Describes environments for concretely enacting multiplication and division. Discusses difficulties occurring when students use one of the concrete environments to model situations involving modified environments. (YP)

How computers have affected diagnosis in mathematics is discussed. A distinction is made between errors and mistakes, followed by consideration of computers as a diagnostic tool. The development of algorithms to diagnose errors and of models of student performance is described. (MNS)

Considered are concept development and errors in using both Logo and BASIC made by 25 prospective teachers in a computer literacy course. Understanding errors that students exhibit in programing may affect the ways mathematics teachers understand the process of learning structured content like mathematics. (MNS)

Research on structural learning theory is reviewed as a base for designing computer-assisted instruction programs. An intelligent "Rule Tutor" emphasizing diagnosis and remediation for whole number concepts is described. (MNS)

This study explored the relationship between traditional item difficulty and cognitive complexity as measured by response time. Rural students (n=43) responded to computer-based tests of the Individualized Study by Technology General Mathematics Course developed by Alaska's Department of Education. Results indicated that mean response times were…

Discusses the use of the computer to encourage a versatile approach to learning involving both symbolic/logical and visual/holistic types of mental activity. Provides experimental data showing the effect of an enhanced Socratic mode of teaching. (YP)

Reports a study to explore student's computational performance on computer-administered testing situations while at the computer. Students from grades 3-6 (n=100) were randomly assigned to treatment order, computer assessment first or paper/pencil assessment first. Significant differences occurred in three areas: completion time, number of mental…

Reports on research designed to systematically examine how the use of personalized word problems as practice examples would affect learning and attitudes. A computer program was used to generate the problems. It was concluded that presenting problems in familiar contexts made materials more interesting and understandable for students. (PK)

Discussed are possible reasons behind the inconsistencies in the learning of calculus. Implicated are students' beliefs, mathematical paradigms including concept image and concept definition, language use, and curriculum sequencing. (KR)