Are you ready for "something completely different?"

My wife gave me The Complete Monty Python's Flying Circus for my 48th birthday. I just got around to watching the first episode and saw the following sketch. It demonstrates perfectly what happens when we fail to use formative assessment to inform planning and instruction.

It is important to understand that formative assessment does not need to be in the form of a test. We can gather data simply by observing. Imagine how this Italian class might have looked if the teacher had really seen the students during the lesson and adjusted his instruction accordingly. In the Design Thinking methodology, this is a part of the first phase - Empathy.

This reminds me of an article by Dr. Rheta Rubenstein titled, "The Learning of Mathematics: Perspectives of Different Researchers." (It comes from our text, Teaching and Learning Middle Grades Mathematics.) Under the section on Vygotsky, she includes the following diagram attributed to Dr. Lauren Resnick.

Vygotsky in Venn Diagram Form

As Terry Jones's character discovers, when teachers use scripted lessons that do not take learners' current level of understanding into account very little learning actually occurs.

How do math teachers in training view learning?

The following is an example of one of our in-class workshops for Teaching and Learning Middle Grades Mathematics. This activity comes at the end of a unit on mathematical learning theory.

Teaching Mathematics Workshop (Learning Math Anchor Charts)

Connection - Schema Activation [10 minutes]
Read NCTM's Learning Principle and make connections to our previous readings

Concentration - Focus [5 minutes]
Simile Survey - providing a vision
Anchor Chart Models - previous and partners'

Construction - Activity [35 minutes]
Develop a group anchor chart on the whiteboard that makes our thinking about learning math visible

Learning Math Anchor Charts - Work in Progress

Consolidation - Reflection [10 minutes]
Learning Math Anchor Charts

Group 1

Group 2

Group 3

Describing our visions - presenters were offered choice to be on camera or off (sorry about the sound quality)

Group 1

Group 2

Group 3

Does Test-Prep Make Sense?

If you drop by a Michigan middle school mathematics classroom this September, chances are you will find yourself in the middle of test-prep instruction. October brings the Michigan Educational Assessment Program (MEAP), our high-stakes standardized test, and schools want to ensure that their pupils are adequately prepared. The test-prep instruction usually entails one part content, one part test-taking strategies, and one part cheerleading.

This is not the relationship between instruction and assessment conceptualized in the Teaching-Learning Cycle. The role of assessment is to gather data about learners’ progress toward predetermined educational goals. Current educational policy stresses standardized tests, however, which stresses out administrators and teachers. Consequently, the MEAP becomes master of instruction rather than partner.

I rallied against this test-prep situation (and other standardized testing practices) for years, to no avail. The stakes were too high for anyone to consider an alternative. It was at a Michigan Reading Association Conference that I found a possible answer. (I learn a lot at this conference.) Patrick Allen led a session on developing deep, long thinkers in the time of standardized testing based on a book he had co-authored, Put Thinking to the Test. I thought that these ideas could reframe test-prep.

Put Thinking to the Test applies the research on proficient readers to taking tests. In other words, it treats standardized tests as a specific genre which readers can make sense of using well-documented comprehension strategies. Each strategy is addressed in a chapter demonstrating how it can be applied to a standardized test. From the table of contents:

• Ask Questions

• Create Mental Images

• Draw Inferences

• Synthesize New Learning and Ideas

• Activate, Utilize, and Build Background Knowledge (Schema)

• Determine the Most Important Ideas and Themes

• Monitor for Meaning and Problem-Solve When Meaning Breaks Down

Even in test-prep, teachers can focus on fostering thinking rather than memorizing facts or practicing skills.

As a result of reading this book, I now have concrete approaches that teachers can use to return instruction to its rightful place in the Teaching-Learning Cycle. I share these approaches in the classes I teach for preservice and inservice teachers and in professional development workshops. I would love to share it with you, but first I need to know what questions and concerns you have about what I have written thus far. After all, asking questions is one of the essential comprehension strategies propelling our thinking forward.

What does a mathematics learner look like?

