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The pre-service teacher followed in this paper aimed to act as an agent of change during a time of reform in Irish secondary mathematics education. A teacher-researcher led action research project was conducted to depict the reality of the situation regarding the implementation of mathematical problem solving from a variety of perspectives-namely those of the pre-service teacher/teacher-researcher, the secondary school students, and the other mathematics teachers in the school. A problem-based approach to teaching and learning was implemented by the pre-service teacher using Van de Walle's teaching through problem solving framework in an attempt by the pre-service teacher to enact change at the classroom level. Following this intervention, participating students showed an improvement in engagement with mathematical problem solving and expressed positive opinions regarding the problem-based approach to teaching and learning. Meanwhile, other mathematics teachers in the school expressed concerns relating to the reality of implementing problem solving in their classrooms; however, these concerns were not issues faced by the author when implementing problem solving in the same setting. When these concerns were indirectly challenged by the preservice teacher a change in conversation occurred.

A lack of knowledge and appreciation of the prominence of mathematics in different careers can have a negative impact on a student's engagement with the subject. A perceived lack of relevance can result in disinterest, and even disengagement with mathematics entirely. This can lead to more serious consequences for the economy of a country who requires a consistent flow of well-educated science, technology, and mathematics graduates to ensure economic and social development. Research shows that the textbook is the most commonly used resource in Irish classrooms. Textbooks impact significantly on teaching and learning as they dictate what will be taught, in what order, and how. For this reason, this research commenced with an analysis of local textbooks to evaluate how well they highlight the relevance of mathematics within careers. This textbook analysis, in conjunction with interviews conducted with secondary school mathematics teachers, indicate a distinct lack of resources and support for teachers who want to highlight the relevance of mathematics within a range of careers as a means of enhancing student motivation and engagement with the subject. These findings motivated the conception of a pilot study designed to support secondary school mathematics teachers to fill this gap in teaching resources.

This study critically examines the mathematics knowledge of pre-service post-primary mathematics teachers (N = 85) on commencing their Professional Master of Education (Level 9) initial teacher education (ITE) programme across four institutions in Ireland. Given the nature of a consecutive approach to mathematics teacher education, pre-service teachers enter their ITE programme from a variety of undergraduate degree backgrounds and it is largely accepted that their mathematical content knowledge does not change during their teacher qualification programme. This study utilises a paper-and-pencil test to assess participants' cognitive and conceptual proficiency with curriculum-aligned mathematical content. Between group comparisons in relation to participants' undergraduate studies and cognitive and conceptual proficiency are also examined. The data suggest that pre-service teachers demonstrate a strong proficiency with Junior Cycle curriculum-aligned content and poor proficiency with Senior Cycle content, irrespective of the curriculum strand. In addition, significant mean differences exist between participants who had undertaken undergraduate degree studies in physics and mathematics in comparison to other degree programmes. Such investigations are essential given the increased focused on developing highly qualified teachers and policy revisions on ITE programmes. This research alerts us to issues within ITE programmes that may be addressed prior to mathematics teachers' induction into the profession.

Mathematics teacher educators in the University of Limerick became aware of a lack of conceptual understanding of key mathematics concepts of prospective secondary mathematics teachers through observation on teaching placement and in pedagogy lectures. A pilot study to enhance the conceptual understanding of prospective teachers was carried out with one undergraduate class in 2009/10 and a longer more in-depth programme was offered to all prospective mathematics teachers in the academic year 2011/12. The intervention was designed to get prospective mathematics teachers "thinking" about mathematics topics they have so far taken for granted and hence better prepare them for classroom practice. This retrospective study divulges a number of observations which emerged, the main one being how rote learning and an emphasis on procedural skills at the expense of conceptual understanding results in a cycle of ineffective teaching which is difficult to break.

This paper reports on an exploratory study designed to determine and enhance the conceptual understanding of a group of pre-service mathematics teachers at one Irish university utilizing an established framework for understanding mathematics. 23 students on a one year Professional Diploma in Mathematics Education participated in the study, which involved the distribution of a pre- and post-test and engagement in a ten week intervention designed to enhance their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). The findings highlight that although there was an improvement in overall conceptual understanding across the entire cohort at the end of the intervention, within certain mathematical topics there was a statistically insignificant improvement and many deep-rooted issues remain. In this paper we focus on the pre-service teachers' understanding of elementary algebra, in particular, how to solve a linear equation.

