A LONGITUDINAL-STUDY OF INVENTION AND UNDERSTANDING IN CHILDRENS MULTIDIGIT ADDITION AND SUBTRACTION

This 3-year longitudinal study investigated the development of 82 chil dren's understanding of multidigit number concepts and operations in G rades 1-3. Students were individually interviewed 5 times on a variety of tasks involving base-ten number concepts and addition and subtract ion 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 al gorithms demonstrated better knowledge of base-ten number concepts and were more successful in extending their knowledge to new situations t han were students who initially learned standard algorithms.