Equational reasoning: A systematic review of the Cuisenaire–Gattegno approach

Abstract

The Cuisenaire–Gattegno (Cui) approach to early mathematics uses color coded rods of unit increment lengths embedded in a systematic curriculum designed to guide learners as young as age five from exploration of integers and ratio through to formal algebraic writing. The effectiveness of this approach has been the subject of hundreds of investigations supporting positive results, yet with substantial variability in the nature of results across studies. Based on an historical analysis of one of the highest-fidelity studies (Brownell), which estimated a treatment effect on equation reasoning with an effect size of 1.66, we propose that such variability may be related to different emphases on the use of the manipulatives or on the curriculum from which they came. We conducted a systematic review and meta-analysis of Cui that sought to trace back to the earliest investigations of its efficacy. Results revealed the physical manipulatives component of the original approach (Cuisenaire Rods) have had greater adoption than efforts to retain or adopt curriculum elements from the Cuisenaire–Gattegno approach. To examine the impact of this, we extended the meta-analysis to index the degree to which each study of Cuisenaire Rods included efforts to align or incorporate curricular elements, practices, or goals with the original curriculum. Curriculum design fidelity captured a significant portion of the variability of efficacy results in the meta-analysis.