Search

Out-of-field teaching refers to the practice of assigning teachers to teach subjects that do not match their training or education. This paper reports on a study evaluating the impact of a national professional development programme for out-of-field teachers of post-primary school mathematics in Ireland -- the Professional Diploma in Mathematics for Teaching. Evidence of impact was collected from three surveys. Two surveys evaluated changes in the prevalence of out-of-field teaching before and six years after the introduction of the programme. The third survey investigated programme graduates' beliefs about mathematics, mathematics teaching and mathematics learning, and reported changes in teaching practices. Outcomes of the programme included a reduction in out-of-field teaching of mathematics and increased opportunities for graduates to teach higher level mathematics in the senior post-primary years. These teachers also endorsed child-centred beliefs and reported teaching practices consistent with the problem-solving orientation of the new mathematics curriculum. The findings go some way towards testing a theory of teacher change in order to enhance our understanding of how professional development works to upskill out-of-field teachers.

This paper describes an empirical study examining action research papers submitted by a group (n = 81) of out-of-field mathematics teachers as part of a professional development programme in Ireland. Utilising document analysis, the papers were qualitatively analysed for evidence of teachers' beliefs and practices with respect to the teaching and learning of mathematics. In particular, demonstration of direct transmission and constructivist beliefs and practices was explored. The authors draw on Valsiner's zone theory in conceptualising the 'teacher-as-learner' in this out-of-field context and it provided a means for analysing teachers' development in terms of their beliefs and practices. Findings indicate a prevalence of direct transmission or traditional teaching practices prior to the out-of-field teachers' action research, with some inconsistency with professed constructivist beliefs. There was evidence of a majority shift towards constructivist beliefs and practices post action research for a myriad of reasons, including increased pedagogical confidence in mathematics and the successful experience of constructivist approaches. Findings also highlight the role of reflective self-study in facilitating the creation of productive tensions, as well as the importance of the teachers' interpretation of their zone of free movement in resolving complex issues and enabling out-of-field teachers' development of constructivist beliefs and practices.

This paper describes a small-scale study examining one facet of pre-service mathematics teachers' knowledge for teaching. While mathematical knowledge for teaching has received extensive attention from researchers with regards to pre-service teachers, there has been little research on the mathematics register proficiency of this cohort. In this study, we examine a group of pre-service mathematics teachers' mathematics register during a peer-teaching lesson. The authors adapt Rowland's Knowledge Quartet as a framework for the study, by conceptually aligning mathematics register proficiency to each of the four dimensions: foundation, transformation, connection and contingency. Findings indicate pre-service mathematics teachers lack understanding of the significance of the mathematics register and its role in mathematics teaching for eliciting mathematical understanding for students. There was evidence of over-reliance on the everyday register and a lack of fluency with regards to the mathematics register in practice. There is an exigent need for greater emphasis to be placed on developing preservice mathematics teachers' mathematics register proficiency during initial teacher education, not only to improve pre-service teachers' own knowledge and understanding, but also their ability to facilitate mathematics register proficiency in their future students.

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination--the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for "image of mathematics" was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students' images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for "image of mathematics" was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination--the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.