Tuesday, November 29, 2011

What do you think about while running?

My colleague, Robert Talbert, wrote a post today connecting teaching and running. The analogies he points out are effective and I have little to add of any substance from this perspective. His post did rekindle my interest in sharing what I think about during a run. And it should come as no surprise that I am usually thinking about teaching.

During the first mile of today's run, I thought about the following idea that I wanted to tweet:
This is related to a concern I have about attendance issues in my Introduction to Learning and Assessment class. I am trying something new this semester by not using in-class participation as part of their grade. In fact, I showed this video the first day of the semester and encouraged the preservice teachers to be learners instead of students. Perhaps I ought not be surprised when they take advantage of their new found freedom. The tweet was intended to remind me that learning has no bounds and that I need to trust a process that values intrinsic rather than extrinsic motivation. I tweeted it because I know I might be wrong and hoped that my Professional Learning Network would challenge me to refine my vision.

Halfway through my second mile, the podcast I had on got my attention. I like listening to All Songs Consider while I run. The combination of new music and analysis supports my pace and offers plenty of distractions as I consider, "How might this apply to education?" Today, I was listening to a question and answer session with Wilco about their new album. About 14 minutes and 45 seconds in, a listener asked, "How do you know when a song is finished?" 

How would students respond to this question as it relates to their work? I would guess the answer would typically be, "When the teacher says so?" whether that means the teacher deciding when the work is good enough or when they call "times up." But Jeff Tweedy said that during the making of the album, it seemed to be when all the band members were satisfied with their personal contribution. This idea of learner autonomy is exactly what I wanted to get across in my #TeachingReminder tweet.

It also reflected the focus of last night's outside observation with four of our student teachers, which is what I thought about during the third mile. We do outside observations to remind our teachers in training that instruction is only one part of the Teaching-Learning Cycle. Last night, the question the student teachers shared on their action plan asked, "How can we make assessment and evaluation less stressful for students?" Based on their experiences over the semester, they were concerned with the unhealthy relationships many of their students seemed to have with tests and grades.

I know that some people have suggested that doing away with tests and grades would solve the problem. In fact, we just read an article by Alfie Kohn on this very topic in Introduction to Learning and Assessment.  While this might be a solution, it is one that is curently beyond the student teachers' control. Therefore, we tried to focus on what we could do to help students have a healthier relationship with those grades.

When I finished my run, I saw this common thread in my thinking: supporting learners in developing autonomy. Now, how do I go about doing that? Maybe that will come to me during another run (or in the comments).

Tuesday, November 22, 2011

What's your problem? Part II

In this series of posts, I want to share an approach we use with student teachers to support their development as reflective practitioners. The first post introduced the idea of using an action plan as a way for teachers to identify an area of challenge and seek out support. In subsequent posts, I plan to share examples of this approach in action.

After reading a teacher's action plan, I assemble any resources that might come in handy and then head to the observation. During the lesson, I keep notes on what is going on and ideas, questions, and concerns related to the challenge identified by the teacher. In the example given below, the teacher asked me to focus on formative assessment.
More specifically, she asked, "What types of formative assessments would be beneficial to student learning and how can I use these assessments?"

The notes are a combination artifact of what I saw and stream-of-consciousness of what I thought. I try to keep everything related to the focus provided by the teacher. (Unsolicited advice is an insult.) All of this is shared with the teacher during the debriefing after the observation but I try to attend to a few important points - highlighted in pink.

When I sat down with the student teacher after this particular observation, she started by saying that she felt there was very little formative assessment in her lesson. She was frustrated that because there was so much material to cover there was little opportunity to check for understanding. This seems to be a common challenge this semester.

I responded by pointing out a particular question she asked early in the lesson. The class was discussing issues with story problems on the homework. The teacher asked, "Is your problem the set up or the solving?" There was a resounding "set up" from the students. So the teacher focused on setting up several problems, leaving the students to do the solving on their own. This was a significant moment where the teacher used formative assessment to make an effective instructional decision but she had not recognized it as such.

Part of my responsibility as a coach is to help teachers to recognize things that they do intuitively and make them more intentional. We spent the rest of the debriefing time identifying places during the lesson where using formative assessment could focus instruction. This would provide more time for the formative assessment.

Finally, the teacher is asked to reflect on the experience. Here is part of what this teacher wrote after the observation and debriefing:
For the in-class observation, I was most concerned about assessing my students informally during class. After the debriefing, I feel I was able to recognize moments in my lesson that could have been altered to include more assessment. I feel that I have learned to consider the one or two important question within the lesson. If I recognize the few points that I really want my students to focus on, I can be sure to form my lesson around those specific ideas. Plus, if they are learning new material that progresses from previously learned mathematics (as it almost always does), I can 'skip' the information that they may already be very comfortable with to focus on the more difficult material. ... I feel this observation was very helpful in giving me ideas to use within my classroom to assess my students, as well as learning to focus more on the 'big picture', rather than material they may already be comfortable with.
These reflections often support teachers in developing their next action plan.