Today my Teaching and Learning Middle Grades Mathematics course ends a unit on learning mathematics. This follows a unit on doing mathematics. At the beginning of this unit, we took a simile survey that asked respondents to complete the following:

Ideally, a mathematics learner is like a(n):

a. Inventor

b. Sponge

c. Mechanic

d. Computer

e. Reporter

f. Explorer

• Choose the simile that you believe best describes a mathematics learner and explain your choice.
• Choose the simile that does the worst job of describing a mathematics learner and explain your choice.
• Is there another simile that does a better job than these of describing a mathematics learner? If there is, then what is it and what makes it better than these?

This survey is based on an instrument I used in my doctoral research to measure beliefs about doing, learning, and teaching mathematics.

How would you complete this simile survey?

Whose job is it anyway?

I woke this morning and found this tweet from Alfie Kohn in my Twitter Stream:

It immediately reminded me of the article I wrote with my GVSU colleague, Dr. Pamela Wells - Are They Wrong? Or Did They Just Answer a Different Question?

But it also brought to mind a cartoon John Golden drew for me after I shared with him a talk I heard at a leadership conference at the University of Michigan's School of Education. This was before Twitter, so he had to wait until I drove back from Ann Arbor to tell him about it. I do not remember who the speaker was, but I do remember the message: we need to be figuring out what learners are saying and not the other way around.

So what is your paradigm?

When will they be ready to go on?

from Teaching-Learning Cycle

Assessments play a key role in the Understanding by Design approach to unit planning. They represent the way that I plan to monitor learners’ progress toward a goal. Therefore, I need to think carefully about what I am going to assess (objectives) and how I am going to assess (approaches) before the unit even begins. In other words, effective assessments require planning.

My first attempt at planning with the end in mind was a middle school math project I called the “Dream House.” I was also interested in using alternative forms of assessment and this project seemed a natural place to start. The summative assessment was a class presentation where each middle schooler shared a scale model of his or her dream house along with specific details like perimeter, area, and cost. This was a 9-week project that covered many of the Michigan state standards in geometry, measurement, and number & operation. And the grade on the presentation was their grade for the marking period. I made this video to model what the final product and presentation might look like:

In order to increase the likelihood of learner success, I set up assessments (I called them benchmarks) along the way. Again, I worked backwards in selecting and designing these assessments. I just kept taking a mental step back and asking myself, “What should they be able to demonstrate in order to do the next task?” and “How will I assess/gather data on their level of understanding?”

As you can see in the example to the right, my plan included some traditional forms of assessments (highlighted in yellow). Learners needed to demonstrate proficiency on the skills assessed by these quizzes before they were ready to move on to the next benchmark. Our school determined that 80% or better was required, but you will remember this did not figure into their final grade; it was merely to monitor progress and ensure success.

This video represents a sample of the eighth graders' efforts on the Name Plaque benchmark:

The planning and preparing for this unit took a great deal of work. Fortunately it was the first marking period in the fall, and I had all summer to work on it. Still, many of the quizzes I used were not developed from scratch but modified from our school’s math text. There was no reason to reinvent the wheel and slight modifications offered the data I needed to analyze understanding and make instructional decisions. After all, these were formative assessments.

I point out my use of textbook quizzes because I had a teacher assistant ask me if using existing curricular resources is “cheating.” Another education class had suggested that using such resources is shameful because teachers should and can create better materials for their learners. Maybe with more time and experience we could make better tests and quizzes from scratch. But why would we if what’s available requires minor, meaningful modifications in order to accomplish our goal? It just depends whether or not it fits within our plan.

How did my teaching go today?

I am willing to acknowledge that I may be wrong about this (which is one reason I am writing about it) but I think the experiment of using Twitter in a college classroom went well today. The other reason I am writing this is because we teachers often spend too much time beating ourselves up over flaws in our lessons. We have just as much, if not more, to learn from examining successes.

