This study investigates the potential of video analysis and a mathematical knowledge for teaching framework, the Knowledge Quartet (KQ), in mathematics teacher education programmes. It reports on the effectiveness of these tools in analysing and supporting secondary level pre-service mathematics teachers' subject matter knowledge and pedagogical content knowledge. This paper describes how a videotaped lesson of one pre-service teacher, teaching a class of mature students, was analysed and makes comparisons between the teacher educators' and the pre-service teacher's observations. Inter-rater reliability was investigated and a Kappa coefficient of .72 indicated substantial agreement between both coders. Findings are presented and implications of the use of video and the KQ for mathematics teacher education are drawn.
A qualitative study was carried out by the authors into the influence of affective variables, the role of conceptions of mathematics and approaches to learning on students in the transition to service mathematics at the University of Limerick. The study is a follow-up study to an earlier quantitative study. The studies focus on first year Science, Engineering and Technological Mathematics students. This second part of the research, through the use of semi-structured interviews, aims to gain further insight into the impact of the aforementioned factors on students in their first year of university Service mathematics. This article reports on the consequences of the findings and enables us to envisage the problems that may arise in the future for mathematics education in Ireland.
This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme.
The low uptake of Higher Level mathematics (highest level examination in the Irish system) and the large failure rate of mathematics in secondary school state examinations each year have highlighted the need for reform of mathematics education in Ireland. A move towards addressing the teaching and learning of mathematics is being implemented under the new initiative 'Project Maths' which sees greater emphasis placed on student understanding of mathematical concepts and applications. Change must also occur in the training of our mathematics teachers since research internationally has shown that poor conceptual understanding often exists among pre-service mathematics teachers. This study uses critical reflection of video-based experiences and live observations to develop pre-service mathematics teachers' awareness of their subject content knowledge, as well as their pedagogical content knowledge. This paper compares the mathematics teacher educators' reflections to that of the preservice mathematics teachers' reflections. The findings and implications for mathematics teacher education are discussed. 2. Initial teacher education in Ireland In Ireland, initial teacher education is in the form of both consecutive and concurrent programmes. For secondary school teachers the consecutive route is a
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