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    Striving toward equity : a story of positioning and status : a thesis presented in fulfilment of the requirements for the degree of Doctor of Philosophy in Education at Massey University, Albany, New Zealand
    (Massey University, 2022) Leach, Generosa Angela
    This study explores how teachers construct equitable learning environments in primary school mathematics classrooms as a means of striving toward equity. The deep complexity of classrooms and numerous connected elements that influence students’ access and opportunities for learning mathematics are highlighted. Under consideration are the different pathways teachers take as they develop and maintain responsive and adaptive approaches to position all students to learn mathematics in ways that meet the aims of equity in mathematics education. A qualitative design research methodology was employed to explore the complexities and challenges of teacher learning and change within primary school classroom settings. The design approach supported the development of a model of professional learning and frameworks of teacher instructional actions to establish and maintain mathematics classrooms focused on equity. Data collection over the school year included study group meetings, participant observations, video-recorded observations, documents, and teacher and student recorded reflections and interviews. Retrospective data analyses drew the results together to be presented as cases of two teachers, their classrooms, and students. The findings show that constructing equitable mathematics learning environments is a gradual and complex process. It involves teachers reconstructing their beliefs and enacting specific instructional actions to position all students to learn mathematics. Reconceptualising mathematics teaching and learning requires transforming the social and organisational structures within classrooms and disrupting assumptions of uniformity across all students from a strength-based approach. Of importance is how the findings highlight possible ways of meeting the needs of diverse, and often marginalised groups of students in New Zealand schools. Significant implications based on these findings include how the aims of equity in mathematics education can extend beyond policy and into practice within primary school mathematics classrooms in the New Zealand context.
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    Mathematics anxiety and primary school teachers : the histories, impacts, and influences : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Education at Massey University, Manawatū, New Zealand
    (Massey University, 2022) Whyte, Julie Margaret
    Maths anxiety is understood to be a pervasive and global phenomenon. What is not so well understood is primary teachers’ experience of this anxiety. This study sought to provide a clearer understanding of teachers’ maths anxiety. Drawing on an interpretivist epistemology, framed by a sociocultural theoretical perspective, and using qualitative semi-structured interviews, the study provides a rich description of the personal histories and professional lives of 12 primary teacher participants who self-reported as experiencing maths anxiety. Each participant offered a unique, personal history of the development of maths anxiety. It was found to develop from a jumble of interactions from multiple sources and with multiple consequences. The teachers’ responses to anxiety around mathematics were wide ranging and included cognitive, affective, physiological, and neural reactions. In attempts to manage their anxiety, participants created specific strategies for particular situations. Amongst these management strategies were distraction and avoidance, eliciting support from trusted individuals, choosing to confine their teaching to lower year-level classes, and lengthy preparation to ensure they, themselves, understood the mathematics. Participants attempted to keep their anxiety hidden from others during their professional roles. Professional development was found to be a context in which the anxiety intensified. In professional development contexts, rather than focusing on new learnings and understandings, the participants focused on their anxiety. As a result, they failed to enhance their mathematical knowledge and failed to develop understanding of how mathematics might be taught. Their lack of confidence in their own knowledge impacted on their classroom teaching to the extent that, where possible, they scheduled less time for mathematics than other subject areas. Since such anxiety management strategies are not conducive to teacher growth and are likely to have negative consequences for students, this study has demonstrated that a carefully paced and sensitive approach needs to be taken by schools and providers of mathematics professional development courses.
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    Teacher professional learning for technology integration in mathematics classrooms through online learning communities : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Information Technology at Massey University, Albany, New Zealand
    (Massey University, 2018) Abidin, Zaenal
    The new school curricula in Indonesia emphasise the integration of technology into instructional practices. The infusion of technology in mathematics education requires teachers to align their teaching practices with ongoing technological innovations. Integrating technology into mathematics classrooms requires teachers to have a good knowledge of mathematics content, technology and pedagogy. Teachers also need to consider their school environments. Existing teacher professional development programmes are seen to be failing to meet teacher needs regarding content delivery that sometimes does not match the existing school conditions. The premise underlying this research is that the use of an online learning community (OLC) may present a possible solution to the current challenges. Thus, the intention of this study was to investigate the potential of OLCs to help develop teachers’ learning to fulfil their professional needs in integrating technology with the teaching of mathematics. An ethnographic approach was used to investigate the phenomenon of teacher learning within an OLC and the implementation of the new knowledge acquired in their mathematics teaching practices. Empirical data from five case studies were used to examine how participation in the OLC affected teaching practices for five teachers. The results revealed that teacher participation in an OLC offered opportunities and challenges. Teachers de-privatized their practices as they actively engaged in social learning interactions to share knowledge and help each other with the appropriate use of technology in teaching mathematics. Teachers also faced some challenges, which impeded them. These challenges included differences in school policies, such as restrictions on using social media and limited technical infrastructure, which hindered teachers from fully leveraging the OLC. Teachers with less experience in teaching with technology and with low levels of technology skills tended to be passive in the OLC. Cultural contexts revealed that lack of experience and caution about expressing opinions made teachers feel ewuh pakewuh, a shyness in openly expressing their thoughts. Despite these barriers, the study provided evidence that teachers improvised and dealt with situations as they rose. The findings of this study provided evidence that participation in the OLC had significant impacts on teachers’ professional learning. Teachers altered their mode of using technology either as a partner or as an extension of self as they gained more confidence in their own learning. The teachers gradually transformed their participation from peripheral to full participation in promoting the use of technology for teaching mathematics. The research provides new insights into ways teachers can be helped to develop their professional learning in the use of technology for teaching mathematics through participation in OLCs. Particularly for Indonesia, the findings of this research provide an OLC-based model that could be implemented in other contexts that share similar technology landscapes and sociocultural heritages.
