So I began incorporating that advice into my PD and found it really sustained engagement from the participants. The rhythms and patterns began to look more like this:

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A less repetitive Think, Pair, Share rhythm.

In addition to what David shared, a major issue with Think > Pair > Share is that it gets so predictable – predictability tends to decrease engagement. While I think changing the structure of Think > Pair> Share has been a helpful and productive move, I have found even more success in deviating from any single protocol as THE way to get participants to reflect. For example, Sara Van Der Werf’s Stand and Talks are a great way to break up that monotony.

Professional Learning – Mathematicians

November 2, 2017

Nicole Dudik at the Logan Art Center

Last year, I stepped outside my comfort zone and attended an evening PD advertised to art teachers – mainly as an excuse to hang out with my friend and art teacher colleague Nicole (pictured above). The subject line of the email she forwarded me was “Upcoming Teacher Workshop: Exploring Text and Image with avery ryoung + Cecil McDonald Jr”.

Artists avery r. young and Cecil McDonald published In the Company of Black – a book of photographs taken by Cecil accompanied by poems written by Avery. That evening, they showed us, a group of twenty or so people, selected pages from their book and told us that we would be creating a photo and poem for someone else in the room. The first thing we did was take a photo of our partner (mine is above). Then, we interviewed our partners from a list of questions ranging from trivial to personal. Lastly, we wrote our poems. The poem writing process was unusual. We started with a 64 word poem about our partner. Then we reduced it to 32 words. Then 16. Then 8.

Still from In the Company of Black

To exhibit our work that evening, the images were sent to Cecil’s laptop and he compiled them into a presentation. We didn’t know the order of the photos, but were instructed to start reading our poems out loud as soon as the image of our partners came up. For example, Nicole’s image would flash up and I would begin reading my poem. My image would flash up and Nicole would read her poem. Oftentimes, the next image would come up before someone finished reading, creating an overlapping chorus of poetry over images.

This exercise was done in tables arranged in a U so we were all facing each other. There were several times during that evening of sharing where I had goosebumps, even times when I felt myself getting emotional from hearing the short, mysterious stories of strangers. I walked out that evening in disbelief. I thought to myself, “why do arts education PDs get to feel like that?”

It felt like I was at a workshop for artists, not a PD for arts teachers. I am sure Avery and Cecil knew exactly who their audience would be. Yet, they chose to design for artists. They knew it was important for arts educators to engage in their discipline.

I’m not sure if that attitude is common design practice across arts PD, but the relationship between art teacher and artist seems to be blurrier than other disciplines. It seems like you can be both. Take Nicole for example, if you click around her school teacher bio page, you end up at a page highlighting her artwork. My website on the other hand? All you learn about me is that I like riding my bike to work.

I began pondering about this ratio,

artist : art teacher :: mathematician : math teacher.

I wondered how to adopt what I experienced from Avery and Cecil and recontextualize it for a math context? What would it mean to experience PD for math teachers as a mathematician?

August 14, 2018

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CMTC Summer Jamboree at Kenwood Academy

I’m writing this post after having attending the Chicago Math Teachers’ Circle Summer Jamboree. If you’re unfamiliar with Math Teachers’ Circles, they are 2 hour sessions typically led by university faculty where you work in groups to investigate really interesting math. If you’re unfamiliar with Jamborees, well then I just can’t help you.

Last Tuesday, from 9 to 3, we sat together and did math – some of which we tirelessly explored, only to find out that no mathematician has proven some of the questions we were exploring!

I’ve had some time to look through the feedback from that day and lots of teachers commented that there were times of frustration, victory, and excitement. Hearing those emotionally charged words made me feel like some people in the room may have had goosebumps…

But my favorite response was this:

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If you take away the scratch marks, it says “Meeting teachers – and mathematicians!” I like to imagine that this teacher had to experience something powerful in order to believe that there does not need to be a separation between teacher and mathematician.

Why Shut Down the Dan Ryan?

I was in Italy for 10 days, not checking my emails and enjoying Chianti with every lunch. When I returned to Chicago, I saw an email from my pastor with the subject line: Details about the Dan Ryan Shutdown Tomorrow. Inside the email, there were details about the event and why it was happening, but the part that struck me the most I’ve copy and pasted below:

Will anyone be arrested?
  1. The expressway falls under the authority of the Illinois State Police (ISP). They have said they will arrest anyone who marches on the expressway. There are lawyers lined up should that happen.
  2. However, at this point it seems unlikely that any arrests will be made. Those planning the march believe that the ISP will not hinder the marchers.
  3. On the off chance that the ISP does begin arresting marchers, those who don’t wish to be arrested can continue the march along State St.

My wife, Michelle, asked me if I was going to go, and she must have not read the part of the email titled “Will anyone be arrested?” I swiftly told her no. No, I wasn’t trying to get arrested. Something about my dismissiveness didn’t sit right with me, but I had important matters to attend to, like checking twitter, watching TV, and walking my dog. I couldn’t focus on any of those activities. The Shutdown was stuck in my mind.

By the end of the day, I set my alarm to wake up and attend the Shutdown. In this post, I’d like to share the reasons why.


