Abstract

Thirteen elements of effective mathematics instruction were developed during a multi-year research project involving middle school mathematics classroom observations and teacher interviews in the U.S., Japan, China, Malaysia, and Singapore. The thirteen elements were derived from about thirty key indicators of lesson design, implementation, mathematics content, and classroom culture found in the Horizon Research “Inside the Classroom Observation and Analytic Protocol”. As an evaluator, the Horizon Research protocol was used to score key indicators, determine synthesis ratings, give supporting evidence for synthesis ratings, and ultimately decide on an overall capsule rating of the quality of a lesson. To simplify this task, the key indicators were condensed down to thirteen specific elements that should be present in every effective math lesson. This paper describes each of the thirteen elements and how they were developed and used.