What does the research say about Number and Operations Base Ten K-5?


Journal for Research in Mathematics Education, Vol. 29, No. 1, pp. 3-20
January 1998
Thomas P. Carpenter, University of Wisconsin-Madison
Megan L. Franke, University of California at Los Angeles
Victoria R. Jacobs, California State University-San Marcos
Elizabeth Fennema, University of Wisconsin-Madison
Susan B. Empson, University of Texas at Austin

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 5 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.