Wednesday, December 28, 2011

School of One

I've recently been asked to help develop a pilot "School of One" program in our district. For those of you not familiar with the project, take a look here. Basically, here's how it works.
  1. Student comes into class and looks at their "playlist" - their options for what to do today.
  2. Student makes their choice. This might be small group work, tutoring on a computer, direct instruction, etc.
  3. Student gets started.
  4. Student takes short formative assessment.
  5. Teachers feed results into algorithm for all students.
  6. Algorithm output lessons and activities to be prepared.
And repeat.

The more I think about School of One, the more ambivalent I am. There are some really amazing ideas and opportunities here, not the least of which is that students are given a higher degree of control and power over how they spend their time. To me, this is the benefit. There are others, to be sure, but I think that they all really revolve around this. Choice allows education to become more personal, more meaningful.  Instead of being instructed exactly the same way as your other 29 classmates, your path is unique, based on who you are, what you're good at, and what you want to do.

I am excited to be involved, but not without some concerns and doubts. Rather than approach these as reasons not to help, I'm looking to these as the points I'll want to make sure are addressed by our work. It is the reason I am writing this post and the reason I hope you will help!

Feedback and assessment
As feedback has been one of the items I've been focusing on this year, this one concerns me. The only assessments built in are the short formatives given to student at the end of each lesson. The results are then fed back into the algorithm. If the student has demonstrated mastery, they move on. If not, they'll have to do a lesson based on the same objective again. Students involvement in this process is minimal, and there is essentially no feedback given to students. I don't like the idea that we just have a student spend another full lesson on the same content without any feedback other than the fact that they didn't get it yet. We need to do better than that.

The algorithm
This algorithm is basically supposed to work like Pandora or Amazon's suggested items. Based on your history, the available resources, and people like you, the algorithm suggests the lessons that will be the most productive for you. Without a doubt, a clever idea. There's a lot of faith placed in the algorithm, and yet remarkably little is shared and public about it. It was developed by a for-profity ed company, Wireless Generation, which is now owned by the News Corporation. That in itself scares me a bit, but I can get past that because we're almost certainly not going to be able to use it.

What scares me about the algorithm is its potential to render a teacher's observations and professional judgment inconsequential. I do not want the role of the teacher to become something like a machine operator. The entire process needs to be within our control, which includes the inner workings of the algorithm. My fear is that the central piece of School of One, the algorithm, is a proprietary blackbox.

The algorithm needs to be open source. It needs to be available to anyone and everyone, free, and without any restrictions. This process and how lessons are sequenced and chosen cannot be a proprietary secret if we really think that this model has the potential to change how we teach. Do not make this simply a tool that teachers use. Make it one they control.

The big picture
Each day's lessons are chosen based on a fairly specific roadmap of objectives that need to be covered. Even though the students path will be personalized, I'm a little anxious that we're not going to be taking students off of the path enough to really show them the world. Mathematics is much, much more than a series of facts and processes. It's a way of making sense of the world. I'm not sure how we're going to roll this in, but it will be a failure if we don't.

Friday, September 30, 2011

Sitting in the Back

In the last week or so, I've tried a new technique when I pose a question to the class, or want the class to solve a problem together: I sit in the back.

Typically, when I pose a question or a problem to the class, there are a few things that impede learning. First, the focus is still on me, so most of the students are just waiting for me to give the answer. Second, whenever a student does contribute an idea or question, it is directed at me. Not what I'm going for.

So, this week I wanted the class to work though a proof together. I drew the diagram on the board, asked the question, and then sat in the back row. This helped in two significant ways. For one, the focus was no longer on me; it was on the problem on the board. There was also a clear implication that with me sitting in the back - that this was their problem, and I'm giving them the time to do it (instead of the usual wait-long-enough-and-Mr.-Krenz-will-do-it-for-us game).

