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

Reflections on Planning and the Nature of Curricular Materials

Quality curricular materials in and of themselves are insufficient

Despite what current trends in public education might suggest, we know that regardless of quality, curricular materials cannot teach themselves. Multimedia records of teaching practice used teacher education are curricular materials and like their pre-K-12 counterparts, in and of themselves, they cannot effectively teach pre-service teachers. Designing instructional tasks in which the CASTL scholars' records of practice could be utilized, required iterative phases of instructional planning.

First, I familiarized myself with the available resources and consider them in light of my personal goals for improving the instruction in my elementary mathematics course. My inprovement goals included nuturing a shared vision of particular teaching practices and contexts, helping my students cultivate a better understanding of the lesson planning process, deeping my students' understandings of classroom discourse in mathematics.

Second, I selected particular elements in the CASTL body of work that seemed to address many of my goals. I selected two very different teaching episodes from Mary Hurley's body of work to help me meet my goal. And, I planned the sequence and timing in which I wanted my students to encounter these records of practice - through virtual observation of one teacher's class.

I decided to have them view Mary Hurley's warm up first for a number of reasons.

  • It is a conventional practice in elementary school mathematics, and thus would be reasonably familiar to novices in their first few weeks of a teaching credential program.
  • While the routine is commonplace, Mary Hurley's practices enable her students to engage in the mathematics in ways that are conceptually substantive.
  • The teaching/learning illustrates NCTMs process standards.
  • The teaching practices illustrate "talk moves" that the students read about early in the semester.
  • I decided to have my students view the Horse Problem later in the semester. While the problem is well-known, it is not at all conventional. There is not a straightforward solution path, and though the arithmetic in the problem uses only small numbers, there are few incorrect answers that solvers routinely come up with. Furthermore, the teaching practice in this lesson do not follow the stereotypical math lesson in which the teacher lectures on a new topic, students review a few problems as a whole class, and then work individually to complete a page of math problems on the given topic. Rather, in the horse problem, students work in small groups over an extended period of time to solve just one problem, focusing on reasoning and communication. Each group then presents their solution and reasoning to the whole class. I wanted my students to observe this lesson after they had read about and experienced this kind of math lesson in our methods class. That is to say, I wanted them to have a framework for understanding the Horse Problem when they viewed it. So, this virtual observation needed to come later in the semester.

    Third, having selected the episodes for observation, and the timing, I needed to design the students assignments. The CASTL materials have two features that I wanted to exploit in my assignments. They included extensive, largely unedited examples of teaching practice, often entire lessons, and they are available for free on-line. These two features enable something that the most of the videos, video and written cases, and other records of practice that are available to math teacher educators do not. I do not have to take a few hours of valuable class time to show video of accomplished teaching practice. I can assign my students to watch the videos from the comfort of their own home.

    I decided to package these observations with other course and programmatic goals, including protocols for observing in classrooms, foci of observations, lesson planning, considering practices that maintain cognitive demand, and the articulating one's repertoire of teacher moves.

    A final aspect of my planning pertained to how we would discuss the students' observations in class, after they completed the assignment. I had to plan for both small group and whole group discussions that would highlight the topics that were part of my instructional goals, while also providing space for my students to raise questions and wonder about aspects of teaching practice that were beyond the scope of my goals, and/or beyond my imagination.

An Educative Curriculum and the Invisibles of Teaching and Learning to Teach

Ball & Cohen (1996) highlight the notion that curriculum materials can be educative for the teachers who use them, and my use of the CASTL materials in multiple sections of mathematics methods course over the past two semesters has certainly been educative for me. In creating new ways for my students to observe teaching practice, I also created new fora in which to get to know my students thinking about teaching practice. Listening to their discussions of accomplished practice helped me understand their own learning trajectories better, and it helped me better understand the contexts in which they are observing practice in the field. Each iteration of using these records of practice also enabled me to learn more about what different tasks and participation structures enable my students to discuss, and who they enable to participate in discussions.

Talking with my QUEST math colleagues, Rick Marks, Megan Franke, Janine Remillard, (in consultation with Tim Boerst and Laurie Sleep) about the various ways in which we have each chosen to incorporate the use of on-line records of accomplished teaching practice has been among the most generative professional development I have ever experienced. We have talked in great detail about our overlapping and distinct goals for our methods classes, and how we have leveraged these materials to accomplish our instructional goals.

The materials and their use continue to be generative as I struggle to think about recording my practices - including the invisible aspects of teaching practice such as the planning of instruction, interpreting student thinking, gauging student learning, and the moment-to-moment decision making that is teaching. Records of my own teaching practice tend to capture what is visible, though ephemeral in teaching. But this work, and the CASTL and QUEST projects push me to think about how we capture the truly invisibles of teaching and learning to teach.

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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