Fractions are important in young students' understanding of rational numbers and proportional reasoning. The teacher is fundamental in developing student understanding and competency in working with fractions. The present study spanned five years and investigated prospective teachers' competency and confidence with fraction operations as they…

This paper gives results of a study on a Personal Response System (PRS). Three sections of college algebra are compared; one section used PRS and PowerPoint, one used PowerPoint, and one was considered a control. Students were given a pretest and posttest with a retired version of a mathematics ACT test, and all students gained an average of one…

In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully…

This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and…

In this study, it was hypothesized that problem solving success is dependent upon two related but district types of mathematical knowledge, content indicators and connectedness indicators. Results did indeed display that the problem solving success of 188 undergraduate students was related to these two indicators. The correlations of content…

This study investigated the influence of regular structured writing about problem solving on college algebra students' locus of control, flexibility of articulation, and accuracy in responding to written problem tasks. The writing assignments, acronym PSOLVE, provided students a framework for expressing their thoughts about mathematical actions,…

Cognitive Restructuring offers mathematics teachers a foundation and working philosophy for helping underachieving students. The philosophy centers on helping students become aware of and break out of a failure syndrome. Inability is not considered the reason for underachieving. This philosophy, shared by the developmental mathematics teachers at…