Additionally, the discussion of how to do the proof changed significantly. Questions and ideas were now being addressed to peers and the rest of the class rather than me. It wasn't me piecing together different students' correct responses to put a proof on the board with the false impression that the students did it. The students were offering ideas, critiquing, and collaboratively deciding on the next step.

When they completed a solidly challenging proof with almost no assistance, which they have been struggling with, I was still sitting in the back row. And I could not have been more proud of them.

It isn't perfect. I still give some guiding hints from the back, which I'm going to try to cut back on. The discussion can be confusing and solutions offered may not be correct. The path that is taken is not necessarily the most direct. But these are good things. Students start to understand that the perfectly linear proofs and thinking in the book isn't the way you need to think. I'm not sure it's the way that anyone thinks.

I'm sure other teachers have tried this. If so, I'd love to hear your experiences. If not, try it. Sit in the back and let me know what you think.

Thursday, September 22, 2011

What Do We Change?

This is long, and I'm unapologetically not going to bother proofreading much. This post is more or less a free write reflecting on the most intense day of my teaching yet. A day in which I didn't teach any math. I wrote this for myself, but I'd love to get some feedback.

This is my first year teaching, and my first experience teaching geometry. I have three standard, blocked geometry classes, and it is hard. The pace is quick, most of my students are freshmen, and we're having trouble "covering" what we need to at a pace necessary to finish.

I introduced proofs for the first time about a week ago, and we had a test yesterday. Scores were, well, less than what I was hoping for. I expected trouble with the proofs, which I found, but I was more concerned with the basic lack of understanding that I was seeing. The core pieces of the test - conditionals, converses, inverses, contrapositives, biconditionals, and the properties of congruence and equality - were simply not there. It's not that the students could properly interpret them and use them to judge and create. They failed to demonstrate a basic recall and application.

As a new teacher, this is difficult to deal with. It's frustrating and depressing. Without a doubt, part of this reflects my (in)ability to effectively teach the material and skills. I think this is more devastating to me than it is to my students.

However, I also know that this isn't all me. For one, I know that my students need to take responsibility for part of this. The choices that they're making in class aren't often the ones that will help them learn, and I think I need to teach that. Learning does not just happen; it is a choice that you make. I will do everything I can to make that a positive and helpful experience if you do choose to learn, but I can only do so much. I need to help my students understand that they are more of the class than me.

So, the response. Even though our schedule is a breakneck pace, I decided to take a full block - 90 minutes - to talk about how we do class. Preparation, learning, studying, review, interaction, behavior, everything. I wanted to do something to help them realize why we are in class, what the goals are, and what drives my decision making process.

So, rough lesson plan:

I asked six very basic questions that only require remembering the information absolutely necessary to doing well on the test. This is basically the lowest bar. I then read off the answers, had students mark their own answers, and then asked them to think about how they did. We talked about Bloom's taxonomoy and the different levels of thinking.

Passed back tests
I gave student a few minutes to go through their tests, thinking about what we had done so far. I explained that most scores were 5's and 6's. I use an 8-point standards-based grading system. A 5 means you demonstrated only a slight understanding of the concept, and a 6 means you're on the right track, but there is still a significant gap in your knowledge. So we have a ways to go yet.

Free write
I gave students about 4-5 minutes to write whatever they were thinking and feeling. Frustration, anger, reflection, ideas for improvement, whatever. I said that I wouldn't collect, so they could write anything. During the third block, I gave the option to turn it in, with or without a name, and I was surprised at how many students wanted to turn it in. They felt a need to be heard.
Next, students got in their groups and had a brief discussion about what they felt comfortable sharing. The discussion was reserved. While some students were happy to talk, I think many were feeling quite vulnerable and weren't entirely comfortable.

Word wall
On the whiteboard, I put a heading of "Thoughts/feelings", and encouraged students to write anything they wished relevant to this class. This was mildly terrifying. At first, only one or two students would slowly walk up. Then a few more, and then more. The atmosphere became markedly more relaxed. Students were seeing that they were not alone - others shared the same ideas, thoughts, and feelings, and I think it was comforting.

Then we spent a few minutes discussing what was up there. I summarized what I could, and students added a few more thoughts. Discussion was starting to roll.

Next, I had students brainstorm ideas for improving things. Class structure, assessments, practice, homework, behavior, teaching - anything and everything was fair game. Groups recorded their ideas, and then as a group, we transferred the ideas to the whiteboard up front. Once a few ideas were up there, more hands and ideas started popping up. I was impressed with the thought that students gave this.

Next, I offered my thoughts on what I was seeing. I explained why a few things were non-negotiables, but left it open for discussion. For example, I do not review immediately before a test. I explained that this is because I try to base every decision that I make on two things: does it help learning, and does it promote accurate assessment. We don't review right before a test because it's not testing true learning - it's testing short-term memory. Not all students liked this, but most understood.

Again, I was impressed with my students' engagement during this discussion. We were truly discussing learning and assessment. They were bring up things that they liked from previous teachers, and then we were discussing it in terms of "will this improve learning?" and "does this promote accurate assessment?" I've got a lot to think about here.

The Plan
To wrap things up, I asked each group to come up with three specific, concrete things that we could change in the context of our discussion. Each group presented their three, and then we voted as a class what three things we could change. There was a remarkable similarity between the three blocks.


This was an incredibly intense day for me. I spent 4.5 hours discussing everything about how I teach. I am emotionally exhausted. It was incredibly powerful, but my energy is gone. 

At the end of my third block, I was speaking to a few students in the last two minutes, and they asked me some innocent sounding questions that really capped off the day:
Why did you decide to teach? Are you sure you like teaching? You should have more fun!
I didn't have time to fully respond, and the questions were asked with true interest. I don't think they were suggesting I shouldn't teach. I think they were picking up on the fact that this job is hard, and this day especially was draining. In the 30 seconds I had, I said that I had been having this discussion for 4.5 hours today, and that it was scary for me. I was letting them write and say anything about my teaching, and I think they understood it.

After the class, I took a walk around the school to let things soak in a bit. I'm tired. I don't know exactly what to do. But, I do know one thing. I need to show students my love. I do love this job, and I love my students. I don't think I share that. Enthusiasm and spirit are tough for me. I've always been a rather reserved, introspective person. People who get to know me learn to pick up my emotion and excitement, but I need to do more than that. But remain who I am.

I need to figure out my way of showing students my love. For them, for my job, for my life.

Tuesday, September 6, 2011

When The Detour Has A Detour

I was driving to pick up my wife today, and the main road I needed was closed for construction. So I took the detour, and then came to a road completely closed off for an emergency. I then took my own detour.

As a new teacher, naturally all that I think about is teaching right now, and I thought this relevant. In the classroom, there will be detours. Sometimes they'll be predictable, sometimes they'll be surprises. The route may change, we may get lost, and maybe we'll see some things we didn't expect to. However, as long as I know where we are going, we'll get there.

I like that.

Friday, August 26, 2011

Doing Mathematics

I had a thought this morning biking home from school (our first day is next Thursday). What is the goal I have for my students? Well, to learn mathematics. In order for that to happen, I need to maximize the amount of time that students are actually doing mathematics. Everything I plan should be centered around this.

This begs the question, though - what is "doing mathematics"? First, it's easy to list a few things that it is not. Doing mathematics is not:

  • taking notes
  • listening to me talk
  • drill & kill assignments
  • taking tests
Already, so there is one guide post - minimize the amount of time doing these activities.

