Publication Date


Document Type


First Advisor

Behr, Merlyn J.

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences


Cognition in adolescence; Reasoning; Proportion


Many studies have focused on the various levels of adolescents’ proportional reasoning as well as the solution strategies adopted by these adolescents. Few studies, however, have dealt with the effects of altering the presentation format of the proportional reasoning problems used in these studies, i.e. data presentation and question presentation. The comparison of mixture problems used in research frequently present data telling the amounts of the two parts and then present a question asking for a comparison of the concentrations of the two mixtures . The present study investigated the effects on adolescents’ proportional reasoning performance of using two different formats of data presentation and two different formats of question presentation in comparison of mixture problems . The data 'presentation of the problem either told the amounts of the two parts being mixed or it told the amount of one of the two parts and the amount of the mixture in all. The question presentation of the problem either asked for a comparison of the concentrations of two mixtures or it asked for a comparison of the dilutions of two mi xture s . Through the match or mismatch of these two data presentation, formats with these two question presentation formats, four tests were presented in each of two distinct physical embodiments: a continuous context of orange juice and water mixtures; and a discrete context of red BB and white BB mixtures. The tests were given to 167 sixth-, eighth-, and ninth-grade students from an upper-middle-class, socio-economic suburban school district. All subjects were enrolled in enriched mathematics classes. Analyses of adolescents" written responses indicated that reasoning performance varied between the test-type using part-part data presentation and asking for a dilution comparison of two mixtures and the test-type using part-whole data presentation and asking for a concentration comparison of two mixtures. Performance also varied between the two test-types in which the data presentation was altered from part-part to part-whole, while the question presentation asking for a comparison of the dilutions of two mixtures remained fixed. While statistically it was inconclusive that performance varied between the two contexts, graphically some differences in performance were found to exist.


Includes bibliographical references (pages 83-86)


viii, 111 pages




Northern Illinois University

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