Content Deficits and Pedagogical Difficulties of U.S. Middle School Mathematics Teachers: A Study of Lesson Analysis

• In Event: 60.023 - Content Representations and Pedagogical Moves in Chinese and U.S. Mathematics Classrooms: Lesson Video Analyses at Elementary, Middle, and High School Levels

Abstract

Objectives. Teachers’ pedagogical content knowledge that relates subject ideas using appropriate pedagogical approach to particular groups of students (Shulman, 1987) is central to mathematics instruction quality and thus, student mathematics learning (Hill et al., 2008). Increased studies support this assumption (Darling-Hammond, 2006; Smith & Esch, 2012). US middle school students failed to learn mathematics well (National Center for Education Statistics, 2004), which adversely impacts their college mathematics readiness (Spielhagen, 2011). Middle school teachers’ mathematics content deficits and pedagogical difficulties can negatively contribute to students’ mathematics achievements. The study identifies the pedagogical difficulties and mathematical knowledge deficits of US middle school teachers as evidenced in their lessons.
Theoretical Framework: The socialmathematical assumption frames the focus, data collection, and analysis of this study (McClain & Cobb, 2001). According to this assumption, teachers’ mathematics ideas and pedagogical considerations can be actualized through their mathematics and pedagogical discourses developed in their lessons (Krussel & Edwards, 2004; Lampert, 1990), which offers or limits students chances to develop mathematics understanding (Cobb, 1995).
Methodology. A video survey analysis was conducted (Stigler, Gallimore, & Hiebert, 2000) with 85 sixth–eighth grade lessons collected from 31 urban school mathematics teachers during the last three of five grading periods of one school year. Mathematics lessons were videotaped to capture data in its entirety and provide flexibility in coding and analysis. Certified university partners scored the teachers’ pedagogical skills using the modified Teacher Advancement Program rubric (Schacter & Thum, 2004) and their mathematics knowledge for teaching were coded using a Mathematics Content Rubric.
Findings and Discussion. The study found that teachers demonstrated deficits not only in mathematics knowledge (e.g., Pythagorean theorem, complementary and supplementary angles, dimension and unit agreement), but also in mathematical justification (e.g., limits of probability, effect of outliers, use of units, moving zeros and decimals). They had further deficits in the utilization of mathematics language to define various mathematics concepts accurately. This finding is consistent with those of other studies from a comparative perspective (Ma, 1999; Zhou, Peverly, & Xin, 2006).
These deficits led them to their misconceptions of what and how students learned mathematics and thus, inappropriate pedagogical moves in lesson structures, use of instructional questioning, time, and activities in the lessons as implied in the literature (Ball, 1992). For example, many did not allocate sufficient time for the beginning and ending activities, were unable to group students for effective mathematics learning, and developed low-level questions not aligned with the curriculum expectation.
Importance. The study contributes to the understanding about the relationship between teachers’ mathematics knowledge for teaching and relevant pedagogical moves as assumed (Hill et al., 2008). Such knowledge is crucial for developing effective policy and practice to improve mathematics teaching (Ball, 2003). Findings will direct the foci of teacher preparation programs and professional development for inservice teachers.

Authors

• Sevket Ceyhun Cetin, Texas Tech University

• Sonya Ellouise Sherrod, Texas Tech University

• Shirley M. Matteson, Texas Tech University