#blackbrillance + social justice + problem-based learning

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One of my summer reads has been The Brilliance of Black Children in Mathematics by Jacqueline Leonard and Danny B. Martin (inspired by Annie Perkins). I’m almost three-quarters of the way through it. It is rather dense because it’s packed with research, but I’ve been enjoying it.

Chapter 6 has stood out. It focused on the development of culturally relevant, cognitively demanding (CRCD) mathematical tasks. The authors of the gave this definition of CRCD:

Culturally relevant, cognitively demanding tasks should be mathematically demanding tasks and embedded in activities that provide opportunities for students to experience personal and social change. The context of the task may be drawn from students’ cultural knowledge and their local communities. But, the use of context goes beyond content modification and explicitly requires students to inquire (at times problematically) about themselves, their communities, and the world around them. In doing so, the task features an empowerment (versus deficit or color-blind orientation) toward students’ culture, drawing on connections to other subjects and issues. CRCD tasks ask students to engage in and overcome the discontinuity and divide between school, their own lives, community and society, explicitly through mathematical activity. The tasks are real-world focused, requiring students to make sense of the world, and explicitly critique society — that is, make empowered decisions about themselves, communities, and world. (p. 132)

The authors go on to caution the reader that finding/creating a CRCD task isn’t enough:

It should be reiterated here that task creation is by far only the beginning. Culturally relevant pedagogy necessitates that teachers learn about students, their culture, and their backgrounds. Ladson-Billings (1994) indicates that the teacher must be the driving force to creating a culturally relevant classroom. The contexts of the tasks alone will not necessarily make for the culturally relevant environment. It is the thinking behind the tasks and the actions during the implementation that make them culturally relevant. Without the appropriate set up of the task and the accompanying discussion and connection to the students and/or their communities, the task although created as culturally relevant, will lose its relevance. (p. 134-135)

This all got me thinking about all of the problem-based learning that I did last year with my kiddos. Our focus all year was thinking about, discussing, and solving problems that built on each other. As such, the big ideas of the algebra 2 curriculum were slowly uncovered through the problems. I used a range of pedagogical approaches but mainly leaned on whiteboarding (VRG and VNPS) to foster small and whole group discussions. On top of all this, back in June, I learned of Brian Lawler, who has done work around how teaching mathematics equitably requires problem-based learning. It’s an interesting take and learning from him provided even more incentive for me to improve my PBL approaches. Here are the slides to a presentation that he gave at the PBL Summitt in 2016.

So reading through chapter 6, it hit me that the PBL setting that I’m constantly improving affords my kids frequent, bite-sized opportunities to have meaningful discussions about relevant, empowering mathematics — exactly what I didn’t do last year. I centered all of the problems in contexts typically found on the Regents exams, which surely has its place, but when considering that 90% of my students are either Black or Latinx, it is an issue. The bottom line was that there was a strong disconnect between the problems I curated and my students’ lived realities. Here’s an example from last year’s problems (I could have chosen many more):


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While fairly procedural, it’s a pretty standard Regents problem. Most algebra 2 teachers in New York wouldn’t complain too much about it.

Other than the unrealistic nature of the problem, what I’m coming to grips with is that the discussion we have a problem like this involves just mathematics, not the implications of the mathematics and how it directly affects how my students view themselves and/or society. The challenge I’m setting forth to myself now is to find ways to change the narratives that my problems present to my students that will help us have more meaningful, transformative conversations.

For instance, after combing through the website Radical Math, I found myself thinking about all those payday loan joints that are everywhere in the city, especially in Black and Latinx communities like where my school is located (and where I myself live). With interest rates as high as 400 percent, they help create a wicked cycle of debt that cripples many folks who are struggling to make ends meet — some of whom are quite possibly parents of my students. In addition, they target people of color. I’m thinking that instead of focusing on Bella, Ella, and their mythical interest rates, I could help my students explore about the damaging impact these lenders have our communities through introducing data from the above sources and through a series of problems that they grapple with. It’s not perfect, but here’s an example:


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I’m pretty bad at using math to generate discussions about broader social issues like race. But then again, apart from beyond the white dudes, I’ve never had math problems to catalyze such discussions. I hope I’m better with facilitating discussions about problems like this, to help students see how they can better identify with math. If so, the result could be something important, relevant, and empowering.

This is a long post.

