Beginning Teaching Practice: Understanding the Complexity of a "Simple" Task of Teaching

• In Event: Beginning Mathematics Teaching

Abstract

Purposes and Objectives
This paper focuses on an ubiquitous practice of mathematics teaching that we call “talking with a representation.” We examine it as a case of the demands of “coordination in teaching” (Authors, 2014) to provide insight into the work of teaching as it is being learned.

Theoretical Perspectives
Our work is oriented by the theoretical perspective that “teaching” consists of interactions among and between teachers, students, and the subject matter material, as these are mutually interpreted and shaped (Cohen, Raudenbush, & Ball, 2003; Lampert, 2001). Our research approach shifts the focus from teachers and their characteristics to the teaching practices enacted by beginning teachers.

In our study of beginning teaching, we uncovered a pattern in the teaching of novices. They frequently struggled to execute routine but complex teaching tasks, an entailment of practice that we term coordination in teaching, and which we have defined as attending to, using, and doing multiple things together in order to accomplish the complex activities of teaching. In this paper, we focus in particular on “talking with a representation” as a paradigmatic case of coordinating in teaching, wherein teachers are talking about mathematics with students, managing the class, and attending to individual students, all while also creating or using a mathematical representation to support their talk.

Methods
We collected video observations of 83 mathematics lessons taught by 13 teachers (grades 1-11) in urban settings. We extracted segments of video during which teachers were “talking with a representation.”

We developed codes to capture multiple elements of the interactions between and among teachers, students, and content. For example, the code “connects students and mathematics” describes the teacher’s attempts to direct students’ attention to a specific mathematical representation, term, idea, etc. (students-content); the code “focusing or illuminating mathematics” includes instances when teachers introduce a mathematical idea, example, analogy, etc. that is productive and sensible from the student perspective (teacher-content-students).

Results
Our analysis of beginning teachers’ efforts to talk with a representation revealed the complexity of this ubiquitous task of mathematics teaching. Although it might seem simple, the patterns that emerged in our study highlight the challenges of attending to multiple aspects of classroom scenarios and executing appropriate actions, and moreover, that novice teachers struggle to coordinate these attentions and actions in order to connect students and content in support of student learning.

Significance
Many analyses of early career teaching focus on features or concerns of the teacher, despite the reality that links between teacher characteristics and teaching quality tend to be weak (e.g., Monk, 1994). This study shifts the focus of inquiry from beginning teachers to beginning teaching and identifies a particular task that may go unnoticed in research, despite the frequent occurrence of “talking with a representation” in practice. Talking while using mathematical representations is crucial for student learning but is difficult to carry out as a beginning teacher. This paper offers ways to support novice teachers in managing this complex work.

Authors

• Lindsey Mann, University of Michigan

• Lauren Hickman, University of Michigan - Ann Arbor

• Deborah Loewenberg Ball, University of Michigan - Ann Arbor

• Hyman Bass, University of Michigan

• Susanna Farmer, University of Michigan

• Kolby Gadd, University of Michigan

• Delena M. Harrison, University of Michigan

• Mark Hoover, University of Michigan

• L. Joy Johnson, University of Michigan - Ann Arbor

• Rachel B Snider, University of Michigan - Ann Arbor