ACKNOWLEDGEMENTS This report draws substantially on my Ph.D. research which was supervised by Professor John O’ Donoghue at the University of Limerick and completed in November 2008. Anyone wishing to read more detailed information about the study can read the dissertation which is available from me on request. Financial support for this study was provided by the University of Limerick’s Advanced Scholars Programme; by the Department of Mathematics and Statistics at the University of Limerick; and in particular by the Mathematics Applications Consortium for Science and Industry (MACSI) and the National Centre for Excellence in Mathematics and Science Teaching and Learning (NCE-MSTL). I am very grateful to each of the funding sources without whose support the study could not have been completed. Publication of this report is funded by the NCE-MSTL and St. Patrick’s College, Thurles. Again, my sincere thanks for this financial support. Finally, I would like to thank all the participants in this study and those whose support, cooperation and expertise ensured the completion of this research project, in particular Professor John O’ Donoghue and the ‘Maths Ed’ group in the University of Limerick. Go raibh míle maith agaibh go léir. Máire Ní Ríordáin Ph.D. Head of Education, St. Patrick’s College, Thurles, Co. Tipperary. Email: [email protected] May 2011 i PREFACE This report/monograph is based on a doctoral study completed by Dr Máire Ní Ríordáin at the National Centre for Excellence in Mathematics and Science Teaching and Learning (NCE-MSTL). We are charged under our brief at the National Centre to engage in evidence-based world class research in Science and Mathematics Teaching and Learning and to bring our findings to bear, inter alia , on advice offered to stakeholders in Irish education. This is the second report in the series following NCE’s groundbreaking report, Out-of-field teaching in Post-Primary Mathematics Education: An analysis of the Irish context (2009) and it focuses on language issues in mathematics teaching and learning. The study focuses on the plight of a significant but growing minority of Irish students studying mathematics in a bilingual setting (c. 7% of the national cohort of primary and 2.5% of post-primary students in 2007). It is the first study to examine whether learning issues arise in mathematics classrooms for students and teachers at the transition from Gaeilge medium to English medium education. This report demonstrates that priorities in science and mathematics education intersect national priorities in language policy, which is timely in the context of a national focus on literacy and numeracy issues. The author applies and exploits international research on bilingual education generally and bilingual mathematics education in particular to ground her study and advance her thesis. Professor Bill Barton, an eminent international authority in the field and her external examiner, concludes that ‘the study is both timely and also represents work at the forefront of research in bilingual mathematics education’. This is underlined by her papers in Educational Studies in Mathematics and the Mathematics Education Research Journal . The report throws light on previously unnoticed and unreported learning issues in mathematics for Gaeilgeoirí (students who learn through the medium of Irish) who make the transition from Gaeilge medium education to English medium education, and demonstrates the advantages of a bilingual approach to mathematics education in Irish schools. The report adds new evidence-based analyses on language issues in ii mathematics education that are timely in terms of the national Irish language policy debate, formulation and implementation. A major finding of the study points to the advantages of bilingualism for mathematics education. Also the awareness that the report brings in terms of equity issues offers the opportunity for these to be addressed in the context of new language policy development. The Directors are pleased to discharge their brief to advise on matters related to Science and Mathematics teaching in this way and commend this report to all who have a stake in Irish education and particularly to those front-line agencies involved in improving matters in Mathematics and Science teaching at all levels. Prof. John O’Donoghue Co-Director (Mathematics) NCE-MSTL, University of Limerick Dr. George McClelland Co-Director (Science) NCE-MSTL, University of Limerick iii SUMMARY OF THE STUDY Introduction Teaching and learning through the medium of Gaeilge (Irish) is the natural school environment for teachers and pupils in the Gaeltacht areas (Irish speaking districts) of Ireland. A parents’ initiated movement in the early seventies was responsible for the establishment of Gaeilge-medium primary and secondary schools outside of the Gaeltacht regions, known respectively as Gaelscoileanna and Gaelcholáistí (Coady & Ó Laoire, 2002). The number of students attending Gaeilge-medium schools has witnessed a marked increase (Fás ar an nGaelscolaíocht sa Ghalltacht, 2006). However, learning issues may arise both for students and teachers at the transition from Gaeilge-medium education to English-medium education. This is inclusive of both key transition periods – primary level to second level education, and second level to third level/further education. Gaeilgeoirí submerged in the transitions under investigation will be required not only to learn new mathematics, but also to learn mathematics through the medium of English (Barwell, 2003). This research report will present findings from a doctoral study undertaken on bilingualism and mathematics education in the Irish context, the first study of its type to examine the Irish situation. Aim of the Study The aim of the study was to investigate Irish post-primary and undergraduate bilingual mathematics students’ (Gaeilgeoirí) experiences of learning mathematics through the medium of English, their second language of learning. This includes examining the relationship between language proficiency and performance on mathematics word problems; investigating additive and subtractive bilingualism in an Irish context; examining sources of difficulty encountered with the English language mathematics register; and in the process developing significant insights into cultural and pedagogical influences on the transition from Gaeilge-medium to English-medium mathematics education. iv Additive and Subtractive Bilingualism There are several different types of bilingual education programmes and within these types further subdivisions arise. These programmes can be classified under the broad terms of weak or strong bilingual education (Baker, 2000). Weak forms tend to include schools/institutions that contain bilingual individuals as opposed to encouraging bilingualism. These schools/institutions usually enrol language minority students with the aim of developing learning through the majority language (Baker & Prys Jones, 1998). On the other hand, strong forms of bilingual education are developed when the primary aim is to develop complete bilingualism in both languages, and both cultures are supported (Baker & Prys Jones, 1998). Furthermore the concept of weak and strong bilingual education programmes is associated with subtractive and additive bilingualism. Subtractive bilingualism usually occurs when a majority language replaces a minority language (Lambert, 1990). Students are forced to adapt quickly into mainstream education where the majority language is used as the medium of instruction. No support is given to the mother-tongue, resulting in it slowly being replaced (Bournot-Trites & Tellowitz, 2002). This is similar to the experiences of Gaeilgeoirí transferring from Gaeltacht schools (Maintenance Heritage Language) to all-English-medium schools. The situation is different in the case of additive bilingualism. In this instance the mother-tongue of the child is the majority language and they opt to study through a second language, which is a minority language (Lambert, 1990). This is similar to Immersion education (Gaelscoileanna/Gaelcholáistí) in operation in Ireland. The intention is not to replace the majority language but to develop the second language (Bournot-Trites & Tellowitz, 2002). Description of the Study The study incorporated three phases and it was carried out over the course of a three year period (October 2005 – September 2008). A mixed methods approach was adopted in the study (qualitative and quantitative data/analysis). In Phase 1 a comprehensive review of literature was carried out in order to gain an in-depth knowledge of the area of learning mathematics through the medium of a second language, as well as examining areas such as psycholinguistic theories, bilingualism v and bilingual education. This Phase incorporated and combined conclusions and recommendations from an undergraduate dissertation with new exploratory research. Phase 1 facilitated the design of the methodology to be employed in Phase 2 of this research project. Phase 2 was devoted to data collection at both transitions, from primary to second level and from second level to third level education. The qualitative and quantitative analysis of the data collected was carried out in Phase 3 and relevant findings discussed. Subjects Involved in the Study This study was concerned with Gaeilgeoirí in the transition from Gaeilge-medium (primary or second level education) to English-medium mathematics education (second or third level education). Two types of Gaeilge-medium