Describes the van Hiele levels of reasoning in geometry according to responses to clinical interview tasks concerning triangles and quadrilaterals. Subjects were 13 students from grades 1 through 12 plus a university mathematics major. Students' behavior on tasks was consistent with the van Hiele original general description of the levels.…

Students were pretested, then 27 first graders were trained using a highly verbal procedure emphasizing class addition activities. On posttests, trained subjects significantly improved their class inclusion and number conservation scores, but no effects were found for substance conservation or transitivity. (DT)

An eight-phase model of processes involved in mathematics problem solving is presented. At each phase, results from factor-analytic studies are used to suggest abilities relevant and prerequisite for successful completion of the phase. Presentation of the model is followed by a discussion of implications for teaching and research. (Author/MK)

First graders' length conservation was measured using a verbal and nonverbal test, and the results were compared as predictors of mathematics achievement. Findings showed that verbal conservation scores were superior to nonverbal conservation scores and to intelligence scores for predicting achievement. (DT)

This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…

This study examined the effects of field dependence/independence and the level of operational development on the mathematics achievement of 450 students in grades 6-8. Field-independent students scored significantly higher on total mathematics, concepts, and problem-solving tests. High-operational students scored significantly higher on all tests.…

Subjects were enrolled in a required science course for elementary education majors at Georgia College during spring quarter 1980. Each student was presented questions during two one-hour interview sessions. Van Hiele's assertions appear to be supported by the investigation, but further examination and development of assessment procedures are…

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

This study investigated the ability of middle school children to perform Euclidean transformations mentally. The results indicated that the tasks were more difficult than Piagetian theory would indicate. (SD)

Piaget's theories concerning the child's development of spatial concepts are considered in comparison with related mathematical concepts. The analysis yielded discrepancies between Piagetian and mathematical use of terms. (SD)

Analyzes the use of the commutative property for solving multiplication problems by children who learn about multiplication in schools and by street vendors who solve multiplication problem through repeated addition. Concludes that the use of commutativity to solve multiplication problems is closely related to the use of multiplication. Contains…

Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

Increased use of cooperative learning methods is a visible change in mathematics education in the last decade. Research questions on cooperative learning concerning different models employed, their effectiveness compared to traditional methods of instruction, their effects on student achievement, and cognitive and affective benefits gained during…

Although many articles in the education literature recommend how to teach statistics more effectively, there is little published research on how students actually learn statistics concepts. The literature reviewed in this paper indicates a need for collaborative, cross-disciplinary research on how students come to think correctly about probability…

In an attempt to bridge the perceived distinction between internalized conceptions of mathematics and their external representations, this discussion treats mathematics both as an individual, constructive activity and as a communal, social practice. It is argued that this approach might transcend the tripartite scheme of teacher, student, and…