reflection – Page 4

My midyear report card

So my midyear report card results are in. As always, they’re a mixed bag. Here are a few comments directly from the kiddos. First, the good:

I like the amount of time we have to explore math in the class. It’s not just sitting down listening to a teacher all period.
I like how resourceful we are and a teacher isn’t always 100% necessary.
I like how we get to put up the problems on the board and are allowed to go to other tables to compare answers or to ask help.
The way we learn from each other’s work.
I like how the students have a right in their teaching in a way.
I have the freedom to walk around and don’t have to be confined to my desk.
I like the freedom in the class and learning from the problems rather than cumbersome units.
Nobody judges others on their work.
We focus on different types of problems that all connect to each other.

And the not-so-good:

It can be improved by actually teaching a lesson so that the lesson can be more clear.
I think there should be more traditional teaching.
You can try to lead the class a bit more rather than the students teaching it.
More lessons and notes rather than just problems.
Topics can be gathered into categories by Mr. Palacios so we know what we’re dealing with.
You should talk more.
Our class should try to identify problems or topics we are confused on therefore allowing you to step in and teach the topic.
I would really want for you to take charge of the class instead of the students.
Teaching in front of the board like once a week.

Notice a theme?

Based on the comments, it’s clear to me that my students are uncomfortable with the high levels of autonomy that I have afforded them. Well, let’s talk about the structure. It doesn’t happen everyday, but usually I assign 5 problems for homework (designed as learning experiences, not traditional practice). I expect them to come in the next day, put their work to the problems up on the whiteboards and thoroughly discuss the solutions they found in small groups. While this is happening, I assess their thinking and step into their group’s conversations to help drive the learning. For the most part, they can move freely about the room, but at times I will strategically move kids to different groups, a.k.a. visible random grouping. Afterwards, I sequence the presenters for the 5 problems and a whole class discussion around the solutions to the problems closes things out.

Through this structure, I have tried to minimize the amount of direct instruction that I do all the while interleaving mathematical ideas through problems. I’ve wanted student discussion to completely direct the learning and the problems to be the vehicle that makes that happen. Damn, that sounds so good in theory. I know in September it did.

Admittedly, I probably went a little too gung-ho about the student-driven, discussion-based learning. It was just so tasty. But I could have taken baby steps. I could have tried it out for a few lessons, learned its flaws and iterated on a smaller scale. But, no, I had to go all in. And I’m drowning because of it.

But all is not lost. The kids really love working on the whiteboards and freely getting help from others in the class. This is liberating for them. They aren’t confined to their seat and they appreciate this. The whiteboards give them an outlet to collaborate, which they have been eating up. If nothing else, at least they are engaged. They just need more guidance from me. And the problem-based learning has enabled the content to be interleaved and naturally spiraled, which has been so worthwhile for long-term learning. For the most part, the kids have gotten over not having discrete units.

So where do I go from here? Well, after seeking therapy from my colleagues all day, I think I’m going to begin incorporating “anchor” problems throughout the problem sets I give students. These should take a full class period to solve and I will help guide students through them with direct instruction. I hope that they will serve as a shared experience that future problems will connect to and provide them with a basic understanding of a concept.

In addition, I want to do some problem strings with them as a whole class. Again, this will serve as another shared problem-solving experience that can allow for in-depth exploration of future problems…and more direct involvement of myself.

Every few days at the start of class, I plan on giving 5-10 minute, unannounced “checkpoints” to check for understanding on what we’ve been learning. A huge weakness of semester one was not giving the kids opportunities to validate their learning. This resulted in them feeling confused and thinking they weren’t learning. Plus, I didn’t measure where they were in their understanding of key ideas until an exam. Not good. The checkpoints will inherently result, again, in more direct intervention by me and will help me adjust how we move forward.

Lastly, we just need to have more fun in class. Things got somewhat tight and tense near the end. I hated it.

I’m going to start day 1 of semester two sharing all this with my students. I want them to hold me accountable. I’ll share my reflections and ask them to reflect on what they can do to make the second half of the year better than the first. They will write a few paragraphs and submit them to me as I’m going to hold them accountable, too. Many of them don’t do the assigned homework each night because I don’t give points for it, so I hope to pull this out of them.

