Mental computation and computational estimation are receiving considerable attention as curricular topics for elementary and middle school mathematics, mainly because they serve important functions in a calculator literate society. A careful study of the role of these topics in the curriculum is warranted based on recent research which shows that the development of computational estimation is closely related to the development of mental computation skills and number magnitude concepts. To explore the interrelationships of mental computation, computational estimation, and number sense, a longitudinal research project involving students in grades four, five, six, and seven is planned. Long-term instruction on mental computation and number magnitude will be given in grades four and five. The effects of this instruction on number sense development will be evaluated both during the instructional period and the following year. Instruction on mental computational and number magnitude will be provided in grade six, and instruction on computational estimation in grade seven. The influence of the grade six instruction on the acquisition of computational estimation skills will be studied by comparing performances of seventh grade students with and without the sixth grade instruction. Transfer effects to related topics such as rational numbers will also be studied. The proposed research is challenging and has potential value for both researchers and practitioners. It has been carefully designed with a reasonable development and implementation schedule. The P.I. is highly respected and the list of associated staff and consultants represents some of the top scholars in the field. All reviewers were enthusiastic about the project and recommended funding. The project is planned for a period of thirty-three (33) months. An award of $254,559 is recommended as follows: $109,467 from FY87, $98,862 from FY88, and $46,230 from FY89.