Thursday, November 17, 2011

What's your problem? Part I

My problem is that I tend to teach as I was taught. I know that research shows that I am not alone in this, but I thought I had gotten over this hurdle. Since 1990, I have been teaching math differently - and I have the student comments and parent phone calls to prove it. The changes I made as a math teacher were one of the reasons I became interested in mathematics education. Unfortunately, these changes did not transfer to all aspects of my teaching.

Early in my career as a math educator, I began doing observations of novice teachers in their first practicum experience. I remember going into classrooms and watching lessons that failed to meet the principles of good mathematics teaching suggested by the NCTM. After an observation, I would sit down with the novice teacher and play "fix the lesson." I would share with the novices everything that was wrong with their teaching and what they could do to improve it. I left feeling as though I was making a difference in math education, much as my university supervisors must have felt after filling me with their ideas. 

Then, one day I took a deep breath. I had just watched an awful lesson where the teacher read the overhead to her students, who were sitting in rows, and then had them work independently on 30 problems from the textbook. I was getting ready to share my fixes when the novice teacher spoke up.

"That didn't go the way I wanted it to go," she said. "If it were my class, we wouldn't be in rows but in groups so that students could learn from one another. And I wouldn't assign all those problems. I would ask the students to pick out the ones they think they needed practice on. But, you know, I am a guest in this classroom and I need to follow the cooperating teacher's plan. Also, I normally don't read the overhead slides but I saw that Jamal didn't have his glasses and I wanted to be sure that he could participate."

I do not remember how I responded but there was the sense that my points of judgment were being ticked off one-by-one - check, check, and check. My problem had reared its ugly head once again but this time in terms of teaching teachers. I was doing what had been done to me. It was time for another change.

Fortunately, I was introduced to a literacy coach from The Learning Network at about the same time. When I shared my problem with her, she responded with two pieces of information. The first was how her motto, "Unsolicited advice is an insult," influenced her practice. The second was the book, Literacy Coaching: Developing Effective Teachers through Instructional Dialogue by Marilyn Duncan. These led to the thing that most affected my teaching of teachers - action plans.

In chapter two of her book, Marilyn Duncan describes action plans as follows:
The action plan is also a tool to focus the support provided by the coach. It allows the coach to see where the teacher needs feedback. It provides the coach with a window into what the teacher already knows and has tried. It becomes a planning tool for their job-embedded work. (p. 20)
Here is her example:

With colleagues from the GVSU Mathematics department, I adjusted the action plan to meet the needs of our novice mathematics teachers. Our form asked:

  • What is my current challenge in teaching for mathematical literacy? Four areas were suggested (assessment, evaluation, planning, or instruction), based on our work with the Teaching-Learning Cycle.
  • What do I already know about this?
  • What questions do I have?
  • Which one of these questions do I need to focus on to develop my understandings?
  • How will I develop my understandings?
  • What support do I need to enact my action plan?
  • How will I monitor my progress?
This framework provided a way for novice teachers to ask for help, which meant that our advice would nurture their developing practice rather than insult it. 

My experience in student teaching 'taught' me that observations were intended to be dog-and-pony shows where I was expected to impress the observers. Consequently, I was actually concealing my flaws from the person best situated to help me address them. I cringe when I think about all the teachers I passed that same lesson on to early in my career. Action plans have been my amends and I have been amazed by the results. 

This action plan from one of our student teachers demonstrates the power of the approach. The plan helped him to self-identify his "problem" and articulate where he wants to be. It provided me with something to focus on. Without this focus, it is easy for me to fall back into my old pattern of judging lessons based on what works for me. It is interesting that by asking teachers to identify their challenges, I have been addressing my own.

In future posts (here and here), I plan to share other examples of how these action plans have aided our efforts to support the development of effective mathematics teaching.

Friday, November 11, 2011

Is this real?

Today, part 2 of Harry Potter and the Deathly Hallows is available in stores. When the movie opened in theaters this past July, I used it as an opportunity to write about teaching as storytelling. In this post, I want to take a look at a particular exchange between two main characters and consider what it might mean for teaching and learning mathematics. Warning - spoilers ahead.

The following happens near the end of the story. Harry has sacrificed himself to save his friends and finds himself in an ethereal version of King's Cross Station talking with his deceased mentor, Albus Dumbledore. The conversation is nearly over when this brief exchange occurs.
     "Tell me one last thing," said Harry. "Is this real? Or has this been happening inside my head?"
     Dumbledore beamed at him, and his voice sounded loud and strong in Harry's ears even though the bright mist was descending again, obscuring his figure.
     "Of course it is happening inside your head, Harry, but why on earth should that mean that it is not real?"
There seems to be a strong push in mathematics education to attach some real-world significance to nearly every topic in the curriculum. I appreciate the effort and agree that content a learner can connect to is more likely to be engaging. For me, however, the search for context to wrap around content can sometimes be distracting and inauthentic.

