What have you been doing?

To wrap things up for 2011, I thought a recount of the year's posts would be in order. This will be my 90th post on this blog this year, which is pretty amazing considering I thought one a week would be a reasonable goal. But I ended up finding a lot to write about. So much, in fact, that I forgot some of what I wrote. This is the main reason I wanted to write this recount - to refresh my memory.

In January, I introduced my blog and the rationale behind it. It was also my intention that some of the posts might inspire me to write a book on the Teaching-Learning Cycle. So the next few posts began a series on the Cycle - assessment, evaluation, and planning.

The instruction post of the Teaching-Learning Cycle started off February. A self-evaluation that I wrote next was the first unplanned post. This was followed by my yoga story, which I share in nearly every class as a metaphor for effective teaching. Another unplanned post shared my students' views of what they thought it meant to do math. The post on frameworks was the last one of the month and probably my favorite one of the year.

I wrote 12 posts in March. The first was an email I sent to our student teachers about time management. Second, I wrote a commentary to accompany my TEDxGrandValley talk. In the third post, I explain why as a math teacher I attend the Michigan Reading Association Conference. In the next two posts I began a series that looked at testing from the Teaching-Learning Cycle (TLC) perspective (assessment and evaluation). The series was interrupted, however, by a pair of unplanned posts: a letter to the editor in support of teacher unions and a description of how I used a Twitter backchannel in a class. Next was the third TLC/testing post focusing on planning. Two more unplanned "interruptions" addressed a Tweet by Alfie Kohn and a simile survey related to learning math. The conclusion of the TLC/testing series (instruction) was next. The twelfth and final post outlined the workshop I used to have my students reflect on what it means to learn math.

April was my most prolific month with 15 posts. A pair early in the month used Monty Python skits to look at teaching and learning. There were four posts that had been in my files for awhile waiting to be shared with the world: Process Standard math centers; an early elementary math poem; and a pair of posts on Pass the Pigs (the first post was the most popular of the year). There were a couple of posts related to work my students on what it means to teach math. I also introduced why I started the Learning Museum (another blog that needs more of my attention). Three posts were related to the NCTM Conference I attended in Indianapolis. A mind map reflecting our teacher assistants' experiences over the semester took up another post. Near the end of the month, I wrote a post that responded to an article suggesting that students learn best from direct instruction. The last post was a copy of a final exam I gave my preservice middle school math teachers.

I kept up the pace in May with 13 posts. The first three were a series based on a student teacher's portfolio project. Next was an impromptu post based on an #anyqs tweet. Another Twitter inspired post considered alternatives to traditional math homework. After attending TEDxGrandRapids, I also wrote a synopsis of the event from an educational slant. I did another three-part series on EdCamp Detroit: introduction, my session, and my reflection. There was another response to the article on direct instruction (which also introduced the clock model for adding and subtracting fractions) and two more posts from my files on grading. And then there was the one where I explained why all the titles of my posts are questions. I'm not sure I'll continue that theme next year.

In June I wrote three more posts associated with the clock model for adding and subtracting fractions. There were also three more posts on activities from my files: data transformations; scatter plots; and Monte Carlo simulations. I wrote a post comparing teaching to training horses, and a pair relating teaching to bike tag-alongs (what I saw and what I thought about it). I ended the month writing about the gradual release of responsibility and my thoughts on the flipped classroom.

I began teaching a graduate class in July and a couple of my posts focused on that experience. The first was based on memories I had as I planned the course. And the second was based on my desire for my grad students to mutiny. I also wrote about teaching as story telling in honor of the last Harry Potter movie's debut, the importance of trusting oneself in teaching and golf, and a letter to the editor on education reform.

August began with one more post about my grad students - their blog addresses so others could offer feedback. I then wrote about how I use the workshop model. Then I blogged about how a TED Talk encouraged me to take the 30 day challenge. Finally, I talked about why I ask questions in class for which I don't have answers.

September was the start of classes, and I began the month writing about a workshop I use on the first day. Then I wrote about how design thinking might apply to education. A post on teacher pay came next. These were followed by two more math activities from my files: one on story problems and the other on empowering students (this became part of a series called, Now What).

In October I finished the Now What series on empowerment with three more posts. I also shared my session workshop on Metacognitive Memoirs from the MCATA Conference. My big post was a 'transcript' of my keynote at MCATA.

Two unplanned posts bookended November. The first post of the month was on phronesis. The post at the end of the month was about running. In between, I wrote about my session on Twitter at EdCamp GR and what makes math real. I also began a series on using action plans to improve teaching. The first introduced action plans and the second gave an example of one in use.

December included two more activities from the archives: fostering creativity and snowman glyphs. There was another impromptu post based on several Twitter interactions. The third in the action plan series focused on an example related to evaluation. I shared a video reflection from one of my learners. And last, but definitely not least, was my blog recount that you might still be reading.

Well, that's all folks. Thanks to anyone who made it this far. And thanks to everyone who supported me through this first year of blogging. I am excited to see what new learning 2012 has in store.

What did we learn?

At the end of each semester, I try to make sure that my learners have time to reflect. If their learning is to last, then they must have a chance to consolidate it. This past semester I used three workshops to support their efforts to look back and look forward.

The first workshop asked the learners to focus on the course objectives.

They identified those in which they considered themselves proficient and what contributed to their proficiency. So much occurs during a semester and too often learners do not recognize what was learned. This task represents a metacognitive activity that makes it more likely that the learners will be aware of all they have accomplished. It also provides me with important assessment data that will inform how I teach the course in the future.

In the next workshop, learners write letters to future students as a way to prepare and encourage them to be successful in my course. Here are two from this semester:

I will share the letters with future learners because people often accept advice more easily from their peers than their teachers. This is not the sole reason for the activity, however. It also provides the letter writers with the chance to reflect on their own growth as learners over the semester. I hope that both current and future learners will benefit from this wisdom borne out of experience.