Last thing. The authors shared some examples of these sorts of problems that were created by graduate students who were also teachers. What was interesting was that, after studying the problems, the authors found that “very few of the teachers used race as a basis for their culturally relevant tasks.” Instead, the primary culture the teachers relied on was age. For me, it’s easy to get excited about some other aspect of problem set and get swept away in White culture, so this is a reminder to deliberately seek to address race in the problems and activities I use.

Through all of this, I feel like I’m getting closer to where I need to be, but I’m still left thinking about the many ideas in algebra 2 and how I might address them in the midst of the looming Regents exam.

 

bp

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Teaching & parenthood

At day 2 of the MfA Summer Think yesterday, there was a teacher poetry circle. The following was the result of the free write at the end.

Early in my teaching career I never thought that about being a parent. As time-consuming and energy-consuming as teaching is on a daily basis, I never thought that I would be capable of being a parent, fathering a child, tending to the everyday needs of another human. I, along with most other teachers I know, are completely drained at the end of a school day. As a parent, I would then have to go home and do something even more involved? Nah, I’m good.

I was so wrapped up in my own professional cocoon that I would privately question teachers who were parents. Was there’s a conscious decision to start the journey into parenthood? If so, WHY in the world would they do it? And how do they maintain their own sanity on an everyday basis?

Well, two and a half years ago I willingly turned my personal life upside down and became a dad. In addition to being the most awesome and adventurous ride I’ve ever been on, it also spurred a dramatic change in me as a teacher.

Before my son arrived, I was an impassioned teacher. I had the career that I had wanted since my junior year in high school. I loved my students, I loved my job. But after his birth, the love I developed for him was deeper and more compassionate than anything I had ever known before. For any parent out there reading this, you know what I mean.

Slowly, during that first year of my son’s fragile life, I began to see my students differently. This was both amazing and unexpected. I realized that the same love I had for my son was also felt by the parents/guardians of my students. In addition to every other aspect of their lives, these parents sent their children to my school, to my classroom, each morning wanting nothing but the absolute best for their kid. This desire was no different than what I felt for my son from the minute I held him in the hospital for the first time.

As a result, I began to see each of the 34 students in my class from the eyes of a parent, not just a teacher. This triggered a shift in mindset that transformed how I felt about teaching mathematics and, coming from a single parent household, why I taught. Because he gave me this beautiful gift of perspective, each one of my students has become a version of my own son.

So, now, while I fail often at meeting this standard, I teach my classes as if he was on the roster. I simply know no different.

 

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End of the 2017-18 school year

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Another school year in the books. As with each passing year, a lot happened in 2017-18. Bullet points seem appropriate.