Why shut down the Dan Ryan?

It’s led by the youth of Chicago Strong (see their website for what they’re all about). As an educator, I project myself as someone who cares about empowering our youth. Often citing Freire, I make big claims about how the purpose of education is to empower students to name and rename the world around them.

So imagine the dissonance I felt when my gut-reaction to the Shutdown was to put on my “adult hat” and make arguments to discredit the students’ plan. If I get arrested and have a record, what will that mean for my current/future career? Are the students aware of these consequences and do they understand the scope of what they’re getting us into? Did they think this through?

I supported student leadership, but only at my convenience. That looked like retweeting inspiring content for a cause I believed in, but never opening my checkbook and giving my money. In theory, I was the biggest supporter. In practice, I was the sharpest skeptic.

I joined the Shutdown as a way to react to my identity crisis. It’s not that any single action allows us to etch our character into stone, but I wanted my attendance at the Shutdown to be a step forward in my personal journey towards trusting student leadership.

It’s important for Asian Americans to support. Gun violence in Chicago is an Asian American issue. (Side note: it’s also a white issue, a black issue, a Latinx issue, etc.) I don’t feel like I should have to follow that up with a “because”, but judging by the number of Asian Americans that were at the Shutdown, it must be said. Gun violence in Chicago is an Asian American issue because it is affecting our neighbors.

Being neighborly is not something that I have seen modeled well by most first generation Asian American business owners in some of Chicago’s black neighborhoods. At its worst, Asian business owners negatively stereotype and dehumanize customers in their own communities. At its best, Asian business owners form authentic relationships and become cornerstones in the community. But in both cases, I wish the conversation about being neighborly also emphasized creating positive, sustainable change in the local economies of the communities they are profiting from.

Second generation Asian Americans like myself have the opportunity to redefine what being a good neighbor could look like. Joining in this fight is one way to do that. When we look at the history of our country, I am eternally grateful for the revolutionaries that took up causes that were bigger than themselves. Otherwise, this couldn’t have been a country where my mom and dad could immigrate and be successful.

The Shutdown is an opportunity for me, as a member of the Asian American community, to publicly show my support. We need to recognize our rich history of protesting for systematic change in this country. Our fights in the past are others’ fights now. I want the youth of Chicago Strong to see Asian faces in the crowd and know that we got their back.

It’s what my faith compels me to do. I can imagine being at the pearly gates, and Jesus is standing there with me, watching the YouTube compilation video of everything happening in 2018. I think he’s going to ask the church, “what were yall doing?”

Construct viable arguments and critique the reasoning of others.

Picture the following scenario. Two students are working on a math problem. They are unsure if they are on the right track. They call over the teacher and ask, “Is this right?” The teacher throws the question back at them, “What do you think? Can you explain how you are solving it?” The students begin explaining, step by step, how they tackled the problem. After each step, they pause to scan the teacher’s face for any sort of tell – but the teacher is poker faced. After the students finish their explanation, the teacher asks again, “What do you think?” Frustrated, the students say, “she doesn’t even teach us!”

This happened at a recent professional learning we were leading for teachers – and it made me realize that the difficulty of determining if you are on the right track or not is true for all learners. The facilitators and I discussed this vignette during the break. We ended up at what I thought was a really interesting question.

Does making “good arguments” or “bad arguments” feel qualitatively different for our students?

signposts-1-e1510318331705.pngBefore continuing, I want to separate the feel of good arguments with the signposts of good arguments that are embedded within so many problems. These signposts subtly communicate that students are on the right track because as they solve the equation (for example) all of the values remain integers. When I was a student, I always looked for those signposts after each step (or maybe more telling, I only double checked my work when I got found a non-integer solution).

So, do “good arguments” and “bad arguments” feel qualitatively different? My gut answer is “ehhh no?” or at least “it’s more complicated than that”. Launch a non-routine problem without signposts and halfway through the process, pause to ask, “Are you on the right track? How do you know?” what would you expect to hear? I’d assume that the students would fall into one of the four cases that are created when comparing the actual mathematical validity of the arguments being made versus the student’s perceived validity of their arguments.

Good and Bad Arguments

Cases I and III.
Students in Cases I and III probably can self-identify where they are at. There’s rich discussions on who these students are, but maybe that’s for another time. Instead, I’d rather focus on Cases II and IV.

Case II. Students with “bad arguments” think they have “good arguments”
Students who are in Case II are working under the assumption that they are correct. The problem is, when they get to the end of a problem and find out their arguments were bad, they get burned. If students experience a pattern of false-positives, then they lose their trust in the problem-solving process.

Case II. Students with “good arguments” think they have “bad arguments”
Students who are in Case IV are working under the assumption that they are wrong. If students proceed with the belief that they are wrong, they are prone to experiencing confirmation bias. They could make nine good arguments and one bad one, but that one experience confirms what they already believe about themselves. In this light, every argument begins to feel bad.


