Collaborative Research: Mental Abacus Education and Spatial Representations of Number

Principal Investigator: 
Project Overview
Background & Purpose: 

We are exploring the potential benefits to learning arithmetic using a "mental abacus", both to mathematics achievement and to outcomes on general cognitive measures like attention and working memory. We are also exploring the mechanisms by which mental abacus is represented using visual imagery.


The project is being conducted in San Diego, California; Boston, Massachusetts; and Vadodara, India.

Research Design: 

The research design for this project is longitudinal and cross-sectional, and will generate evidence that is causal [experimental, quasi-experimental, and statistical modeling]. Original data is being collected using school records [school records or policy documents], assessments of learning [achievement tests], and survey research [self-completion questionnaires, structured interviewer-administered questionnaires].

The analysis plan includes a longitudinal comparison of experimental and control groups examining training related changes to attention, working memory, in-school math achievement, performance on standardized tests, and fluid intelligence. One half of the children are trained to use the abacus in the intervention group, while children in the comparison group are given additional standard math curriculum.


In the first phase of the project we have documented the basic visual mechanisms that support mental abacus in a submitted manuscript. Additional findings will be posted as they become available.

Publications & Presentations: 

Frank, M.C., & Barner, D. (under review). Constructing exact visual representations of number.