Mairéad Hourigan

Mathematical under-preparedness: the influence of the pre-tertiary mathematics experience on students’ ability to make a successful transition to tertiary level mathematics courses in Ireland

Internationally, the consequences of the ‘Mathematics problem’ are a source of concern for the education sector and governments alike. Growing consensus exists that the inability of students to successfully make the transition to tertiary level mathematics education lies in the substantial mismatch between the nature of entrants’ pre-tertiary mathematical experiences and subsequent tertiary level mathematics-intensive courses. This paper reports on an Irish study that focuses on the pre-tertiary mathematics experience of entering students and examined its influence on students’ ability to make a successful transition to tertiary level mathematics. Brousseaus ‘didactical contract’ is used as an intellectual tool to uncover and describe the contract that exists in two case mathematics classrooms in Irish upper secondary schools (Senior Cycle). Although the authors are professional mathematics educators and well informed about classroom practice in Ireland, they were genuinely surprised by the very restrictive nature of this contract and the damaging consequences for students’ future mathematical education.

The challenges facing initial teacher education: Irish prospective elementary teachers’ mathematics subject matter knowledge

Given the acknowledged relationship between teachers’ knowledge, their teaching and pupil learning, teachers’ mathematics subject matter knowledge (MSMK) has received increased attention internationally. As childrens early mathematics experiences have been recognized as a critical stage, elementary teachers’ MSMK has become a focal point among researchers and policy makers alike. International research findings have uncovered that in many cases, there is a mismatch between what is perceived to be an appropriate MSMK for teaching elementary mathematics and that demonstrated by many qualified and prospective elementary teachers. Following repeated incidences of weak MSMK during interactions with prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme for elementary teachers), this study sought to examine and address the issue purposefully through two cycles of action research. This article focuses on the data collected prospective teachers’ MSMK in the initial stage (reconnaissance) of these cycles, i.e. pre-test findings. While considerable differences were evident among the pre-test population, the findings suggest that prior to the intervention stage many participating prospective teachers; regardless of previous mathematics achievements or the level of mathematics study; demonstrate weaknesses and gaps in their ‘common’ MSMK. Particular difficulties were evident in relation to pre-test items requiring knowledge of rational numbers, conceptual understanding or problem solving. These findings highlight the inadequacy of previous mathematics achievements and indeed minimum entry requirements as predictors of MSMK for teaching. As well as its contribution at a local and national level, the findings provide an Irish perspective on this international issue.

Addressing prospective elementary teachers’ mathematics subject matter knowledge through action research

There is international dissatisfaction regarding the standard of mathematics subject matter knowledge (MSMK) evident among both qualified and prospective elementary teachers. Ireland is no exception. Following increasing anecdotal evidence of prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme) demonstrating weaknesses in this regard, this study sought to examine and address the issue through two cycles of action research. The examination of the nature of prospective teachers’ MSMK (as well as related beliefs in the main study) informed the design and implementation of an intervention to address the issue. A mixed method approach was taken throughout. In both cycles, Shapiros criteria were used as a conceptual framework for the evaluation of the initiative. This paper focuses on the perceived and actual effects of the intervention on participants’ MSMK. As well as its contribution at a local and national level, the study provides an Irish perspective on approaches taken to address the phenomenon internationally.

Come in with an Open Mind: Changing Attitudes towards Mathematics in Primary Teacher Education.

Abstract Background: The relationship between attitudes and behaviour has led to a focus on the role played by attitudes in the teaching and learning of mathematics. Purpose: This paper reports on an investigation into student teachers’ self-reported attitudes towards mathematics in the context of a mathematics education programme. The programme had been developed by the authors in response to a new, reformed four-year undergraduate initial teacher education (ITE) for primary teachers in Ireland. The authors aimed to use the feedback to evaluate and develop the course further. Sample: We report on the attitudes of 345 pre-service primary teachers enrolled in a four-year undergraduate ITE programme. 281 of these participants had matched survey data before and after participating in the mathematics education programme. Method and Design: Four evaluation criteria were used as a conceptual framework for the evaluation of the mathematics education programme. A multi-method approach was taken in investigating the students’ attitudes to mathematics by using a scale as a quantitative measure of attitude alongside open-ended survey items that provided qualitative insights into changes in attitudes. Results and conclusions: Results from the survey data suggested overall that the participants’ attitudes towards mathematics were more positive after they had experienced the mathematics education programme. Overall, the written responses suggested that according to self-reportage, participants perceived that participation in the mathematics education programme had affected their attitudes towards mathematics positively. Comments indicated that the ‘small group’ tutorial structure was particularly well received and was associated with opportunities to actively engage, explore, interact and reflect. Suggestions offered by the participants will be used to inform planning and development of the mathematics programme.