A solution? One starting point could be to teach metacognition by strategically using activities like Harvard’s Contrasting Cases. In these problems, we’re presented with two characters who are solving a problem using different methods and explaining their thinking along the way.  Contrasting Cases are often used to emphasize the most common mistakes made in solving a problem, or to encourage multiple approaches to solving a problem. But I wonder how we could also use these to teach students about metacognition? One way this could look is by pointing to a particular argument and asking questions like, “Does this person think they are on the right track? How could they figure out if they are or not?”

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To sum things up, I’ll harken back to something I heard at the professional learning session we were hosting. As the break was finishing up, one of the facilitators made a really insightful comment about this topic. She said that in order for students to construct viable arguments, they need to learn (and we need to teach) what it means to be held accountable to the mathematics.

re: let’s retire #MTBoS

If you’re unfamiliar with the #MTBoS, the first thing you’ll be encouraged to do is watch what I think is the MTBoS sanctioned welcome video – The #MTBoS and You. After watching the video, here was my response.

I’ve recently been thinking a lot about what it would take to have an inclusive online learning community for Chicago Public School teachers, which led me to read this paper by Judy Larsen and Peter Liljedahl. I found so many intersections between the paper and the conversation around diversity in the MTBoS that I want to reframe my wondering, and dive deeper into the following two questions: Why is the MTBoS so white and what can be done to make it more racially diverse?

First up – authority. Out of the firestorm that was Dan Meyer’s post “Let’s retire the #MTBoS”, one of the most interesting discussions was on whether or not MTBoS had leaders (authorities) or not. I believe the general sentiment of the MTBoS contributors is echoed in this response:

And that seems to align with Larsen and Liljedahl’s observations. They note, “Further, because of decentralized control, no agent is ever in a position of final authority, and knowledge is always tentative.” And this seems to be true. Dan Meyer, as an example of a reputable MTBoS contributor, doesn’t go around declaring the final say on discussions happening in the MTBoS. So the “decentralized control” structure allows authority and authorship to flow and cycle through many users of the MTBoS.

But what struck me most about Larsen and Liljedahl’s research is that they were able to identify how people hold, be it transient, the position of authority. They write the following,

Holding authority within a complex system means to have the capacity to use a prevailing discourse, or to act within the consensual domain of the system, with the overall aim of occasioning ‘collective-knowing’ (Davis & Sumara, 2006).

If you’re like me, the term “consensual domain” is not in your everyday vernacular (and it makes you feel funny on the inside), so you need it defined. Fortunately the authors do that for us, they write this,

This investigation shows that the consensual domain of the MTBoS includes patterns of interaction such as thinking like a learner, generating examples, invoking shared language, and using instructional routines, as well as being guided by pedagogical values related to teaching without telling and guiding students towards mathematical generalization.

Larsen and Liljedahl observed that to hold authority in the MTBoS, you have to participate in the invisibly-agreed-upon (or consensual) culture of the MTBoS. In the section above, they describe the elements of consensual domain as the pedagogical topics that participants discuss. It’s what you talk about, not how you talk about it that determines the ability to hold authority.

But that doesn’t explain why the MTBoS is so white. I think that is because there also exists an invisibly-agreed-upon (or consensual) how you talk about pedagogy that is missing from the definition of consensual domain. My hunch is that Larsen and Liljedahl are looking too closely at what is being discussed, and if we were to step back and focus on how they are being discussed, then we see that to join in the prevailing discourse, one has to speak using a certain communication style.

The MTBoS is so white because it functions like most other white-dominated community in the United States. If participants of the MTBoS think that the communication style, or the cultural language, of the MTBoS is neutral, what is really happening is white people are functioning in their usual way while people of color are conforming to white cultural values. It’s not a hostile atmosphere, but it is a subliminal one. And in atmospheres like these, you can expect to see fewer non-white people participating (you should see the dog park in my neighborhood).

What can be done to make the MTBoS a more racially diverse place? If you even feel like this discussion is worth taking up space on the MTBoS, then the responses boil down to four possible buckets:

  1. White people change their authentic voice to try to sound like the voices of underrepresented groups as a way of making others feel welcome. No, seriously, I LIKE your whiteness. Subtract supremacy from the equation and there is nothing wrong with white culture, especially when that’s who you are.
  2. White people invite people of color as token-authorities as a way of making others feel welcome. Often sounds like, “Let’s be intentional about pushing people of color owned blogs to the top?” I think cultural shifts are more complicated than that and no one wants to be a token.
  3. MTBoS is not white, it’s post-racial. Fish don’t know they’re in water. For more clarity around that idea, as a Korean-American who grew up in the United States, you go to school and learn that sandwiches for lunch is normal while kimchi, seaweed, and rice is foreign.
  4. MTBoS is white, own it. This is the response I’d advocate for. If more people in the MTBoS were acknowledging the whiteness of the MTBoS, it would make non-white people more comfortable. And I mean acknowledge it not in a 1000-word blog post kind of way, but in a I can laugh at Dave Chapelle sketches with with my non-white friends kind of way.

So to wrap up, let’s reflect. How in your non-digital life do you participate in racially diverse communities? How are you drawing on your experiences of being the only non-white person in the room (small caveat: room full of black and brown students doesn’t count if most of the teachers are white) to create a more inclusive community? And if none of that is happening in your non-digital life, why would you expect it to happen here?