Proportional reasoning is important to students' future success in mathematics and science endeavors. More specifically, students' fluent and flexible use of scalar and functional relationships to solve problems is critical to their ability to reason proportionally. The purpose of this study is to investigate the influence of systematically…

This report focuses on prospective secondary mathematics teachers' understanding of irrational numbers. Various dimensions of participants' knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the…

The relationship between a cognitive style variable, field-dependence-independence, and instructional treatments that differed in two dimensions of discovery learning, level of guidance and level of abstraction, was investigated with 116 prospective elementary teachers. As predicted, field-independent students did better with minimum guidance,…

The hypothesis was tested that students with a field-independent cognitive style would learn most about numeration systems if they had minimum guidance and maximum opportunity for discovery through the use of manipulative materials. Data were gathered on 46 prospective elementary school teachers. The hypothesis was supported. (Author/MH)

Preservice elementary teachers enrolled in a mathematics course were randomly assigned to one of two treatment groups for instruction on computation in bases other than 10. Group 1 (Min-M) involved minimal guidance and a concrete level of abstraction, while group 2 (Max-S) had a large amount of guidance and dealt with concepts at a symbolic level.…

Investigated (n=124) preservice school teachers' reasoning and concepts of invariance of fractional numbers under numeration systems in different bases. The majority of students believed that fractions change their numerical value under different symbolic representations. (Author/MKR)