In this session we will consider what education research can contribute to the problems mathematicians face in their own teaching, and what mathematicians can contribute to the precision of education research. The teaching and learning of reasoning and proof will serve as the context for the session. What are some of the fundamental problems and what are the conceptual and empirical tools that enable disciplined inquiry into them? We will consider three specific tools drawn from across mathematics and education that support research on the teaching and learning of reasoning and proving:(1) the discipline of mathematics as a source of theory for research; (2) careful analysis of video records of teaching and learning as a source of primary data about the problems; and (3) measures of mathematical knowledge with which to study learning.
The Mathematics Support Centre (MSC) in the National University of Ireland, Maynooth (NUIM) appears to be improving the grades of students and changing their attitudes towards mathematics. Many students consider dropping mathematics or even leaving university because of mathematical difficulties. We found that for students who attended the MSC, the majority of their grades, particularly for the weaker students, were significantly better than those who did not attend. These students also reported an increased confidence in their mathematical abilities and a significant number were more likely to retain mathematics or to remain in university as a result of the help they received in the MSC.
In 2008, a PISA style test was administered to over 180 first year students in three institutions across the third-level sector. The test was designed to measure mathematical literacy, where the emphasis is on the understanding of concepts, the mastery of processes and the students' ability to function in a variety of real-life situations. In addition, students were asked to rate their self-efficacy in specific presented here and possible correlations between literacy levels and self-efficacy are explored.