Recording the Use of Records of Practice over time in Mathematics Teacher Education

Modeling Pedagogical Strategies

Below are a sampling of the pedagogical strategies that I employ in teaching my math methods course. Each of these examples entails different opportunities for students to interact with each other while focusing on issues of teaching and learning that they are learning about in conjunction with their use of Mary Hurley's CASTL website.

In general, I try to select particular participation structures for my methods class that can be models for them to incorporate into their own teaching practice. Each participation structure has particular affordances and constraints that we try to articulate in class.

Small Group Discussions - Fall 2005

I plan small group discussions to ensure that all students are participating in the conversations. As in an elementary classroom, there are often students in the methods courses that are hesitant to share their thoughts in front of 25 or so of their peers.

In the case of the first virtual observation of Mary Hurley's warm up problem, small group discussions were used to help my methods students recall and articulate what they had considered/learned in completing their homework. Students had a chance to see that their ideas were generally in line with that of their peers which helped them trust their own emerging "teacher thinking."

Focus Group Discussions - Spring 2006

In the spring, students were assigned to specific focus groups for their observations of Mary Hurley's warm up. The focus group discussions served many of the same funtions as the small group discussions we had held in the fall: helping students recollect and articulate what they had considered/learned in completing their homework and reassuring them that they were on the right track.

In addition to the obvious distintion between the focus group and small group discussions -- that each group discussed their observations with repsect to their specific focus (math talk, praise/critique, or classroom routines), focus groups also prepared for an publically reported their focused observations to the whole class.

Whip Discussion - Fall 2005

A whip discussion is one in which comments by students "whip" around the classroom. Sitting in a circle, each student shares their comments in turn. Students may share a unique idea or may connect to something that another student has already articulated and build on that idea. The whip necessitates listening to what others are saying because a student may not simply repeat a previous comment.

This model enables all students to voice a thought in a non-judgemental environment. As the whip proceeds around the room, some topics are voiced more often than others. These resonating topics become the basis for a less structured whole class discussion. We held a whip conversation after the small group discussions of the first observation of Mary Hurley's class. Students had a wide range of observations on a variety of topics, both observations related to the four prompts in their homework, and others. To faciliate a collective memory of the whip comments, I asked some students to be recorders, who had the task of categorizing the topics according to our pre-determined themes.

Group Presentations - Spring 2006

Here, each group prepared talking points about their specific topic to explain to the whole class. This strategy was used following the focus group discussions. All of the students had seen the same video of Mary Hurley's teaching - the warm up - yet they had focused on different aspects of her practice. So, after each group shared their observations about their focus, other students contributed additional ideas or questions and the main points were discussed.

Doing the Math - Both Fall 2005 & Spring 2006

One of the quintessential instructional strategies used by mathematics teacher education is to ask the pre/in-service teachers to engage in doing the math task before they consider artifacts of practice (video, student work, written case...) that result from students engaging in the same task.

Sometimes I ask students to "do the math" individually, sometimes in pairs, and sometimes in small groups. Before my students viewed the horse problem, we took time in class to solve the problem first. In the fall, students worked in pairs to solve the problem, and then we had a whole class discussion about the range of solutions. In the spring, students solved the problem individually first, and then in groups of 4-5. I specifically asked each group to come to consensus and select one solution method to share with the whole class and create a poster to represent their thinking. The approach of having small groups identify and represent one solution path to share with their classmates models a strategy that would be appropriate in an elementary class because it forces students to grapple with each others' reasoning.

Distributed Group Investigation - Fall 2005

In this model, small groups are each assigned to work on a distinct subsection of the task at hand, such that when all the groups have completed their work, the class as a whole will have completed the task. This task structure is related to the cooperative learning strategy, "jigsaw", that we use for other projects during the semester.

This approach was used to recreate Mary Hurley's lesson plan for the horse problem lesson. Small groups were assigned to write different phases of the lesson plan, including mathematical learning goals, CA standards, into, through, beyond, materials, grouping, etc.

After small group work was completed, each group shared their part of the work at the overhead, and discussed what went into their "teacher reasoning."

Collective Brainstorming - Spring 2006

Brainstorming is a teaching strategies that enables students to see a wide variety of possible ways to respond to a give prompt/situation. In this case, it was used as a whole class activity so that we could generate as many options as possible.

Specifically, the video of Mary Hurley's horse problem was used in a culminating course activity to illuminate the wide-range of teacher moves, teacher decision making, and teaching strategies that the math methods students have learned about during the semester. I projected the video of the horse problem on the classroom projection t.v., pausing as pre-determined junctures where the teacher had many options for how to procede. I asked the students questions like: "If this were your classroom, what might you do next, and why?" "What else might be a reasonable next step?" "What would your goals be if you..."

My objective was to help my students become aware, not only of the teaching strategies they were beginning to cultivate, but also that at any moment in teaching, there are options, and that teachers should be able to articulate why they might choose a particular approach.

This electronic portfolio was created using the KEEP Toolkit™, developed at the
Knowledge Media Lab of The Carnegie Foundation for the Advancement of Teaching.
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