Mathematics Education Research

Two sessions on mathematics education research are planned, on Tuesday and Wednesday afternoons between 2.15 p.m. and 5.30 p.m.

Authors are invited to offer papers on their research in this field, and a proposed title and 100 word abstract should be submitted to Rachel.Quinlan@nuigalway.ie.

Mathematics Education research: What's in it for the Mathematicians?

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.

15:15 - 16:00 *D'Arcy Thompson Lecture Theatre*

The Impact of Mathematics Support on Students' Grades and their Attitudes towards Mathematics.

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.

16:30 - 17:15 *D'Arcy Thompson Lecture Theatre*

How Do First Year Mathematics Students Validate Mathematical Arguments?

The study of proofs is a major obstacle in the transition from school to university mathematics. Given the importance of argumentation and proof in the spectrum of mathematical activities, the incoming students' understanding, appreciation and knowledge
of the nature and role of proof must be considered.

Proof is a difficult mathematical concept for students. Research shows that most university students do not know what constitutes a proof and experience difficulties not only in constructing proofs but also in determining whether a proof is valid. Selden and Selden see the lack of validation skills as linked to beginning university students' well-documented inadequate conceptions of proof.

We describe the results of an exploratory study of first years mathematics undergraduates' criteria when validating mathematical arguments or proofs. The study is based on several tests and interviews with first year honours mathematics students at NUI Galway. We confronted the students with numerous (correct and incorrect) proposed proofs of mathematical statements, and asked them to evaluate and criticize those.

The first year students' comments on different correct and partly incorrect 'proofs' of mathematical statements gave us a clear
picture about the student's criteria when validating mathematical arguments. We see on the positive and encouraging side that
most of the students recognize the difference between a demonstration by example and a proof as well as the importance of mathematical definitions and convincing mathematical arguments. On the negative side we have to note the students' formulaic and inflexible picture of valuable proofs. Structure and 'mathematical-looking' formalism seem more important to some students than
the ideas comprising the argument.

In recently held interviews with eight randomly chosen students we focussed on some questions which arose after analysing the written test results.

Mathematical Literacy and Self-efficacy of First Year Third Level Students

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.

15:00 - 15:45 *D'Arcy Thompson Lecture Theatre*

Teaching mathematics with online tutorials

In 2008, the Mathematics Online team at the Open University organised a trial of online mathematics and computing tutorials using the web-based synchronous communication software Elluminate Live!. The trial involved 29 tutors across 19 different courses in mathematics, computing, science and technology, ranging from level 1 "openings" through to MSc level. In this talk we shall report on the technical and educational aspects of the trial and on its evaluation from both the student and tutor viewpoints.