In August 2008, the Mathematics Learning Centre at the University of Limerick initiated a mathematics bridging course, entitled "Head Start Maths", to provide mathematics revision for adult learners about to embark on science or technology degree programmes. The aim of Head Start Maths was to revise mathematics fundamentals before the commencement of third-level education so as to lessen the anxiety levels of adult learners towards mathematics. Negative preconceptions have been noted as being of major concern with adult learners, both preconceptions of mathematics in general and also of their own abilities. In addition to this, it was hoped that Head Start Maths might lead to increased retention rates among adult learners and lead to less dropouts within the first semester. Results found that there were statistically significant increases in self-efficacy scores across some, but not all, of the mathematical topic areas and that there was an increase in the retention rates of adult learners who participated in Head Start Maths compared to those who did not.

The power and value of mathematics cannot be underestimated in today's society. Thus, it is pertinent that education systems worldwide help students to develop an appreciation of the subject. However, research has shown that students often lose interest in science, technology, engineering and mathematics subjects, particularly mathematics, as they cannot see the relevance of it in their lives. This, in turn, leads to the development of negative attitudes towards mathematics, which have been shown to have a knock-on effect on students' academic performance, their participation and engagement with and motivation for the subject. The purpose of this paper is to describe and evaluate the impact of an innovative programme, known as Career Mathways , designed to improve secondary school students' attitudes towards mathematics by highlighting the applicability and usefulness of the subject in a multitude of careers. Career Mathways was piloted in five Irish secondary schools in the 2018/2019 academic year. It involved professionals (n  = 13) from a variety of industries sharing insights with students (n  = 156) and teachers (n  = 6) about how they use mathematics in their day-to-day working lives. Based on these insights, a suite of resources for use in the classroom was developed and implemented with students across the five schools. This paper reports on the impact that this pilot study had on students' attitudes towards mathematics. The results from pre- and post-student surveys and teacher interviews show that Career Mathways had a moderate but positive influence on students' appreciation of the usefulness of mathematics and this impact was more profound among lower-achieving students. [ABSTRACT FROM AUTHOR]

This paper offers insight into teachers' perspectives on the role of manipulatives in the mathematics classroom on either side of the primary to post-primary transition (sixth class teachers in Irish primary schools and first year mathematics teachers in post-primary schools) to examine if discontinuities exist around their usage. The transition from primary to post-primary education is considered the most difficult of all educational transitions that students face, with negative effects more pronounced in the subject of mathematics. A questionnaire involving several open-ended questions was distributed to teachers teaching students in the final year of primary school and teachers teaching mathematics to students in the first year of post-primary education. Results of the qualitative data analysis reveal insights into teachers' perceptions of the benefits, supports and obstacles to manipulative use. It reveals that, in general, teachers on either side of the boundary crossing are in agreement regarding the perceived benefits of using manipulatives and also the potential factors that inhibit their usage. On the other hand, their opinions regarding the factors that support the use of manipulatives are more divergent. [ABSTRACT FROM AUTHOR]

The transition from primary to post-primary education is considered the most difficult of all educational transitions, with negative effects more pronounced for mathematics. One factor affecting the fluidity of transition is discontinuities in pedagogical approaches. This study investigates one pedagogical approach, the use of manipulatives, to identify if discontinuities exist in their usage between primary and post-primary mathematics education. A questionnaire was distributed to teachers teaching students in their final year of primary school and teachers teaching mathematics to first-year students in post-primary school. Results reveal disparities in teachers' responses. A significantly larger proportion of primary teachers report using manipulatives in three or more lessons per week than their post-primary colleagues. This shows a discontinuity in the educational experiences of students which contributes to ineffective transition. Reasons for the existence of this discontinuity were identified. Teachers' confidence levels and the perceived usefulness of manipulatives may account for greater use of manipulatives at primary level but this study found that these reasons stemmed from the lack of training available to post-primary mathematics teachers. A large number of primary teachers reported receiving training in the use of manipulatives but for post-primary teachers this training, consisted of 'one lecture on algitiles', at best. [ABSTRACT FROM AUTHOR]

This pilot study explores the effectiveness of a strategy for overcoming post-primary students’ misconceptions within the topic of algebra. Although central to the study of mathematics, algebra can be an area of difficulty for many students. A misconception is typically classified as flawed understanding of a concept causing repeated errors, and the prevalence of algebraic misconceptions has been well documented in the literature. Previous studies in probability and statistics have shown that the use of analogies to misconception-prone situations can act as anchors to effect conceptual change and assist in correcting misconceptions. This project follows a framework that has been successfully utilised in previous research, with two versions of a test and interviews conducted with 25 students. The results identified the presence of, and links between, some common misconceptions among the students regarding their knowledge of algebraic equations and also provided insight regarding an effective technique for addressing these misconceptions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]