Novice Mathematics Teachers' Enacted Practices: Developing an Observation Protocol to Use in International Settings

• In Event: 73.023 - Toward a Fair Evaluation of Teachers: Methodological Challenges in a Cross-National Study of Mathematics Teachers

Abstract

Objective

The purpose of this paper is to describe the development and validation of an observation instrument suitable for capturing important features of enacted practice of novice mathematics teachers worldwide.

Theoretical Framework

Too often, the logic model of teacher preparation or professional development programs moves straight from measuring or increasing teachers’ mathematical knowledge for teaching to measuring student outcomes. We know many factors mediate teachers’ enacted practices, including teachers’ knowledge (Ball & Bass, 2000) and beliefs (Cooney & Shealy, 1997), school culture (Gutierrez, 1996), uses of curriculum (Drake & Sherin, 2006), classroom culture (De Corte, Verschaffel & Depaepe, 2008), and student characteristics (Albert, 2000). A rigorous international study of novice teachers thus needs a measure of enacted practice that goes beyond self-report surveys.

Methods

We reviewed existing observation protocols—both general and math-specific—and determined that no single instrument existed to capture what we wanted. We also extensively reviewed teaching quality literature to determine the dimensions of enacted practices we wanted to measure. We determined key constructs include: uses of time, uses of instructional materials, student engagement, precise mathematical language, representations, errors, quality of mathematical tasks, and quality of mathematical discourse.

While the Mathematical Quality of Instruction (MQI; Learning Mathematics for Teaching Project, 2010) instrument is an excellent measurement of quality mathematics instruction, it is intended for use with video records of classroom practice and not live observations. Other instruments for live observation (Stallings, TIMSS, CLASS, IQA) contain some but not all of the constructs of interest.

We used the measures of time, instructional materials and engagement from the Stallings (1980) observation framework. This observation protocol has been extensively used reliably in international settings (Knight, 2008). We used several MQI and IQA constructs to capture holistic measures of language, representations, errors, tasks, and discourse. We also added a lesson flow component, adapted from (Author, 2014).

Data Sources

The initial form of the instrument was piloted on classrooms in the USA and using videos of international primary and secondary classes. The pilot data analyses led to an extensive revision of the instrument for the field test, involving 120 classrooms in 15 countries.

Results

The results of the field study include further modifications to the instrument to better capture essential features of effective mathematics instruction. Additionally, the data confirm that wide variation exists in classrooms along the key dimensions of the instrument.

Scholarly Significance

Having a valid observation instrument to capture primary and secondary mathematical quality of instruction in classrooms worldwide is an important contribution to the field. Such an instrument allows researchers to more closely tie teacher knowledge, beliefs and characteristics to student outcomes via enacted practices.

Authors

• Wendy M. Smith, University of Nebraska - Lincoln

• Maria Teresa Tatto, Michigan State University