The final workshop asks them to create a 3 minute (or less) TED Talk about what they have learned this semester. This year I found out the power of showing the Student vs Learner clips early on. Many of them commented on how these videos helped to frame the entire semester. I will now try using them the first day in all of my courses.

The presentations are ungraded and usually very informal. Amazingly, this sometimes leads to more preparation on the part of the learners. Regardless of the time they put into them, I find their sharing to be quite profound and at times moving. Here is an example from this semester:

I remember teachers saying to me, "You'll thank me for this later." This typically accompanied some particularly distasteful tasks. I bristle at this notion and hold the belief that I am not in this for people's thanks but because I believe in what I do. Still, I hope I am getting better at accepting people's gratitude as well as their criticisms. After all, both are a part of the learning process.

What's your problem? Part III

Previously in this series, I shared about action plans (here) and how one teacher used an action plan and observation to improve her use of questions in assessing learners (here). In this post, I provide another example - this time focusing on evaluation. (I have explained before that our framework treats assessment and evaluation as different phases of the Teaching-Learning Cycle.)

The teacher being coached was using entry slips to gather data on her learners but was unsure how to interpret the data. Her question to develop her understanding literally asked, "What do I do now?" It was with this in mind that I entered the class and saw the following on the board in the front of the room.

After about five minutes, the teacher collected the sixth-graders' efforts, looked over them, and, satisfied, moved on with the rest of her lesson. 

During a lull in the lesson, I asked if I could look over the slips. With her consent, I began to analyze the assessment data. I organized it using the table shown. As you can see, there were no incorrect answers, however, there was a problem. Approximately 22% of the learners were unable to complete the task in the time provided. Fortunately, the teacher had asked the learners to show their work so that some of their thinking would be made visible to us. This would provide further insight into the problem.

I began to apply the evaluation framework by asking myself, "What can they do? What are they trying to do? What comes next?" Looking over their work, it became clear that they were fluent in comparing fractions using common denominators. Below is an example of how nearly all of the learners went about finding the first answer.

This also seems to suggest where they were approximating. By trying to apply this method (finding a common denominator by multiplying the two denominators) to all the comparison problems, some learners had run out of time. It seemed clear to me that what came next was considering alternative approaches to comparing fractions that might be more efficient. I shared the following list with the teacher:

• Using benchmark fractions like one-half and one;
• Comparing like numerators;
• Finding least common denominators; and
• Converting to decimals.

We talked about ways to introduce these strategies and how to make subtle shifts to the worksheets that she was expected to assigned. By asking the learners to look over the worksheet and match each item with a preferred method, they would be engaging in more meaningful work than simply applying a particular approach over-and-over again. As always, I left it open for this shift to be a part of the teacher's next action plan.

How do you celebrate the holidays?

The following is an activity I included on a final exam I gave to preservice teachers at the end of the fall semester years ago. The activity began the class period before the final with the students filling out this Holiday Survey:

1. During winter (on a typical day), are we likely to see you wearing a hat?
2. During winter (on a typical day), are we likely to see you wearing a scarf?
3. What is your favorite winter activity?
• Skating
• Downhill Skiing/Snowboarding
• Cross-country Skiing
• Sledding
• None of the above
4. Which is your favorite holiday television show?
• Rudolph the Red-nosed Reindeer
• Santa Claus is Coming to Town
• The Little Drummer Boy
• Frosty the Snowman
• None of the above
5. Do you like winter or not?
6. Which is your favorite holiday treat?
• Sugar Cookies
• Candy Canes
• Pumpkin Pie
• Fruit Cake
• None of the above
7. What is your favorite color for wrapping paper?

Their answers were used to create snowman glyphs based on the key (here) and the template shown below.

Here are some examples of how the students' snowman gyphs came out:

There were typically 24 students in the class and they used the 24 different glyphs (here) to answer this problem-set on the final.

You should use the data found in the glyphs to fill in the contingency table. In class, we explored two methods for determining independence. You should use both to determine if wearing a hat and wearing a scarf are independent events.

You should make a graph to represent your favorite holiday treat. You may use grid paper if you wish.

Disregarding wrapping paper color, how many distinct snowman glyphs are possible based on the key?

And, in case you were wondering, here's my snowman glyph.

Happy Holidays!

How do you foster creativity?

The following was on a bulletin board in the art class at the middle school where I taught.

Because I wanted my math class to be more like that art class - learners exploring the boundaries of their knowledge and skills - I posted a copy in my classroom.

Twenty years later, a copy is now thumbtacked to my office door. It reminds me that fostering creative problem solvers is one of my primary goals as a teacher of teachers. Some of the ideas may not be reasonable, but creativity sometimes requires a certain suspension of rationality.

Why do you like Twitter?

People not on Twitter ask me this a lot - usually as they back away slowly. Last night's Twitter stream provided two answers. But I'm still not sure they would get it.

First, Erin Ochoa tweeted that she had posted her reflection on EdCamp Edmonton. We did a joint session together on using Twitter that day, although we were nearly 1,500 miles apart. (I wrote my reflection on that session at EdCamp Grand Rapids here.) It was good to be reminded of how Twitter supports professional collaboration.

Second, John Spencer started a Twitter meme with #pencilchat. He explained how it started here. Seventeen hours later and it is still going strong. Whatever the reason behind #pencilchat, it provided a lot of teachers with a laugh. And I for one could use the comedic relief.

PS The link in the tweet above pointed out another positive aspect of Twitter - connections. You can find out why here. I don't want to ruin the "rest of the story" surprise.

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).

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.

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.

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?"

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: