Investigating mathematics teacher efficacy beliefs in primary initial teacher education

This paper will discuss the mathematics teacher efficacy beliefs (MTEB) of primary initial teacher education (ITE) students. We are interested in studying how ITE students’ MTEBs are influenced (or not) by mathematics education modules undertaken as part of an undergraduate Bachelor of Education (BEd) programme. We will detail how approximations of practice (Grossman, Compton, Igra, Ronfeldt, Shahan, & Williamson, 2009) have been incorporated into mathematics education modules to create opportunities for the development of MTEBs and will report on focus group interviews which explored MTEBs of ITE student

The construction of general terms for shape patterns: strategies adopted by children attending Fourth class in two Irish primary schools

Generalisation is considered by many to be a highly significant component of algebraic thinking (Carpenter & Levi, 2000; Kaput et al., 2008). In particular, constructing general terms for shape patterns supports children in reasoning algebraically about covariance and rates of change (Rivera & Becker, 2011). Generalisation is not mentioned within the current Irish Primary School Mathematics Curriculum, and shape patterns are not presented as learning activities, beyond simple repeating patterns explored with very young children (Government of Ireland, 1999). This thesis reports on a research study that explored the strategies Irish children adopted in seeking to construct general terms for shape patterns. Within the context of task-based group interviews, patterning tasks were presented to groups of three or four children (aged nine or ten years old), where the children were asked to describe and extend the patterns, and to consider near and far generalisations. Following the interviews I analysed the strategies that children used to generalise from the patterns, drawing from the work of Lannin (2005) and Rivera and Becker (2011). Taking a hermeneutic phenomenological approach, I included identification and analysis of factors that contributed to children’s strategy choices, which included explicit, recursive, numerical and figural approaches. Findings evidence the potential of children to respond in complex and sophisticated ways to novel tasks, when rich engagement with the mathematics was facilitated through the context of a task-based group interview. The research study demonstrates the necessity for conceptualising children’s thinking as multi-faceted whereby observations of relationships within patterns interact with attention to numerical and figural aspects. In addition, evidence is presented to support the contention that observations of structure exist along a continuum from numerical to figural. The study highlights the potential of task-based group interviewing coupled with hermeneutic phenomenological analysis in facilitating in-depth research into children’s emerging mathematical thinking

Algebra in the senior primary classes: Commissioned research paper

Children’s engagement with algebraic thinking has traditionally commenced in senior primary or secondary school, preceded by primary school curricula that prioritised computation and understandings of number (Kieran, et al., 2016). Increasingly during the latter decades of the 20th century, educators and researchers identified that such an approach may contribute to insurmountable challenges for some children when they first encounter formal algebra, typically after six to eight years of school. In this paper I present the research underpinning the Early Algebra movement that arose from a motivation to address such challenges, and the implications of Early Algebra for the Irish Primary School Mathematics Curriculum (IPSMC). While the 1999 IPSMC included algebra as a content strand, key concepts of Early Algebra, such as generalisation, and exploration of structure, are absent (Twohill, 2013)

Young children's use of subjective thinking in response to probabilistic tasks

This paper reports on a study that investigated young children’s responses to a range of probabilistic tasks. A central aspect of the study was our examination of the children’s use of subjective thinking. Most research that has been conducted in relation to young children’s probabilistic thinking has focused on the extent to which young children can identify the most and least likely outcome of experiments. There is, however, limited research into the types of judgements children use when making these identifications. For example, while a small number of studies have reported on children’s use of subjective thinking, there is an absence of research focusing on the role of subjectivity and the range of beliefs on which these judgements are based. In this research, the subjective thinking of children aged 5–6 years in Ireland was examined to address this gap in current knowledge. The data were collected through task-based group interviews and analysed using thematic analysis. Results suggest that a range of personal beliefs and experiences influence young children’s probabilistic thinking including the physical position of objects, personal affinity for one possible outcome, a desire to win, and the influence of previous experiments

Investigating the mathematics teaching efficacy beliefs of student teachers

This research study seeks to explore the Mathematics Teaching Efficacy Beliefs of student teachers as part of a longitudinal design-research study, whereby research findings will guide planning for future modules. The Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) of Enochs, Smith and Huinker (2000) was employed to measure the overall efficacy beliefs of teachers, and also the beliefs within two subscales, the Personal Teacher Efficacy, and Teaching Outcome Expectancy. A convenience sample of 40 undergraduate students participated in a questionnaire based upon the MTEBI with additional questions relating specifically to the content of a Mathematics Education module recently completed by the students. The sample was drawn from a year group of 440 students by invitation

Young children's identifications of the most and least likely outcomes of experiments

The aim of this study was to investigate the probabilistic thinking of young children, focusing in particular on the judgements that influence their identifications of the most and least likely outcomes of experiments. Research studies present conflicting results pertaining to young children’s potential to engage in probabilistic thinking and a wide variance exists across international mathematics curricula regarding the age at which children receive formal probabilistic instruction. At present, young children in Ireland are not formally introduced to probability until Third class when they are approximately 8 or 9 years old. In this study, the probabilistic thinking of 16 children aged 5-6 years was examined using task-based group interviews. The results suggest that young children are capable of engaging in sophisticated probabilistic thinking and highlights that the current practice of formally introducing children to probability in Third class warrants further investigation

Associations of students self-reported efficacy beliefs towards mathematics education on completion of their first year in initial teacher education.

