The Nature and Quality of Algebra Instruction: Using a Content-Focused Observation Tool as a Lens for Understanding and Improving Instructional Practice

Abstract

Algebra is a key course in the high school mathematics sequence. Despite its prominence, large-scale examinations of algebra instruction are rare and it is not clear whether and how instructional practices that support students’ learning of algebra content manifest in classroom instruction. Drawing on video from 108 ninth-grade algebra lessons from 5 districts recorded as part of the Measures of Effective Teaching (MET) Project, I describe instruction using scores from a newly developed, algebra-focused observation tool to ground the description of instructional practice in the content being taught. I present the range of instructional formats and the nature and quality of algebra-focused instructional features related to the teaching of procedures and to the ways in which teachers leverage connections to support students’ algebra learning. To illustrate these descriptive results, I present case studies of 2 lessons: 1 rated typical and 1 rated high-quality. I find that although the majority of lessons in the sample follow traditional formats, specific instructional features that benefit student learning in algebra are present to a modest degree across lessons, though not often at high levels of quality. The case lessons demonstrate both glimmers of promise and missed opportunities to engage in instruction that benefits student learning of algebra. I discuss the implications of these results for improving the quality of algebra teaching and argue for the affordances of a content-focused observation tool as a lens for instructional improvement efforts.

Acknowledgements

This article stems from research conducted for my doctoral dissertation at the Harvard Graduate School of Education. I am grateful to Heather C. Hill, Jon Star, and David K. Cohen for their support and guidance in the early stages of this research. I appreciate the support of ICSPR at the University of Michigan for facilitating data access. I thank Amanda Jansen and Teresa Dunleavy for feedback on earlier drafts of this article. Finally, I thank Jeff Shih and the anonymous reviewers for their careful and critical read of the article and for their insights at each step of the process.

Notes

1 This design raises concerns about the degree to which selected video is representative of teachers’ typical practice. Analysis by Ho and Kane (2013) of a different subset of MET video data found that teacher-chosen video rated higher on average than nonteacher chosen video on MET observational instruments. Thus, the quality of instruction presented herein may be higher than might be considered typical.

2 Teachers who participated in the MET study had the option of whether or not they wished to make their video available to researchers outside of the original MET study for secondary analyses. Not all teachers consented to do so. The MET project administered an assessment of mathematics knowledge for teaching and not all teachers had scores on this measure. Although this measure was not included in the analyses used in this study, these scores were important to additional analyses in related studies (Litke, 2015).

3 Teachers’ names are pseudonyms.

4 Technically, symbol (rather than sign) is the correct mathematical term, so as to distinguish the greater or less than symbol from a positive or negative sign. Although I acknowledge this imprecision, the buttons on the display along with Ms. Rose’s gestures made clear that she was referring to the inequality symbol.