My first (and second) memory of learning math

Some time ago Wendy Menard got me thinking about my first memory of learning mathematics. What was it?

Its two things, actually. Both happened in fifth-grade. My teacher was a redheaded man with a great beard, Mr. O’Discoll (a.k.a Mr. O). Great guy, great energy. He made learning fun. He even played me and a couple of my friends in basketball at the end of the school year in the school gymnasium. We lost 100-98. I’ll never live it down.

Anyway, I digress. Back to learning math. The first vivid memory I have of learning math is the multiplication worksheets that Mr. O would give us. He would time us. I don’t recall it ever being a race or competition to finish, but I do remember being pressured by time constraints.

The second memory comes from an exam that I took in his class. I don’t remember the math that was on it, but before the exam, I remember him telling us to always check our work after answering the problems. Well on this particular exam, I remember following his advice for about 3/4 of the exam, finding and fixing several mistakes, but then stopping — thinking that I had already done a great job. I was presumptuous. When Mr. O handed the exam back, I had a perfect paper — up until where I stopped checking my work. I had so many errors in the unchecked portion of my exam. I distinctly remember a comment he wrote directly on the exam: “why did you stop checking your work, Brian?”

Sometimes I think about how these two distant moments from my childhood have impacted how I teach mathematics.

Firstly, I teach mathematics the way I was taught math. I think this is the norm for so many teachers regardless of the subject — and it’s not a bad thing. It’s reality. In my case, drill-in-kill was what I experienced early and often, like in the case of Mr. O’s multiplication worksheets. This experience brainwashed me equate math with speed and correct answers…and this is very evident today in my teaching. I try hard to combat this, but I am not the most inquiry-based math teacher. I struggle to move beyond test-prep style learning. Its a product of the culture in which I teach, yes, but its also a direct result of the math education I received. This bothers me.

Secondly, through the years I have always been prone to mistakes when it comes to learning and teaching math. I consider myself a slow thinker, but I don’t want to be. Thanks to my fifth-grade class (and others no doubt), I want to get it on the first attempt. Sometimes I feel like I have to get it on the first attempt. Whether it is typos in handouts, mistakes in grading, or my blunders in planning thoughtful mathematical experiences for my algebra 2 kids, I always find errors that could have easily been edited had I not been too lazy or overconfident to dig deeper. Heck, even my typo-laden tweets are evidence of this. Mr. O’s exam and his advice are always in the back of my head. I do my best to follow his advice, but I fail much more often than I succeed.

Growing pains

Today a student in my class was brought to tears.

She cried because of my teaching. Specifically, the problem-based, discussion-based learning that I’ve adopted has been troubling her. She said that she was lost and hasn’t learned anything so far this year. Knowing the student, I politely disagreed, but she was having none of my excuses. On top of this, she’s also missed several days because of an illness. She told me more – and then the tears came. She cried, hurting because of the confusion and emptiness she felt for her math class.

It was after class and I did my best to console her, but I didn’t really know how to react. It’s not every day that a kid cries in my classroom. I tried to reassure her that I’m not out to make her life miserable, that I was on her team, that she should trust the process, that she needs the teacher far less than she thinks she does, that I would never abandon her or any other student. I offered tutoring.

Tutoring?? The girl is crying!

It’s needless to say, but my response failed miserably.

If I wasn’t already aware, this powerful moment shed light on how my own growing pains with PBL have transferred to the students I serve. I’m learning to teach again. They’re uncomfortable and worried. All in all, it sucks.

Afterwards, I couldn’t help but wonder whether or not overhauling my teaching is really worth it in the end. Do the perceived long-term benefits outweigh the hopelessness that may be creeping into the minds of my students?
bp

My experience at Phillips Exeter Academy

To build upon my experiences this summer at the Exeter Mathematics Institute and to improve the newfound problem-based classroom, yesterday I paid a visit to the renowned Phillips Exeter Academy in Exeter, New Hampshire.

