Using Observation Data to Support Equitable and Ambitious Mathematics Instruction

• In Event: Formative Intervention Research to Enhance Equitable Mathematics Teaching: Lesson Learned From Multiple Data Sources

Abstract

Objectives. In this paper, we present data from observations of mathematics classrooms to address the following research questions:
1. What do classroom observations indicate about the quality of instructional tasks, task implementation, and discussion in mathematics teachers’ classrooms?
2. In formative intervention research, how can observation data inform professional development (PD) efforts and support teachers’ self-directed progress towards equitable and ambitious mathematics instruction?
Theoretical framework. Consistent with Perry (2013) and Jackson and colleagues (2013), we define opportunity gaps specific to mathematics, as differences in students’ opportunities to learn mathematics due to the presence or absence of key components of ambitious mathematics instruction (Franke, Kazemi, & Battey 2007). Specifically, we examine the nature of instructional tasks (Stein, Grover & Henningsen, 1996; Tarr, Reys, Reys, Chavez, Shih, & Osterlind, 2008), task implementation (Stigler & Hiebert, 2003; Stein & Lane, 1996), and mathematical discussions (Boaler & Staples, 2008; Stein, Engle, Smith, & Hughes, 2008).
Methods. We observed 21 mathematics teachers, 14 middle school (MS) and 7 high school (HS), each during two lessons in spring 2015. Two pairs of MS teachers “team-taught,” resulting in observations of 19 classrooms and 38 lessons. Lessons were videotaped (30/38; 79%) or observed (8/38; 21%) by two trained observers. Lessons were rated using an observation tool assessing instructional tasks, task implementation, and mathematical discussions. Ten lessons (26%) were consensus-scored for rater-calibration and 28 lessons (74%) were scored independently by two trained raters. Exact-point agreement was 84% overall, with discrepancies resolved through discussion. Analyses include descriptive statistics and one-tailed Mann-Whitney tests for differences between MS and HS lessons.
Results and conclusions. Tables 1-3 provide results and illustrate two important patterns. First, MS lessons exhibited high means, percentages of high-cognitive demand scores, and numbers of teachers with high scores in Tasks, Implementation, and Questioning. MS lessons scored significantly higher than HS lessons in Tasks (z=2.86; p<.01), Implementation (z=3.04; p<.01), and Questioning (z=3.6; p<.001). Second, discussion-based rubrics scored low overall. However, MS lessons containing a discussion (non-zero scores) posted moderate means for Discussion, Teacher-Press, and Student-Providing.
Results indicate significant differences in opportunities to learn mathematics between MS and HS lessons, and lack of opportunities for rich mathematical discussions overall. As formative intervention research, data suggest directions and foci for PD efforts, such as supporting teachers to orchestrate mathematical discussions. Differences between MS and HS lessons may result from differences in the nature of tasks and instructional support provide by each curriculum, suggesting HS teachers require additional resources and strategies to enact ambitious instruction. Formative intervention research also requires using data to support teachers’ self-directed efforts to enhance instruction, presenting a need to balance directing PD efforts towards specific instructional practices and encouraging teachers to initiate direction/foci.
Scholarly significance. Our work can elevate the importance of classroom observations as mechanisms for enhancing ambitious and equitable instruction, thereby improving students’ opportunities to learn mathematics. Classroom observations suggest pathways towards improvement unidentified by decades of achievement testing or hyper-focus on achievement gaps (Gutiérrez, 2008).

Author

• Melissa D. Boston, Duquesne University