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.