I observed six mathematics classrooms, had a private meeting with some students and had lunch with a few Exeter teachers. In between all of that, I also had some time to roam freely about the leafy campus, spending a good chunk of time at their library. I was on campus from 8am to 5pm.

I tend to process experiences pretty slowly. I say that because I know that I won’t be able to fully synthesize this visit for at least a few days — especially after I’m back in my own classroom. Nonetheless, I’m going to get out my immediate reactions with what else? Isolated bullet points whose main ideas are scattered and disorganized. Clearly, I still blog for myself.

This place is very old. Some of the classrooms looked like they hadn’t been renovated since the 1800’s (see photo above). The look and feel aren’t for everyone, but I found it charming.
The teachers were so welcoming. Each one mentioned my presence in the room and had every student introduce themselves. I shared the purpose of my visit and thanked them all for allowing me to share their space for the day. I got the vibe that they are accustomed to having visitors almost every day, but I still loved their transparency. One of the teachers valiantly tried all period to get my last name right until the moment I walked out of his classroom. It was a small thing, but I really appreciated that.
The students were highly motivated. I fully expected this. Maybe what I didn’t expect was how helpful and respectful they were. I got lost several times while on campus and each time I was politely helped and redirected. They also gave me some student-driven advice on how to encourage buy-in from my own students in this type of learning environment.
Most all of the students I spoke with came from a traditional learning setting and they all enthusiastically preferred the problem-based, discussion-based environment that Exeter has pioneered. Their families are also paying upwards of $50K a year for tuition, so yeah, there’s that.
In terms of instruction, I saw the same thing in every class. The period opens up with kids spending about 10 minutes putting up the homework problems (~7) on the boards around the room. For the rest of the period, the students present their own (or someone else’s) work and/or solution and the class discusses and draws conclusions. The onus was put on the students to push the lesson forward. This confirmed what I’m doing in my own classroom.
Every teacher spent a good amount of time sitting at the Harkness table with the students. I don’t have a Harkness table nor would I want one (give me couches and coffee tables instead), but actually sitting amongst the students during class has been a game changer for me.
With that said, just like in any class, there was some variation to how teachers enacted this structure. Some teachers assigned students to certain problems when they walked in by having their names on the board. In others, students openly chose their own problems. In some classrooms, students could not present their own work; they had to present someone else’s.
In a couple of the classes I visited, when the class got stuck, it felt like the teachers wanted to lecture — and sometimes they did…for like 15 minutes. Maybe it shouldn’t have, but this was surprising given the completely student-centric classroom that Exeter pushes.
This made me think about the problem sets. Every Exeter mathematics teacher uses them and they all did while I was there. If the need for direct instruction was as evident as I witnessed, are the problems scaffolded enough? How much flexibility do the teachers have when it comes to class time? Must it always be problems, problems, and more problems? Or can they filter in occasional days of enrichment based on the concepts learned from the problems?
Desmos was widely used in the class discussions around the problems. Most all of the classrooms had a slick setup with an Apple TV and Airplay where students could easily toggle between whose laptop/tablet screen was displaying on the projector. Other than that, there was no sign of using Desmos Activity Builder or any other structure to help maximize its obvious benefit. Maybe a problem requiring Activity Builder to answer it?
A few teachers used doc cams for student work. Nice.
I constantly saw kids taking photos of the boardwork with their phones. Since my kids can’t use their phones, this affirms why I now have a class iPad and a volunteer that snaps photos of the boardwork and emails it to everyone at the end of each class.
I only spent one day on campus, but if I’m honest, I felt a gulf between the teachers and students in the classrooms I visited. The focus at any given time (even at the onset of the period) was overwhelmingly on the standardized problems and less on the individual students in the classroom. Shouldn’t the problems be supplemented with other materials/resources for different classes based on the needs of the kids? Again, my sample size is incredibly small, so I may be way off.
From what I saw around campus, Exeter seems to be in touch with the revolution that is happening in our country right now around race, gender, sexual orientation, and other social issues. The library was exceptional on this front. At the same time, students of color were disappointingly scarce both on campus and in the classes I visited.