As for doing mathematics, I like the way that Keith Devlin describes it:
"Doing math" involves all kinds of mental capacities: numerical reasoning, quantitative reasoning, linguistic reasoning, symbolic reasoning, spatial reasoning, logical reasoning, diagrammatic reasoning, reasoning about causality, the ability to handle abstractions, and maybe some others I have overlooked. And for success, all those need to be topped off with a dose of raw creativity and a desire - for some of us an inner need - to pursue the subject and do well at it.
However, I'm having a difficult time describing exactly what "doing mathematics" means. In my mind, it's more of "I know it when I see it", so I need to work on clarifying what it means. Some activities that I think do fall under this umbrella:
  • Solving novel problems
  • Student-generated questions
  • Investigations
  • Cooperative groupwork
  • Communicating reasoning and thinking
  • Proving conjectures
  • Finding patterns
This list could go on and on, but my takeaway has been this. All planning should be focused on maximizing the amount of time that my students are doing mathematics.

Thursday, August 18, 2011

Making Assessment Part of Teaching

I spent the first part of the summer thinking about whether I should give standards-based grading a shot my first year or not. Actually, that's not true. I spent the first month of my summer in Germany and Spain. After that I started thinking about grading.

My wife and I hiking up to Schloss Neuschwanstein

Anyway, all it took was a little nudge from some teachers on Twitter along with support from my chair and administration. Over the past couple of weeks, I've been working on designing my grading system, and discovered a major reason to implement SBG: it actually gets me excited about assessment!

During my student teaching, I felt that assessment was one of the worst parts of teaching. A necessary evil. I loved teaching, but when it came to giving tests and passing out only vaguely meaningful grades, it was just something I had to make it through. And then I had to deal with students negotiating for another point or pleading for extra credit. We were never discussing their learning, we were discussing how many points they had and how many they needed. Ugh.

Now, when I'm working on designing my system and assessments, it feels more like teaching than test giving. The focus is specifically on what I want students to learn and their progress. Hopefully the conversations will mirror this.

I think this alone is a good enough reason to try SBG.

Monday, July 18, 2011

The Coming Year - Technology In My Classroom

In a little more than a month, I will begin my first year as a high school math teacher. Having a vague understanding of how challenging it is going to be, as well as knowing my tendency to take on too much, one of my goals before the year starts is to have a plan for the technology I am going to use, its purpose, and how I am going to incorporate it into my teaching.

In choosing which technologies I will use, I am using the following as my requirements:
  • Free to use as in cost. Truly free software is a bonus.
  • Cross-platform. Works with Windows, Mac, and Linux without a fight.
  • No downloads or installations required, other than a reasonably modern browser.
  • Limited number of registrations and sign ups.
  • Ease of use. I want to teach math, not technology.

That being said, here are the weapons I plan on brandishing:

Absolutely amazing mathematics software designed for teaching and learning mathematics. While it's not always the most intuitive software to use, its dynamic and interactive nature make it a powerful tool in the classroom. There are loads of tutorials and ready-to-use materials on the main website.

I absolutely agree with Conrad Wolfram that teaching a bit of programming is crucial in teaching mathematics in the twenty first century. Python is my programming language of choice for many reasons. Also, Google's Exploring Computational Thinking is a great resource (and they even posted one of my lessons from my student teaching!).

If you have never used Google Docs before, I highly recommend it. I often hear it described as Microsoft Office in the cloud, but it is much more than that. It puts collaboration and sharing at the center of the process. Students are able to work on the same document at the same time, chat online together, track who made changes and when, and so much more. And it keeps getting better.

For most of the summer, I simply assumed that I would be using Twitter, but the recent (beta) release of Google+ has been rethinking that. I love the idea of back-channeling, communication, and collaboration inside and outside of the classroom, as well as giving students a different way to contribute. Circles, hangouts, and sparks (Google+ features) are promising features. Here is an evolving presentation on some potential uses of Google+ in education (and a great example of Google Docs in action!).

The math and tech geek in me is excited. These tools have the potential to engage students with mathematics at a level far beyond my high school experience, and that was not all that long ago.

Oh, and please leave comments! I would love to hear your thoughts and suggestions and learn about new resources.

Next post: How I plan on using technology for continual professional development and reflection.