Using the Concrete-Representational-Abstract Sequence to Teach Conceptual Understanding of Place Value,Rounding, and Expanded Notation

This study investigated the effects of a place value intervention with third-grade students with learning disabilities. The intervention added content to a research-based intervention using the concrete-representational-abstract (CRA) sequence. The added content reflected current mathematics standards for third grade. Students’ place value understanding was measured using probes in which students had to identify the value of each digit within a three-digit number, round three-digit numbers to the nearest 10 or 100, and write three equations showing an expanded form of a three-digit number. A single-case, multiple-probe-across-students design showed a functional relation between CRA and completion of items requiring place value understanding. Students completed a generalization task by estimating the sum of a given equation.     

Soliciting,vetting, monitoring,and evaluating: A study of state education agencies’ use of external providers for school improvement efforts

Journal of Educational Change - Recent United States (U.S.) educational policies—especially the passage of the Every Student Succeeds Act of 2015—have challenged state education...