Recent changes in the landscape for primary initial teacher education (ITE) in Ireland prompted the first stage of this longitudinal design-research study on Mathematics Education which sought to establish a model of teaching and learning based upon iterations of research upon practice (Borko, Liston, & Whitcomb, 2007). The challenge was to design a research led undergraduate Bachelor of Education (B.Ed.) mathematics programme of study that would focus on the development of students’ efficacy, and more particularly in Year 1, on students’ knowledge of and approaches to the teaching of Measures and perceived implementation of same on their first teaching placement in schools. This first phase of the study gathered students' views retrospectively on the B.Ed. 1 programme, and explored their perceptions of the skills and abilities they possessed whilst teaching mathematics on School Placement. The entire cohort of 430 first year ITE students were invited to participate in an online questionnaire based upon Enochs, Smith and Huinker’s (2000) mathematics teacher efficacy beliefs instrument (MTEBI) with a small number of more open questions pertaining to the particular content of the first year programme. This paper presents an analysis of the responses to the questionnaire and the implications for future research. While the response rate to the questionnaire was disappointing (40 questionnaires completed from 430 students invited) some preliminary findings include moderate self-efficacy scores across the MTEBI subscales, many students’ inclination to draw from research-based resources in planning, and a specific lack of self-efficacy relating to the use of manipulatives

Design and redesign: investigating mathematics teacher efficacy in primary initial teacher education

This research was initiated as a proactive response to a major reform of the structures of initial teacher education (ITE) in Ireland to support best practice (Teaching Council, 2017). We are undergoing an iterative process of design research with the intention of investigating and refining the mathematics education modules undertaken by students on our undergraduate Bachelor of Education programme (Borko, Liston & Whitcomb, 2007).The first phase of the research involved the design of a module on Measures for 460 first year ITE students. Students’ perceptions of the module and their mathematics teacher efficacy beliefs were investigated using an online questionnaire based on Enochs, Smith and Huinker’s (2000) Mathematics Teacher Efficacy Beliefs Instrument (MTEBI). The second phase of data collection will commence soon. This involves inviting the same cohort to participate in focus group interviews

Working Group Report: Task Design for Early Algebra

The focus of this newly established working group is on the complexities of designing tasks for engaging children in algebraic thinking. The working group aims to engage PME participants in interrogating the multiple ways in which robust task design supports teachers in facilitating children’s learning, within the topic of early algebra. The facilitators of the working group will present relevant theory from the distinct research fields of task design and early algebra, and participants will be invited to explore how insights from task design may be made manifest to address the specific needs of children engaging with algebraic thinking in elementary school

The construction of general terms for shape patterns: strategies adopted by children attending Fourth class in two Irish primary schools

Generalisation is considered by many to be a highly significant component of algebraic thinking (Carpenter & Levi, 2000; Kaput et al., 2008). In particular, constructing general terms for shape patterns supports children in reasoning algebraically about covariance and rates of change (Rivera & Becker, 2011). Generalisation is not mentioned within the current Irish Primary School Mathematics Curriculum, and shape patterns are not presented as learning activities, beyond simple repeating patterns explored with very young children (Government of Ireland, 1999). This thesis reports on a research study that explored the strategies Irish children adopted in seeking to construct general terms for shape patterns. Within the context of task-based group interviews, patterning tasks were presented to groups of three or four children (aged nine or ten years old), where the children were asked to describe and extend the patterns, and to consider near and far generalisations. Following the interviews I analysed the strategies that children used to generalise from the patterns, drawing from the work of Lannin (2005) and Rivera and Becker (2011). Taking a hermeneutic phenomenological approach, I included identification and analysis of factors that contributed to children’s strategy choices, which included explicit, recursive, numerical and figural approaches. Findings evidence the potential of children to respond in complex and sophisticated ways to novel tasks, when rich engagement with the mathematics was facilitated through the context of a task-based group interview. The research study demonstrates the necessity for conceptualising children’s thinking as multi-faceted whereby observations of relationships within patterns interact with attention to numerical and figural aspects. In addition, evidence is presented to support the contention that observations of structure exist along a continuum from numerical to figural. The study highlights the potential of task-based group interviewing coupled with hermeneutic phenomenological analysis in facilitating in-depth research into children’s emerging mathematical thinking