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

 

Spring 2006

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Rethinking how Novices Use Records of Practice

for Virtual Observation of

Accomplished Practice:

Two Cycles of Activity

addressing slightly different course & programmatic objectives


Cycle 1: Weeks 2-3

Revising what I ask of my students

In the second semester of assigning a virtual observation of Mary Hurley's 4th/5th grade class, my primary objectives are the same. I still want all of my students, regardless of their actual field placement, to have a chance to see an accomplished teacher effectively use constructivist teaching practices and classroom discourse to enact a conventional daily warm up in a manner that encourages student thinking and engagement in concepts as well as skills.

Based on the conversations of my students in the previous semester as well as conversations with my QUEST colleagues, I have tweaked their assignmnet to push for a bit more depth. During my first enactment, I asked all students to focus four elements of practice: math content, classroom routines, math talk, and how praise/critique and right/wrong answers are handled. Because all students we asked to focus broadly, much of our in-class conversations stayed at a fairly general level. This semester, in assigning the virtual observation, my goal was to help these novices, many of whom had spent very little time formally observing in a classroom, focus their attention more effectively. Towards that end, I divide the class into thirds. All students were responsible for identifying the mathematical content of the lesson; additionally, each student was responsible for focusing on one of the remaining three elements of practice: class routines, math talk, and praise/critique & right/wrong answers. Regardless of their group, all students completed the department's observation form.


Key ideas from readings and classwork

5 Productive Talk Moves (Revoicing, Asking students to Restate someone else's reasoning, Asking students to Apply their own reasoning to someone else's, Prompting for further participation, and Wait Time) from Classroom Discussion: Using Math Talk to Help Students Learn Grades 1-6 by Suzanne Chapin, Catherine O'Connor, & Nancy Canavan Anderson.



Homework Assignment

Pre-Service Teachers conduct a Virtual Observation of Mary Hurley's Warm Up & Debrief Lesson

They complete this assignment individually as homework and it is discussed in class the following week. In addition to addressing course objectives regarding classroom routines and discourse practices, this assignment addresses departmental objectives by helping students learn to conduct a classroom observation using our protocol. (Note that in this version of the observation form, I have included their focus groups).



Focus Group Talk

Students warm up for the discussion of Math, Class Routines, Classroom Talk, and Being Right & Prasie by revisiting their obsevations in small groups, with classmates who shared their same observation focus. After about 10 minutes of talk, they identified main points that they wished to share with their peers about their focus.



Focus Group Share Out

After a whole class discussion in which students shared their observations about the mathematics and the math task, each focus group articulated their observations about math talk, classroom routines, and praise/critique. After the group shared their observations, students from other groups contibuted their thoughts about these aspects of teaching practice and added additional ideas. While they shared their ideas, I recorded their ideas in some detail on the whiteboard. We concluded the discussion by talking about how they might use what they were learning about class routines, math talk, and praise/critique in their own teaching practice.


Cycle 2: Weeks 13-14

Revising what I ask of my students

In the second semester, I decided to leverage the observation of Mary Hurley's horse problem in a ver different way. Recall that in the first semester, students watched this "adventurous teaching" in order to help them develop habits of mind that would enable them to plan (and enact) adventurous lessons. Because the video includes an extended focus on a group of 4 children solving the horse problem, with a student teacher promting them with powerful questions, I also had students focus on questioning techniques and student thinking.

This semester, I chose to use this virtual observation as a culminating in-class activity. Prior to observing the Horse Problem students worked on an activity designed by Margaret Schwan Smith and Mary Kay Stein, that provides a framework for thinking about aspects of math tasks and their enactment that contribute to or diminish the cognitive demand of a task.

The goal of our observation was to use Mary Hurley's teaching as a springboard for them to articulate their own ideas about the myriad of options teachers have at every junction. Towards that end, I would play a few minutes of video, and then pause. Then ask my students to articulate as many viable options as they could think of for what the teacher might do next. This, then also served as an informal assessment of what kinds of teacher moves my students had learned (about) during the semester.


Key ideas from readings and classwork

Task Analysis for Cognitive Demand and the role of the teacher in maintaining cognitive demand. Based on the work of MaryKay Stein and Margaret Schwan Smith and their COMET colleagues, from Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development, by MaryKay Stein, Margaret Schwan Smith, Marjorie Henningsen, and Edward Silver.


Homework Assignment

There was no corresponding homework assignment for this virtual observation.



Identifying Cognitive Demand in a Math Task

Prior to working with the Horse Problem, the class engaged in a set of activites designed to help them understand two aspects of cognitive demand. First, math tasks can be sorted according to how demanding they are for students; second, that when math tasks are enacted in the classroom, there are practices that either maintain the cognitive demand inherent in a math task, or that contribute to diminished demand. The cognitive demand matters, because the extent to which students are engaged in thinking about substantive mathematics is correlated with increases in mathematics achievement.

Students first worked in small groups to categorize tasks, then had a whole group discussion about their findings, followed by a discussion about teaching practices that can maintain or diminish the cognitive demand as a task is enacted.



Whole Group Brainstorming of Teacher Moves

I showed the class Mary Hurley's horse problem in small segments, pausing at particular junctures to ask the students what they might do next, if it were their classroom. For example, students viewed the first 5 minutes of the lesson in which Mary Hurley posed the horse problem, "a man buys a horse for $30, sells it for $40, buys it back for $50, and sells it for $60; did he make money, lose money, or break even". I then paused the video and asked students what a teacher might do next. Students brainstormed ideas - many of which were teaching practices we had discussed in class throughout the semester: ask a student to restate the problem, ask children if they have any question; go over rules and tools for solving the problem; assign children to group; have children record the problem in their notebooks... We then discussed what might be entailed in each option. And then we watched to see what an accomplished teacher chose to do in this instance. Again, pausing at an interesting juncture to consider the teacher's options and explore teacher reasoning.




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