  • First and foremost, my adventures with problem-based learning took up most of my mental real estate. That journey deserved its own post.
  • This was truly the year of the whiteboard. I had 12 of them wrapped around the edges of my classroom this year that we used every day. It was great.
  • I need to step my game when it comes to the cohesion and collective responsibility that my department shows for one another. Just like last year, I felt isolated this year. More than ever, this year I desperately needed support from colleagues that I didn’t receive. There are lots of reasons for this, but my own introverted nature certainly didn’t help matters any. Next year I hope I can be a better teammate and leader.
  • While PBL took off in room 227 this year, I’m very disappointed that my push to address racial inequities in my classroom stalled. I failed to build on many of the conversations that I started with my students last year. For example, my Mathematicians Beyond White Dudes initiative halted after Vivienne Malone-Mayes (No. 3). This was due primarily to my borderline obsession with implementing problem-based learning and all the struggles related to it. This issue is deeply personal and I’m very very dispirited that I let it trail off. Several of the kids even called me out on it near the end of the year. This only adds more fuel to the fire for next year. Specifically, with all this work on PBL and discussion-based learning, I’m now interested in exploring the intersection of those two strategies and the racially relevant pedagogy that I hope to espouse. I have a few books lined up this summer that I hope will help me think more about this.
  • I’ve begun toying with the idea of planning and organizing a ‘Math Night’ next year.  This is an exciting idea that I hope I can follow through with.
  • For the first time ever, I had my kids meaningfully write about the mathematics they were learning this year. It was a ‘metacognitve journal,’ a way of reflecting on their thinking about a particular problem that we solved. I only did one in late spring and it helped me realize that critical reflection like this journal must a component of my classroom moving forward, especially as I move to intentionally develop problem-solving skills in my students. I dramatically underestimated how long it would take me to grade them! Agh!
  • I checked no homework for credit this year. Sadly, this meant that the majority of kids didn’t do their homework. Am I ok with this? No. But I’m still not ok with checking it each day for points. #teacherproblems
  • This year I thought a lot about public and private school collaboration. I spent full days visiting both Phillips Exeter and Horace Mann schools. Both were worthwhile experiences. I hope to continue this work next year – especially with Horace Mann because of proximity.
  • In the spring, I was very close to having a parent observe my class. I was inspired by an NYCDOE survey that asked whether I’ve had any parent visit my class this year. Although it never happened, for the first time it made me seriously think about the inherent boundaries that exist between parents and the spaces in which their children learn. I may be opening a can with this one, but I would really like to have at least one parent in my room to observe instruction next year.
  • I got away from standards-based grading this year. As a result, I wasn’t able to help students identify and understand their strengths and weaknesses in any sort of accurate way. This should change next year.
  • Recently, a colleague of mine just spoke about getting kids to ask more questions in class and he mentioned the use of sentence starters. I’ve been exposed to them for years and never used them. I think they’re so inviting and accessible for students and can help elevate how they articulate themselves. I would love to try them next year.
  • I taught a math elective this year called ‘Explorations in Mathematics’ that started off strong but fizzled out after the first semester. Much of this had to do with programming.
  • One of the non-teaching highlights of the year was chaperoning a trip to Denmark in April. Along with 5 other teachers, guidance counselors, and administrators, we accompanied a wonderful group of 24 students on this unforgettable overseas adventure that included homestays with Danish families.
  • For the 2nd year in a row, I was nominated for a Big Apple Award. I don’t know why I was, but I am grateful and humble nonetheless.
  • I helped my school adopt the Math for America PLT model as part of our Monday PD cycle this year. This was a useful and engaging way to give teachers a direct say in the PD they experience. As far as I know, a first for school too.
  • I submitted the two remaining components of my National Board Certification. In December we’ll see what Pearson thinks of me.
  • Being the second year at my school, I found myself considerably less stressed about everyday happenings than last year. My sense of community grew.

 

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PBL v2

So my yearlong experiment with problem-based learning has concluded.

After attending Exeter Math Institute last summer, I decided to overthrow my units and use problems as the foundation of how my kids learned each day. Throughout the course of the year, week by week I wrote a bunch of original problems, edited others that I already had, and stole the rest. In the end, there were 349 problems which I would classify as mediocre at best. These problems (and other practice, including DeltaMath) were the vehicle that my students used to learn algebra 2…and be adequately prepared for the Regents exam on June 14. The 12 whiteboards wrapped around the walls of my classroom provided the platform for my students to dig into these problems each and every day.

It was idealistic, but this change was inspired to help my kids be more independent and interdependent problem solvers. I took a huge risk because I didn’t know what heck I was doing. Despite some early struggles, I stuck it out because I believed in the process and knew that real change would take time. I constantly adjusted to support my kids as they pushed themselves out of their comfort zones. There were tears. There were instances where I felt like I bit off more than I could chew. Despite support from my admin, I still felt alone because I was doing something so different, so radical, from the rest of my colleagues. It wasn’t their fault. I was hard to relate to. Mine was a messy, nonlinear pedagogical stance to teaching mathematics and, as such, others stayed away. In the end, although folks wished me well, I had no one to talk to about the day-to-day, nitty-gritty roadblocks that I ran into. Other than an independent trip to Exeter and an awesome visit from one of their teachers, I worked in isolation. This only intensified my struggles.

Anyhow, the result of all this was an uplifting, rejuvenating, and stressful school year. I have some major takeaways that will inspire next year’s work, PBL v2. I’ll let them breathe here.