How can real-world examples be inauthentic? Let me provide a personal example. As a middle school mathematics teacher, I often extolled the practicality of learning to add and subtract fractions with unlike denominators. I would say, "You'll need this skill in cooking and building." Now maybe someone else can pull this off in an authentic way, but I cannot remember ever adding or subtracting fractions outside of an educational setting. Granted, I do not cook or build anything from scratch so I may be missing something. This only reinforces that this purpose was inauthentic to me and a distraction to my learners.

My problem was that I was confusing context with purpose. I now explain to learners that the rationale behind our lessons on fractions are related to the NCTM Process Standards and not some potential future use. I do not know if my learners will ever need to add or subtract fractions while cooking. I am sure that their future success will depend on their ability to problem solve, reason, communicate their thinking, use representations, and make connections. Yes, even connections to the real-world. 

Let me be clear that I am not suggesting context is not important. In order to learn something new, we need to connect to something known. Looking back, I am not sure how many 8th-graders have experience with cooking and building. They are familiar with time, however, which is why I like using the clock model. They also have worked with whole numbers, and I often try to connect to these computational experiences. Sometimes the mathematics itself is the context.

Essentially, it is about finding what is real for my learners. Certainly, there will be times when their reality is at odds with that of the mathematical community - that is when the fun begins. I can only hope that my learners, like Harry, will begin by asking, "Is this real?"

Wednesday, November 9, 2011

Are we the first?

I admit it. I am a bit on the competitive side. But the question I tweeted to Dan Callahan about hosting a Twitter chat between two edcamps was also about gaining perspective. If it had been tried before, then I wanted to be able to build on previous successes and avoid prior pitfalls. Dan's response meant that we were on our own (and that we were first, but that's not what's really important here.)

The idea was the result of a Twitter conversation I had several months ago with Erin Ochoa. We were chatting about assessment and wishing that we could talk face-to-face about it at Edcamp Edmonton. It was then that I realized that Edcamp GR was being held the same day. Initially, we thought about a Skype session. I had seen it done at Edcamp Detroit and thought it went well (I wrote about it here) but wondered if we could get things started the same way Erin and I had begun our conversation - via Twitter. Therefore, we organized an "edchat" between the two edcamps around the following questions:

We worked out a schedule that took into account the two-hour difference between time zones. The first 10 minutes would be spent getting participants acquainted with Twitter, the next 30 minutes engaging in the Twitter chat, and the last 20 minutes Skyping, which would allow us to extend the conversation beyond 140 characters. So on November 5th, John Golden and I signed up to lead the following session:

It worked out well. I lead the conversation and highlighted some of the nuances of Twitter chats while John tweeted links supporting our discussions. You can see a transcript of the chat here. At about 12:40 pm EST, we Skyped between the sessions. Fortunately, Janet Bell, in Edmonton, took a picture and tweeted it:

Interestingly enough, the Skype conversation we engaged in was mostly about Twitter, not assessment. Participants wanted to talk about how we use it inside and outside the classroom. It was not what I expected (real learning rarely goes as planned) but I would say the first ever edcamp edchat was a success. But being first is not what is really important here. This is what is important:

Tuesday, November 1, 2011

Phronesis - What is that?

This was the question guest host, Susan Page, asked author, Eric Greitens, on an episode of The Diane Rehm Show. Greitens responded:
Phronesis is so interesting because it's a concept that we really don't have a word for in English. You could say that it's something like common sense, but it is really more than that. What phronesis means is practical wisdom. And phronesis is the ability to both figure out what to do in any given moment while also knowing what is worth doing. So the idea is that it's a practical wisdom - that you are wise about your intentions, wise about your ends, and at the same time you have a very clear understanding of the means that you need to actually get there.
Upon hearing this, I immediately said, "That is what I want teachers to have - phronesis!"

Teacher effectiveness is an important topic to me and I am not alone. There are centers devoted to teacher quality (TQ Center) and programs popping up dedicated to improving how teachers learn how to teach (Teaching Works). Distilling teaching to a few measurable points is beyond my current level of comprehension, however. Which is why I wanted to write about it - to try and, as Cambourne suggests, "talk" my way to understanding.

As I read the description above, it suggests four things for teachers to consider in supporting the development of their educational phronesis.

  • Can I identify my learning goals (ends)? 
  • Can I provide purpose for my instructional choices (intentions)?
  • Am I aware of the resources available to support teaching and learning (means)?  
  • Am I able to make decisions about what is "worth doing" in my educational setting?
It is tempting to affix to this list the things I stress in teacher preparation and professional development. In fact, I have written and deleted numerous sentences that use these four questions to support my use of particular teaching frameworks or instructional approaches. (I think Grace would say I was trying to make sense instead of developing understanding.) But are these things truly necessary for all teachers or are they just the resources available to me that I have deemed worth doing?

I'm done talking for now. This has certainly helped me develop a better understanding of phronesis but I am left with many questions. Is it enough for teachers to be working to answer the bulleted questions above or does effective teaching require more? And how do we design teacher preparation to support the development of phronesis? I look forward to your ideas.