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.

 

bp

 

Factoring trinomials by first rewriting them

So back in December, I gave this problem to my students:

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To my surprise, it got a lot of traction with the kiddos. We spent the entire period talking about it. The idea was for them to see how rewriting a trinomial with four terms helps us to factor it. I’ve used this approach, often called the “CAB method” and used with a large “X” to organize the product and sum of the A and C terms, to factor trinomials for the last several years and I really like it for two reasons:

  • It doesn’t matter if a is greater than 1.
  • It naturally integrates factoring by grouping. Traditionally, grouping is learned after factoring trinomials. But with this approach, I teach grouping before we even see trinomials. Yeah:

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So, yeah, this is all great, but as I was explaining this approach to a colleague, she asked me why it works. It was in that moment that I realized that I had no idea.

Well, it turns out that later that day she went ahead and wrote up a proof of the method.

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I read a quote somewhere or heard someone say that the real usefulness of algebra is the ability it affords us to rewrite things in order to help reveal their underlying structure. This method surely epitomizes that idea.

 

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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? 
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I threw all of my units out the window.

So I’m noticing a trend. it seems like every few years I have an epiphany that causes me to blow up my teaching and rethink what I’m doing in a major way.

Case in point, six years ago I flipped my classroom and realized what is really important when it comes to learning. Three years ago I implemented standards-based grading and learned how to be more analytical with assessment. I now find myself smack in the middle of another major shift in my practice: problem-based learning.

Attended the Exeter Mathematics Institute in August was the catalyst. Experiencing a purely problem-based classroom was new. I had known the “PBL” buzzword for a long time and thought I understood what it meant. I didn’t.

Here’s the workflow: Students explore problems for homework and we use the entire next period analyzing and discuss them. The problems are designed to enable key ideas to organically emerge during homework and class discussions. There are no units. No direct instruction. This is what they call the Harkness Method, I think.

Now I find myself thinking through and sequencing the problems I give my students like never before. This has been pretty fun. All problems need to be inherently scaffolded and since they are now a learning experience (and not just practice), they are everything. Well, I shouldn’t say everything, because the class discussions are crucial too…but without the problems, you have no meaningful discussions.

Without knowing it, I think I have been moving towards PBL for a while now. For a few years, I have been trying to think about sequencing questions/prompts to naturally guide students towards a learning objective — so many of my problems have come from handouts that I’ve developed through the years. Now I’m finding myself weaving these prompts/problems together that is problem-based and not concept-based.

And about the class discussions, that’s something that I feel I’ll be tweaking with throughout the course of this year. I’ve started out doing whole-class discussions and, with classes of 30+ students, I watched as equity quickly crashed and burned. Kids were hiding their ideas and drifting off. I’m now transitioning to smaller groups of around 6-8. I plan to move around the room to guide the group discussions. I’m still debating whether I should give solutions. Maybe towards the end of class to avoid it being a conversation killer?

If I’m honest, I’m worried. I have no idea how this will go and I’m pretty sure that I may have bitten off more than I can chew. I really believe in the process, but this is a pretty drastic change. Because I have no well-defined arrangement to the curriculum, my SBG is gone. And did I mention that I have no units?!

Patience, be with me.

 

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