  • Don’t think that students will value my perspective on learning simply because I say its valuable and worthwhile. There was going to be a natural struggle involved with learning through problems, but I did a poor job of setting them up for dealing with it. Next year, the first 1-2 weeks will be all about helping them meet my expectations. This may include modeling how they should approach the problems using prior knowledge and independent research, encouraging uncertainty, showing them how to document their thinking, and how to use classmates as resources. I also want to present the research behind how and why I’m structuring their learning experiences.
  • A more diverse set of instructional routines to discuss problems. This year I used student-led Harkness discussions, rotating stations (group speed dating), Desmos Activity Builder, structures unique to the specific problems, and traditional, teacher-directed lessons that focused on anchor problems. Before the year began, I was worried about having the right problems as they are so pivotal in this setting. As the year progressed, I realized that I overlooked the pedagogy behind implementing the problems. Even with a focus on small groups, uniform Harkness discussions simply won’t cut it for a class of 30 every day. While it is and will continue to be a foundation of what I do, students quickly tire of the routine. I’m also thinking that exploring the use of protocols may be worthwhile.
  • Better engagement during group work. On most days, I gave students lots of freedom when discussing the problems of the day. For much of the period, they were on their own to construct their own (with guidance from me) understanding of the problems and the related concepts. Trust was baked into each day’s discussions; their thinking inspired the success we had each day. Some days were great, but on plenty of occasions, they did what teenagers do: be lazy. I’m wondering what else I can do to foster more consistent engagement during these small group discussions.
  • More metacognitive journaling. I did one in the spring and I liked it. They chose a recent problem and analyzed their own thinking around it. They told the “story” of how they arrived and understood the solution. They were a lot to grade though. Maybe one per marking period?
  • Be better with parents. I need to have a much more transparent and stronger relationship with my parents. I almost got around to inviting one into my classroom. Nonetheless, I need to clearly communicate how students are learning, why it’s important, and how I will support them along the way. Some parents had reservations about my approach and they definitely didn’t hold back from sharing their thoughts.
  • Use standards-based grading. Because I didn’t have explicitly defined units for students, when they encountered the problems, they didn’t have the crutch of knowing they were working on “section 2-4,” for example. They needed to use the context of the problem (and work done on previous problems) to discern what to do. I really like this because it made more challenging for students, but it handcuffed me when because I couldn’t find a way to accurately identify and document their understandings on exams, other than a vague, overarching percentage like “74%.” I thought deeply about this a lot and decided I will need to sacrifice a little PBL to assess meaningfully and authentically. Next year, I still don’t see having units, but I do think I will attach concepts to problems, at least to start. At the start of the year, when I give them their problems, I will also give them an exhaustive list of concepts that the problems elicit over the course of the year. I will number the concepts (eg 1-52) and each problem will have an indicator showing which of the concepts the problem connects to. Maybe over time, I can move away from this and students can make the problem-concept connection on their own. Either way, with well-defined, itemized concepts, I should be able to assign qualitative measures to each student’s understandings (needs improvement, developing, proficient, mastery). Whew.
  • The above would allow for more meaningful retakes of exams. With “corrections,” this process was a joke this year. There was no meaningful learning and we were all simply going through the process of applying an informal curve to their exam grades. With SBG back in the fore, this means that my post-exam procedures will look more like last year.
  • A nonlinear approach to learning mathematics. A huge plus of the PBL as I implemented it was that it gave me the opportunity to interleave concepts like never before. Not only did I marry concepts together in natural ways that are harder to achieve with discrete units, but I was able to space out concepts over the course of several months when it would traditionally be crammed into a three-week unit and subsequently forgotten. The most obvious example of this is trigonometry. We did many problems over the course of four months, each being a small step that got us closer to learning all the concepts from the unit. All the while, students were learning about other concepts as well. I can definitely improve my sequencing of problems but, again, since concepts learned are nonlinear, this makes recall more challenging for students and harder to forget.
  • One formal group assessment per marking period. These are just too valuable to not include on a regular basis. The kids love them. Plus, real learning happens during an assessment! They include two-stage quizzes, group quizzes, and VNPS quizzes.
  • Assign problems that will be formally collected and graded. In addition to the daily problem sets that are worked on for homework and usually discussed the following day, I want to give one meaty problem that’s due every two weeks. I’ll expect integrity and independent solutions, but students are free to research how to solve them using whatever resources they want. This will hopefully promote deep thought and a formal write up of math on a complex problem. I would love to have students type up their responses. I foresee using the Art of Problem Solving texts to find these problems, at least to start.
  • Using DeltaMath as a learning resource, not just practice. I was surprised by how big of a role DeltaMath played in my students’ learning. Given the lingering Regents exam, my kids relied heavily on the ‘show example‘ feature of the site to explore and solidify key ideas brought out by problems that we discussed during class.
  • Check homework randomly, I think. Because I didn’t check homework at all, the majority of students didn’t do it. Since the homework consisted of problems that were the centerpiece of following day’s discussion, it was a necessary component of the class. I wanted students to internalize that if they didn’t do it, they would be lost the next day. It’s ok if they didn’t understand, but they had to try. Well, that didn’t happen. Most kids just tried the problems in class the next day and set us all back. A colleague gave me feedback that students will give priority to things that have incentives, like points. I get it, but refuse to accept giving a carrot for homework. To compromise, I may check the homework of a random set of 5-7 students each day. Any student is fair game and, by the end of the marking period, every student will have roughly the same number of homework checks. I had tested this out in May and I think it triggered some initiative amongst students to do homework. I also like the idea of possibly administering a homework quiz that’s based on the previous day’s homework. If they didn’t do the homework, they’ll struggle…and I’ll offer tutoring for them to make it up.
  • Deliberately teach problem-solving skills. I had a flawed expectation that students would somehow become better problem solvers by simply solving a bunch of problems and have discussions about them. While that happened for some, at the end of the year most of my students grew minimally when it comes to their actual problem-solving abilities. I’m still trying to figure out exactly how to get better with this, but I know purposeful reflection will play a big role. I will also need to help surface specific PBL skills for kids. I want to bring in the question formulation technique and problem posing. This is still up the in air…and I’m reading a lot about this right now.
  • Be uncomfortable. It’s a great thing. In past years, I unequivocally strived to have students that were comfortable and at ease with everything we did in the classroom. I hoped they would find what and how they learned as easy and unproblematic. If I’m frank, I did a pretty good job of that. This year, I landed on the cold realization that, in many ways, my students should be uncomfortable. How else will they grow? As this post showcases, I led by example.

