ERIC Number: ED342647
Record Type: Non-Journal
Publication Date: 1990
Reference Count: N/A
Sense-making and the Solution of Division Problems Involving Remainders: An Examination of Students' Solution Processes and Their Interpretations of Solutions.
Silver, Edward A.; And Others
This paper reports the latest in a series of studies investigating children's performance in solving division story problems involving remainders. One aspect of the work involved examining the way in which "sense-making" is involved in the interpretation of the numerical solution obtained. Subjects were 195 sixth, seventh, and eighth grade students from a large urban middle school, with a student population of approximately 40% Caucasian and 60% African-American students of all ability levels, taught in mathematics classes by volunteer teachers. Each student was administered a practical problem requiring division with remainder. Three versions of the problem were used so that although the remainder was either equal to, greater than, or less than one-half, the solution required a whole number answer one greater than the quotient. Students' responses were examined with respect to four distinct aspects: (1) solution process; (2) execution of procedures; (3) numerical answer; and (4) interpretations. Responses were analyzed in relation to a hypothesized model. Results indicate that over 70% of the students applied division or another appropriate procedure, that 61% obtained a correct numerical answer, and that 45% of the subjects responded with the augmented quotient. Few students brought "real world" knowledge to bear on the problem and on making appropriate interpretations of their numerical process. Discussion of correct solution model, incorrect solution model, influence of remainder size, and task format is provided and implications for further investigation are given. (MDH)
Publication Type: Reports - Research
Education Level: N/A
Authoring Institution: Pittsburgh Univ., PA. Learning Research and Development Center.