We are evaluating several educational initiatives led by school districts that seek to improve student achievement in mathematics by refining their approach to mathematics instruction.
One approach commonly used by our district partners is the Concrete-Representational-Abstract (CRA) model for teaching mathematics, a research-based, three-part, systematic approach designed to build student understanding. At the concrete step, the concept is introduced using manipulatives (base ten blocks, fraction bars, counters) to solve a problem. During the representational stage, students use drawings (pictures, tallies, dots, graph paper) to represent the concrete objects to solve the problem. The abstract step problem solving moves to using symbols, operations, and formulas to solve a problem. Implementing this systematic approach to teaching mathematics has been shown to build student understanding of mathematical concepts.
We frequently support implementation by gathering data on fidelity of implementation through the analysis of teacher lesson plans using a rubric and/or classroom walk-through data with an observation protocol. In both cases, the data collection instruments are tightly aligned with the instructional model. Monitoring the observed frequency of specific instructional indicators provides formative feedback to the project team, which is used to plan for continued professional learning and/or support specific areas of need and monitor implementation progress over time.