That’s all I have for now.

A lingering thought. Years from now, I’ll probably look back at all this and realize that I was fighting a losing battle, that I was too idealistic, that my time with students could have been used more effectively. I’ll look back and see how foolish I was. Yes, foolish to think that I could somehow establish a subculture within my classroom of independent and interdependent problem solvers that relied more on themselves than on the teacher. A subculture that places little value of remembering a formula or procedure for a quick fix, but instead focused on the mathematical relationships, collaboration, productive struggle, and prior knowledge to own what and how they learned. I’ll laugh at myself and shrug it off as me being ignorant. I’ll recognize that my goals were too lofty and practically impossible in a day and age of teacher-driven learning, high-stakes exams, and point-hungry motivations.

With this in mind, I can’t help but quote Maya Angelou: “I did then what I knew how to do. Now that I know better, I do better.”

 

bp

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We have a lot to learn from skateboarders

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Last week I was sitting in the park watching a skateboarder. He was alone and clearly practicing his moves, trying to get better at a variety of different stunts. I must have watched him for 15 minutes and, I estimated that he nailed about 20% of his attempts, probably less.

As I watched him fail over and over again, I couldn’t but realize the rarity of his public display of failure. But in most other situations where we are around others, let alone perfect strangers, this is far from the norm. Rarely do we openly display our imperfections for everyone to see. If anything, we hide them to protect our image. Yes, in the public sphere, your weaknesses are yours and yours alone. We are only allowed to put our best foot forward. Otherwise, we’re uncomfortable and sometimes embarrassed.

Not skateboarders. In the skateboarding culture, public failure is not only commonplace but its desirable. Falling off your board is a necessary means of getting better, no matter if everyone in the park is there to witness it. You do it. You inherently admit weakness. Sure, getting better at maneuvering a skateboard requires lots of room and public spaces (like parks and empty parking lots) are the most convenient and accessible places to do so. Nonetheless, the willingness of skateboarders to outwardly showcase their shortcomings is fascinating to me.

My intrigue is heightened when I think about the culture of education in which I function. Students (and teachers) work in a system that often downplays struggle, placing lots of emphasis on correct responses. Case in point, its a regular occurrence for students in my class to erase their whiteboard work that hasn’t led them to a correct final answer. They refuse to be wrong publically — especially when all eyes are on them. This is certainly a reflection of my own inability to champion mistakes and struggle in my classroom, but its also representative of how formal schooling has made our kids feel and think about being wrong. If you don’t land on the correct answer, it’s not worth showing your process publically. No, you must keep that valuable part of learning all to yourself until you arrive at a “correct” answer when, only at that time, it is acceptable show your thinking.

There’s a lot we can learn from skateboarders.

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