• A Longitudinal Study of Invention and Understanding in Children's Multidigit Addition and Subtraction

    Thomas P. Carpenter, Megan L. Franke, Victoria R. Jacobs, Elizabeth Fennema, Susan B. Empson
    This 3-year longitudinal study investigated the development of 82 children's understanding of multidigit number concepts and operations in Grades 1-3. Students were individually interviewed five times on a variety of tasks involving base-ten number concepts and addition and subtraction problems. The study provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords and the role that different concepts may play in that invention. About 90% of the students used invented strategies. Students who used invented strategies before they learned standard algorithms demonstrated better knowledge of base-ten number concepts and were more successful in extending their knowledge to new situations than were students who initially learned standard algorithms.