TPACK Framework

My idea started last week after listening to Dr. Punya Mishra talk about the intersection between technology, pedagogy, and content knowledge (TPACK) at the GVSU 2011 Technology Symposium (connect to his talk here). We have used Twitter with our teacher assistants (TAs), mostly outside the seminar, as a means to monitor what is happening in their placement, communicate information to them, and model how social networks can be used to develop professional learning networks (PLN). But Dr. Mishra got me to thinking about how to use Twitter IN the classroom in meaningful ways.

The goal for the experimental lesson was to consider ways to improve teaching by focusing on engagement. This reflects two elements of the seminar’s content knowledge (the content being promising practices that support TAs’ efforts to improve their teaching).  The first is the text we use in the class, The Teaching Gap. We like the book’s message that change takes time and commitment, and teachers should be at the center of this development. We also focus on Action Plans as a professional development approach that supports teachers in identifying and addressing teaching challenges.

Here is where the pedagogical piece intersects. We know learners need to have a purpose in order for an activity to be meaningful. Therefore, I told the TAs to imagine that a colleague had developed an Action Plan asking for support in writing plans that would engage more learners. (An improvement would be to have a mock Action Plan – I just can’t help seeing what is missing). It was their job to watch his instruction and offer him, or his representatives, feedback after the lesson. The other pedagogical intersection was that the lesson was a video of one of the American lessons described in The Teaching Gap. Thus, it was a connection to the known – a pedagogical imperative if learning is going to occur.

The technology overlapped the content knowledge and the pedagogy in two ways. We accessed the video via the internet and used Twitter to take notes on our observations, questions, and ideas during the lesson. We chose an unused hashtag, #e3pd (ed 331 planning dialogue – shortened to make it easier to tweet), and then projected the video and the Twitter stream on a split screen.

Split Screen Reenactment

As the TAs tweeted, I noticed that some were not showing up on the list. I soon realized that because they had protected accounts their tweets were on my personal stream but not in the list. I quickly began quoting and retweeting but it became obvious that I was not going to be able to keep it up throughout the lesson. This is another thing to think about for next time.

Once I stopped retweeting I began noticing trends in the Twitter stream. The TAs were identifying some of the same actions and offering the same advice. Many of these were issues and ideas that we had discussed throughout the semester. They also began communicating to one another (and me) in pure backchannel fashion. And there was a record of it for us to look at later. If you had been in the seminar, you would have seen me smiling.

The lesson ended and the TAs immediately wanted to offer the teacher feedback. I told them he was unavailable but three of his representatives would be meeting with individual groups. As luck would have it, these TAs meet with me prior to seminar to discuss planning engaging lessons. I coached them ahead of time to be open to ideas but to push back with some of the constraints we had discussed earlier (time, classroom management, culture, …). One of the groups welcomed a representative saying, “Oh, you must be Mr. J’s student teacher.” I will stow this nice touch away for next time as well.

I walked around eavesdropping on these dialogues. It was great to hear the TAs offer ideas and support their point with successes from their own experience. One representative/student teacher took copious notes as she listened to her colleagues’ suggestions. (I need to remember to get a copy of those notes to see exactly what she wrote.) The reflection for the activity was for TA’s to tweet one final subtle shift that the teacher might consider incorporating into his planning to improve engagement.

The last piece of business was to get feedback about the experience. A couple TAs said they had been skeptical about tweeting during a video but they were now sold. Tweeting allowed them to remain engaged in an otherwise non-engaging lesson by bring their thinking to the surface. (Fostering metacognition is another example of how the lesson landed in the TPACK framework’s center.) We discussed trying the same approach while watching a German or Japanese lesson. They also appreciated that there was a record of their thoughts available to examine latter.

John gathered the tweets in Twapper Keeper and we may do an analysis at some point. What I observed in real time reminded me of the work Deb Roy shared in the second part of his TED Talk.  You can watch it here.

Looking back on the experiment, I remain pleased with the outcome. There are certainly things to improve, and I wonder if it will be as meaningful the second time.  Was it the novelty that made it so engaging?  How can I maintain this TPACK momentum?

Now that you have heard my story, I would be interested in your perspective.