This paper presents a research study of children using on-screen manipulatives (objects represented graphically on the computer screen) in learning mathematics. The paper begins by offering the rationale for the use of manipulatives in mathematics education, an assessment of why manipulatives are not more commonly used in schools, and a discussion of the potential benefits of on-screen computer manipulatives. It then discusses a program of research in which sixty-three kindergarten and first-grade children used software to construct "computer beansticks" as part of a series of classroom activities focused on number patterns, grouping, and addition. Among the results was the finding that the open-ended nature of the software offered children an environment for independent and collaborative exploration and expression, and provided teachers with a tool for class presentations and informal assessment. (Author)