Where was I using the Process Standards?

MTH 110 is an Intermediate Algebra course that explores topics typically found in Algebra I and II. Most of the students have seen the content before but for some reason it did not stick (nobody's fault, just a fact). Instead of simply re-teaching the topics, we are using the content to extend our understanding of what it means to do mathematics.

One of the ways we are attending to the mathematical process is by making our thinking visible is through Metacognitive Memoirs. Because this is a new approach to many of my students, I spend a good portion of Flight School (the first three weeks of the semester) developing the idea of how we can go beyond showing our work. This past week, I facilitated a workshop that demonstrated one way to share our thinking.

Schema Activation: Predict how many small cubes are in Step 43

from Visual Patterns

Focus: NCTM Process Standards

As I share my thinking, please keep track of where I am attending to the bullet points associated with these processes

Activity: Metacognitive Memoir Demonstration

Reflection: Where was I ...

• Problem Solving
• Reasoning
• Communicating
• Connecting
• Representing

It might help to see my notes.

Please share your thinking (where I made the processes visible and opportunities I missed or messed up) in the comments.

How did you teach it?

The idea of MTT2K began when a group of preservice teachers could not wait until the end of a Khan Academy video to voice their concerns about the quality of its content. (You can learn more here.) Once the movement to critique Khan Academy videos gathered some momentum, it was suggested that teachers do more than nitpick (although, as this post explains, nitpicking is important). Consequently, a group of bloggers set out to make 101 alternative lessons.

Nine alternatives were scheduled as of today - the day before the MTT2K prize deadline. While this is less than we hoped for, it is a start. The energy behind projects like the mathtwitterblogosphere demonstrates how we all benefit when teachers make their own lessons available for others to use and improve on.

The lesson I want to share comes from that same day when the preservice teachers watched the Khan Academy video. We were focusing on NCTM's Communication Standard that day, and I wanted to share examples of people communicating the ideas associated with integer multiplication and division. Many of the area schools use PowerPoints in their math classrooms, so I wanted to model how I might use this medium to communicate my thinking.

The think-aloud focused on my approach to trying to understand some integer rules I memorized years ago. I used "I language" to remind the learners that I am making my thinking visible, not telling them what to do. Afterward, we debriefed about what they saw and heard and how what I shared might support their ability to understand the concept for themselves. (The demonstration is split into two parts because Jing only allows for 5 minute recordings.)

Part One

Part Two

Having watched this demonstration, how would you respond to these points:

• What did I do?
• What did I say?
• What did I think?
• Develop a consolidated recount regarding multiplication and division of integers.

And how might you improve on this demonstration?

What did you see/hear?

Last week, I attended the Michigan Reading Association's Annual Conference where I went to a session lead by Doug Fisher. He was presenting on Response to Intervention from a gradual release of responsibility perspective. It was the gradual release model that I was most interested in - especially since his book with Nancy Frey presents a slightly different version of this approach than the one I use. But I will leave that discussion for a later post. Today, I want to share my current thinking about what makes for an effective demonstration lesson (what Doug labels Purpose & Modeling).

From Doug Fisher's Michigan Reading Association Presentation

The demonstration I am sharing comes from a workshop for my Teaching and Learning Middle Grades Mathematics [TLMGM] course (a combination content and methods course that our secondary majors take prior to student teaching). This workshop focuses on comprehending the purpose behind a lesson that a teacher might encounter in an unfamiliar curriculum. Many of our student teachers find themselves using curricula that typically require a significant amount of professional development. Because our student teachers have not had this support, they sometime struggle to implement the lessons effectively. Therefore, I hope to share an approach I might use to better understand the rationale behind a lesson.

I used the ShowMe App to take a picture of a number string from a lesson found in the Context for Learning Mathematics series and then added my thinking. ShowMe records both my whiteboard annotations and voice to create a video that I can share with others.

A key piece to any demonstration is the debriefing: What did you see and what did you hear? This reflects Cambourne's perspective on who is ultimately responsible for learning: "Learners need to make their own decisions about when, how, and what 'bits' of information to learn in any learning task." By asking the learners what bits of information they attended to during the demonstration, the teacher is gathering important data that can inform future instruction (formative assessment). If the observers did not attend to something important presented in the demonstration, the teacher can highlight the missing points by saying, "I noticed that I was also..." The resulting list provides an anchor chart that learners can refer back to as they take more responsibility for employing the approach.

After I shared this demonstration with my learners in TLMGM, they noticed that I was trying to understand the string by:

• making connections between the expressions;
• considering different representations that might further my understanding;
• recognizing that computing the answers might help but wasn't enough;
• thinking about ways to put the expressions into a context; and
• analyzing my options before jumping into any plan.

Satisfied that they had attended to the major points of the demonstration, I provided them with further resources related to the Ratio Table unit and had them work collaboratively. They tried to look at the strings from the various angles in order to understand the purpose of the lessons.

During the workshop's reflection, I provided the opportunity for them to share what they had uncovered through Twitter. This provided everyone who wanted to contribute a voice and me with another artifact that I could use for formative assessment. Here is a sample of the discussion:

UPDATE 3/21/12
Reflecting back on this post, I have come to realize that if I were going to embrace the idea of "flipping" my class, this is what it would look like. I would use ShowMe to create demonstration lessons and have my learners watch them. When they finished, I would ask them to Tweet those things that they noticed in order to assess what they paid attention to and create an anchor chart for the class.

I know that my learners (college students) may differ from your's if you teach in a K12 school. But what do you think? Would this work for you?