Rate Your Course! Student Teachers' Perceptions of a Primary Pre-Service Mathematics Education Programme.

Abstract Although research suggests that many pre-service mathematics education programmes are weak interventions having a negligible effect on student teachers’ knowledge, beliefs and attitudes, there is consensus that programmes that model and engage student teachers in reform teaching and learning approaches have the potential to effect positive change in attitudes and knowledge of mathematics. This paper focuses on the perceptions of 345 student teachers regarding their mathematics education programme. The authors consider that in order to further our understanding of the characteristics of an effective pre-service mathematics education programme, the opinions of participating student teachers are fundamental. Participants reported improved mathematical subject matter knowledge and pedagogical content knowledge in addition to greater confidence and decreased anxiety towards mathematics. Programme features such as small group tutorials and interactive engagement were identified as impacting this positive change.

Developing potentiality: pre-service elementary teachers as learners of language immersion teaching

ABSTRACTResearch has shown immersion to be effective, yet our understanding about the integration of language and content in Irish-medium immersion (IMI) pedagogy remains incomplete. This article r...

Inscriptional Capacities and Representations of Young Children Engaged in Data Collection During a Statistical Investigation

Recent research has provided important insights into young children’s statistical reasoning when engaged in core components of data modelling, namely attribute selection, data representation and metarepresentational competence. The research described in this chapter, however, explores the stage prior to attribute selection—the collection of data. We describe young children’s inscriptions when collecting data within the context of a four-day statistical investigation. The investigation involved 26 children aged 5–6 years in interpreting and investigating a context of interest and relevance to them. The context involved decision making around the design of a zoo. We describe the repertoire of inscriptions that children used to track the appearance of zoo animals and explore their justifications for their invented inscriptions. The rationale for and genesis of inscriptions ranged from aesthetic considerations, ease and simplicity, to contextually driven decision making and approaches motivated by efficiency and by efforts to distinguish between repeated data values and different instances of the same attribute. We argue that when task interest is high the context provides affordances that support authentic data inquiry and data-based reasoning. Moreover, when the focus of the statistical investigation is on having children reason about and understand situations, what emerges are relatively sophisticated approaches to data inscription arising from efforts to make sense of and communicate statistical situations.

The influence of entry route to teaching on Irish pre-service primary teachers’ attitudes towards mathematics

Abstract Research examining the characteristics of both qualified and pre-service teachers focuses on traits including gender, socio-economic and socio-demographic background, knowledge and a variety of relevant affective constructs. Studies also investigate such traits among entrants to initial teacher education (ITE). The desire for more diversity within the teaching profession has led to alternative entry routes to the teaching profession (consecutive model for post-graduates) for those who may be unable to gain entry via the traditional concurrent (undergraduate) route. Internationally, there are divergent viewpoints and practices in relation to the value and use of the respective routes. This paper presents a comparative study within the Irish context, examining whether the consecutive model route to ITE promotes diversity in terms of entrants’ attitudes to mathematics. The study examines the entry-level mathematics attitudes of two distinctive groups of ITE entrants, namely 419 concurrent and 59 consecutive elementary pre-service teachers, in one Irish ITE institution prior to engagement with their ITE mathematics education programme. It compares their enjoyment of mathematics as well as their beliefs regarding the value of mathematics and examines the extent to which any distinguishing differences are apparent among the respective cohorts using the Aiken’s Revised Mathematics Attitude Scale. Analyses indicate generally positive attitudes among both cohorts; however, differences are evident between the cohorts with the consecutive route cohort demonstrating particularly apposite attitudes. The findings support the belief that the consecutive ITE route holds merit and prompts further investigation regarding the unique dispositions that these entrants possess.