Juli K. Dixon

Relationships between Gender, Cognitive Ability, Preference, and Calculus Performance

In this research, we examined the relationships between gender, spatial ability, verbal-logical reasoning ability, calculus performance, and preference for visual or analytic processing. Data were collected from 150 calculus students at four high schools in two school districts. The results suggest that spatial and verbal-logical reasoning abilities are important factors of calculus performance. Preferred mode of processing was unrelated to spatial and verbal-logical reasoning abilities suggesting that cognitive abilities did not predict students’ preference for visual or analytic processing. There were no significant differences between the two sexes in cognitive abilities, preferred mode of processing, and calculus performance.

Improving the Quality of Mathematics Teaching with Effective Planning Practices.

Although it has been two decades since National Council of Teachers of Mathematics Standards were published, research underlines the lack of essential practices for quality reform teaching. The literature also emphasizes the importance of planning in reform teaching although few studies focus directly on the planning of the teacher. This study attempts to shed light on teacher planning through a particularistic case study within a design research experiment which was performed to improve the quality of teaching. In particular, this study aims to extract the planning practices of an expert seventh-grade mathematics teacher before and during instruction on integers. The extracted practices were interpreted through the teaching-in-context theory, which uses beliefs, goals, and knowledge as the backbone of the analysis. The results indicate that five core practices underlay the development of effective planning: preparation, reflection, anticipation, assessment, and revision. Each practice included multiple actions performed in an environment of collaboration.

Redefining the Whole: Common Errors in Elementary Preservice Teachers’ Self-Authored Word Problems for Fraction Subtraction

Abstract A goal of this study was to examine elementary preservice teachers’ (PSTs) ability to contextualize and decontextualize fraction subtraction by asking them to write word problems to represent fraction subtraction expressions and to choose prewritten word problems to support given fraction subtraction expressions. Three themes emerged from the data: (a) subtraction problems were represented by an incorrect redefinition of the whole; (b) the type of unit chosen for the whole (e.g. cups, gallons, pounds vs. pizzas, pies) influenced the success of PSTs in representing Separate (Result Unknown) context problems for subtraction; and (c) the structure of the problem influenced PSTs’ performance in writing subtraction word problems.