Abstract of thesis (Ph. D.)--George Peabody College for Teachers, 1939.

The concern over undergraduate engineering students’ mathematical skills and the means of addressing this through the provision of mathematics support is the main driver of this research. With the emergence of mathematics support within mathematics education there has been an associated research community interested in measuring the effectiveness of mathematics support provision. Recent studies have measured improvements in mathematics performance for students who have used mathematics support against those who have not by comparing prior mathematical ability against examination results. This does not address the issue of individual differences between students and resulting changes in mathematical ability. However the provision of mathematics support for individual students is resource intensive hence evaluation of the effectiveness of the support is essential to ensure resources are efficiently used. This mathematics education research examines the effectiveness of mathematics support in addressing the mathematics problem. It does this by considering individual differences and the mismatch of mathematical skills for studying at University by analysing the effectiveness of mathematics support in improving mathematical skills. The dataset for the analysis comprises of over 1000 students from a Scottish Post-92 University, over 8% having made use of mathematics support, and nearly 2000 students from an English Russell Group University, with just over 10% having made use of the support. It was discovered that in both sets of data the students who came for mathematics support in comparison to their peers had a statistically significant lower mathematical skills base on entry to their course, and at the end of their first year had improved their mathematical skills base more than their counterparts. Although the analysis is based on data from UK Universities we believe the findings are relevant to the international community who are also engaged in the provision of mathematics support.

The purpose of this non-experimental, causal-comparative study was to examine how gender, reading ability, and mathematics ability differentially moderated students' mathematical problem-solving processes, linguistic explanations of those solution processes, achievement on a mathematical problem-solving test, self-efficacy on a self-reported rating scale, and self-assessment on a self-reported rating scale. The investigation addressed five research questions. First, to what extent are students' mathematical problem-solving processes related to gender? Second, to what extent is children's performance in mathematical problem solving related to gender, reading ability, and mathematics ability? Third, to what extent is the quality of students' linguistic explanations of their problem-solving processes related to gender, reading ability and mathematics ability? Fourth, to what extent is the relationship between students' feelings of self-efficacy when commencing work on a mathematical problem and their actual performance related to gender, reading ability and mathematics ability? Finally, to what extent is students' ability to assess their own performance on mathematical problem-solving tasks related to gender, reading ability, and mathematics ability? After being briefed in the use of the self-efficacy and self-assessment reporting scales, the students from 16 fifth-grade classrooms were tested with a 12-item mathematical problem-solving test. The final sample consisted of 237 students, 129 boys and 108 girls. All student responses were scored for performance and linguistic explanation using holistic rubrics, and were coded according to the solution process employed. The results indicate that gender does not play a significant role in students' choice of problem-solving processes. As expected, mathematics ability was significantly related to performance as was reading ability. Gender was not found to be a significant predictor of performance. Reading ability and mathematics ability were both strongly related to the quality of students' linguistic explanations of their problem-solving processes, but gender was not. Boys consistently exhibited higher levels of self-efficacy, but girls were more accurate in their self-efficacy feelings. Reading ability was also found to be a significant predictor of the accuracy of students' self-efficacy feelings, but mathematics ability was not. Reading ability was found to be the strongest predictor of the accuracy of students' self-assessment, with gender also showing a significant relationship.