Nine members of the EPI*STEM centre, Prof John O’Donoghue, Dr Patrick Johnson, Dr Niamh O’Meara, Dr Ciara Lane, Dr Richard Walsh, Aoife Smith, Kathy O’ Sullivan, Bernie Ní Dhonnchú and Aoife Guerin travelled to Hamburg University, Germany to participate in the ICME 13 conference.
Prof John O’Donoghue
John was an invited lecturer at ICME-13. John’s paper attempts to develop an understanding of the concerns, issues and developments in mathematics education in Ireland in recent years as they impact on adult learners of mathematics and adult mathematic education generally. John’s paper placed emphasis on the mathematical underpinnings of numeracy, while acknowledging the interdependence of literacy and numeracy. A small number of perspectives are offered to frame the Irish mathematics education landscape (IMEL) and used to clarify issues and priorities and generate insights regarding adult mathematics education in Ireland. While the framing of the landscape activity is of its nature ‘macro level’ work, John also pursues some ‘micro level’ issues for a more balanced view where appropriate. The framing perspectives offered in John’s paper include: government policy imperatives; mathematics education; the ‘mathematics problem’; recent reforms and developments in mathematics education in Ireland; numeracy policy. Potentially, significant benefits are available but largely unrealised, for acknowledging the mathematical nature of numeracy. Understanding the mathematical nature of numeracy and its ramifications for adults’ mathematics/numeracy is a mathematics education question that falls squarely under the remit of mathematics education researchers. John concluded his presentation with noting that putting numeracy on mathematics educators’ research agenda is an immediate benefit that could lead to more numeracy research, and it also makes available in a more systematic way the whole gamut of mathematics education research for application to the lifelong mathematics continuum encompassing numeracy for all learners including adults. Finally, John noted how such engagement creates a two way street between mathematics education research and research in adult mathematics education/numeracy that must lead to mutual benefits.
Dr Patrick Johnson
Research indicates that many pre-service mathematics teachers lack the conceptual understanding required to teach effectively when they graduate from their Initial Teacher Education [ITE] programme. Patrick reported on a study designed to enhance the conceptual understanding of a group of pre-service mathematics teachers at one Irish university by utilizing Usiskin’s (2012) framework for understanding mathematics. 23 students on a Professional Diploma in Mathematics Education participated in the study which involved the distribution of a pre-and post-test test and engagement with a mathematics thinking intervention. The findings of this study demonstrate that while overall an improvement in conceptual understanding was observed, the improvement was not as pronounced as the researchers would have hoped and many deep rooted issues remain. The focus of Patrick’s presentation was on the preservice teachers’ understanding of elementary algebra, in particular, how to solve a linear equation.
Dr Niamh O’Meara was also co-author of the paper presented by Dr Patrick Johnson, along with Dr Olivia Fitzmaurice and Dr Sean Lacey.
Dr Niamh O’Meara and Dr Mark Prendergast
Niamh’s and Mark’s study focused on the inequity surrounding the time spent in instruction in mathematics. This study investigates variations in time and also examines the provision of additional voluntary classes to some students outside of the regular school day. The sample for this study was 400 deputy principals and 1600 teachers and the findings highlighted that the time allocated to mathematics varies between schools and the provision of additional voluntary classes is prevalent. The majority of teachers who responded provide additional classes in their own time and without pay. This finding combined with the differences in the allocation of time to mathematics between schools means there is an inequity for some students in relation to the time they spend engaged in mathematics education. Due to the correlation between time allocation and achievement in mathematics, this means that some students are not given the same opportunities as other students to succeed in mathematics. For example, the majority of teachers of Senior Cycle involved in this study stated that the class time provided on a voluntary basis resulted in their students being exposed to an additional 41 – 60 minutes per week. Again when the cumulative time over the course of the two years is considered the students of the 68.8% of teachers who stated that they provide additional classes would be exposed to 3700 additional minutes (61.6 hours) more than students who were not given the opportunity to engage in these classes. Niamh and Mark spoke about how these discrepancies, both in terms of allocated class time and the provision of additional class time, are serious concerns that need to be highlighted in order to ensure a fair and balanced education system for all and to ensure that each Irish student has an equal chance to succeed in mathematics.
