Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

This paper, presented at the 1979 meeting of the American Educational Research Association (AERA), investigates student errors in high school mathematics. A conceptual framework of hypothetical information-handling processes such as procedures, frames, retrieval from memory, visually-moderated sequences (VMS sequences), the integrated sequence,…

Using R. S. Siegler's retrieval-required task, 19 male and 22 female third graders were examined before they had been introduced to multiplication in school. Examination of error patterns suggests that the basic assumptions of the distribution-of-associations model need to be tested directly and that the retrieval-required task confounds retrieved…

We report a study of 10-14 year old children's use of additive strategies while solving ratio and proportion tasks. Rasch methodology was used to develop a diagnostic instrument that reveals children's misconceptions. Two versions of this instrument, one with "models" thought to facilitate proportional reasoning and one without were…

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…