Dr Ciara Lane and Dr Fiona Faulkner
Ciara’s and Fiona’s paper reported on a study of an innovative Continuing Professional Development (CPD) program established in the Republic of Ireland for out-of-field Mathematics teachers in second-level education. Research on out-of-field mathematics teachers in Ireland conducted in 2009 (Ní Ríordáin & Hannigan) motivated the development of a unique two year, part time Professional Diploma in Mathematics for Teaching (PDMT) that was first offered in 2012 jointly by the University of Limerick (UL) and the National University of Ireland, Galway and currently has 550 graduates. Initial findings regarding students’ opinions of this unique programme are outlined in Ciara’s and Fiona’s paper. Initial findings from the evaluation surveys indicate that, while there were some issues in the initial years of the PDMT, participant satisfaction with this unique programme has increased over time as preliminary technical difficulties were overcome. While the programme requires a significant time and work commitment, which can be stressful for participants as they are also teaching full-time, the general consensus is that the programme is a positive means of achieving professional development and advancement as a mathematics teacher. Currently, various aspects of the PDMT are being investigated, not only in terms of CPD, but also with regards to blended-learning, mathematical content knowledge, action research and teacher identity. As this programme is a novel initiative, it has the potential to provide the education community with invaluable information and feedback that could be of benefit not only in Ireland, but on an international level.
Dr Richard Walsh
Richard presented a paper which focused on an aspect of his PhD research ‘A Purpose-Built Model for the Effective Teaching of Trigonometry: A Transformation of the van Hiele Model’. His presentation focused on a 16 item trigonometry assessment which he developed as part of his research. This assessment examined trigonometric concepts from primary level up to the end of secondary level. In Richard’s presentation, the findings from the evaluation of this assessment, after it was administered to a sample of 50 pre-service secondary level mathematics teachers at an Irish university was discussed. The study showed that the sample of pre-service teachers at this university were not at a level required for teaching trigonometry at secondary level. The sample of pre-service teachers had gaps in their subject matter knowledge (SMK) which were revealed in the concepts of trigonometric ratios and Pythagoras’ theorem, amongst some of the sample, as well as in the concepts of quadrants, radians and trigonometric functions amongst the majority. The study showed that the sample had deficiencies in their understanding of secondary level trigonometry and had a level of subject matter knowledge (SMK) that would only allow them to teach the early years of secondary trigonometry for understanding. Richard’s talk concluded with the implications that the findings of his study has on teacher education. Without understanding fundamental concepts in trigonometry, a teacher cannot teach the topic for a conceptual understanding and will resort to rote methods of teaching and learning for higher order content. Teacher training institutions must ensure that fundamental concepts and their links to higher order concepts are understood by all of their pre-service teachers before the completion of their studies.
Aoife Smith
Aoife’s poster for ICME-13 presented information on the Maths Eyes initiative in Ireland, with a focus on the Maths Eyes National Poster competition. The poster presented is focused on the number of entries to the competition and an initial evaluation on one of the Maths Eyes projects, namely the Dominican Campus Project. The poster concluded with the research questions that will inform Aoife’s overall PhD research investigation.”
Bernie Ní Dhonnchú
Bernie presented a poster titled ‘Let’s Learn Literacy for Mathematics Teaching from Pólya and Meyer’. Her presentation focused on an aspect of her research that aims to define literacy and numeracy for second level mathematics teaching in Ireland. A comparative analysis of George Pólya’s teacher/student dialogues and Dan Meyer’s digital resources is presented in Bernie’s poster. Her research examines patterns of verbal communication in Pólya and Meyer’s mathematics instruction with the aim of identifying literacy elements necessary for mathematical proficiency.
Kathy O’ Sullivan
Kathy’s poster for ICME-13 presented information on key issues in numeracy at post-primary level, focusing on policy framing, definitions and teacher knowledge. Kathy’s presentation focused on many key issues surrounding the teaching and learning of numeracy which pose significant challenges. From a policy perspective numeracy is increasingly seen as an important, if not essential, component of all teachers professional remit. A significant challenge at both the levels of policy schools, especially secondary schools, is the issue of defining numeracy. Differing perceptions often revolve around the common misconception that teaching numeracy is solely the role of teachers of mathematics. The issue of where numeracy resides in terms of teacher knowledge frameworks is examined in Kathy’s PhD work.
Aoife Guerin
Aoife presented a paper on the formulation of a framework for teaching and assessing problem solving in second level mathematics. Her presentation focused on an aspect of her research which addresses the complexity of problem solving in mathematics, by amalgamating theories in relation to knowledge and affective factors, which affect the growth of problem solving ability in individuals. Mathematical thinking is central in this framework. Part of the findings of an assessment in problem solving in the area of number and algebra, undertaken by pre-service teachers at an Irish university were presented. These findings indicate the need to implement instruction in problem solving in mathematics as part of the teacher education program in mathematics at third level, with the intention of such instruction being on gaining insight into how students develop proficiency in problem solving and how teachers can best support this development. The design and implementation of an intervention aimed at improving problem solving was also briefly considered in her presentation.
Researchers Previously Affiliated with EPI*STEM:
Dr Fiona Faulkner, Dr Mark Prendergast, Dr Páriac Treacy, Dr Terry Maguire and Dr John Keogh. ICME-13 provided an opportunity for current and past researchers affiliated with EPI*STEM to reunite. These researches all presented papers on various topics in Mathematics education during the ICME-13 conference.