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    Preparedness to teach : the perceptions of Saudi female pre-service mathematics teachers : a thesis presented in fulfilment of the requirements for the degree of Doctor of Philosophy in Education at Massey University, Palmerston North, New Zealand
    (Massey University, 2019) Alsaleh, Fatimah Ibrahim
    Being well prepared and experiencing a sense of preparedness for teaching is a key learning outcome of any initial teacher education (ITE) program. In order to understand more about the nature, development, and sufficiency of mathematics teacher readiness to teach, this study explores the phenomenon of preparedness. The aim of this study was to investigate how well Saudi pre-service teachers (PSTs) feel prepared to teach mathematics at secondary or middle schools (i.e. to explore their sense of preparedness to teach), delving into the nature and origins of that sense. The participants in the study were a sample of female mathematics PSTs (N=105), who were near the end of their teaching methods course in the final year of their 4-year education degree. The construct of preparedness was operationalized through a survey of PSTs’ efficacy to teach mathematics and an interview-based exploration of the factors influencing these perceptions. The data were collected over 4 months from 2015 to 2016. The quantitative data were analysed in SPSS and thematic analysis was used to analyse the qualitative data. The key findings of this study indicated that for the PSTs, being prepared to teach means having teaching efficacy, good knowledge for teaching, a sense of preparedness, and professionalism. However, PSTs are not fully aware of all the kinds of knowledge needed for being prepared. The study showed that PSTs were generally confident that they were sufficiently prepared to teach. They felt most confident in the areas of content knowledge (CK) and pedagogical knowledge (PK) rather than pedagogical content knowledge (PCK). The findings showed that the PSTs felt inadequately prepared in some aspects of their teaching roles, and needed more support and guidance from their university–school communities. The majority felt that classroom and behaviour management was the aspect in which they felt least prepared. They also expressed only a moderate level of general teaching efficacy (GTE), expressing a lower sense of efficacy relating directly to supporting students as learners. These were related to the disjunction between theory and practice that resulted from the two most influential factors shaping PSTs’ sense of preparedness and feelings of efficacy: the practicum experience and the ITE. Although these factors had positive impacts on their perceptions, they also expressed how the classroom environment, challenges, and school culture encountered during the practicum had lowered the PSTs’ sense of preparedness and teaching efficacy. Indeed, half of the PSTs felt that the school was neither sufficiently prepared nor sufficiently resourced to support PSTs learning the work of teaching. The challenge of closing the gap between theory and practice has led to PSTs’ desire to have more time in the mathematics methods course, as well as extra time in the practicum. It is hoped that the findings from this study concerning PSTs’ current perceptions about preparedness, combined with the suggestions for improving their levels of preparedness, will contribute to improvements in ITE and teaching quality in Saudi Arabia.
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    The influence of an open method of mathematics instruction upon the attitude and comprehension of first year students in a primary teachers college : presented in partial fulfilment of the degree of Master of Education in the Department of Education, Massey University
    (Massey University, 1977) Ruhen, Douglas Eric
    This investigation reports an experimental study of the influence of two methods of intruction (open and conventional) upon the mathematics attitude and mathematics comprehension of one hundred and twenty-four first year primary teachers college students. Approximately equal numbers of first year students were randomly assigned to four groups in two experimental conditions. Sex, testing, method of instruction, and type of studentship were the major independent factors of this study. The concepts and principles of one domain of primary mathematics content (number and numeration) were taught to the four groups of students for approximately two hours each week over a ten week period. The specially trained staff were paired for instruction. Each pair was randomly assigned to two sections of students, one in the open group and one in the conventional group. The same staff participated in both methods of instruction. Two independent measures were used to assess the mathematics comprehension and mathematics attitude of the students. An attitude scale based on the Rasch (1960) model was especially constructed for the purposes of this study. The measures of student attitude to mathematics were obtained immediately after instruction from one half of the students in each of the experimental conditions and from all students immediately after the period of instruction. The major hypotheses postulated higher mean comprehension and attitude scores for students who experienced the open method of mathematics instruction. These hypotheses were not supported by the data. Analyses of variance and covariance found no difference between the mean attitude scores of male and female students, direct entry and mature age students, and between pretested students and those who were not pretested. Similar results were found with the comprehension scores except for those obtained from the direct entry and mature age students. After instruction the mean comprehension score of direct entry students was significantly higher than the mean comprehension score of mature age students. A similar difference was observed between these two groups before the period of instruction. Also after instruction, irrespective of method, the students comprehension and attitude scores were significantly higher (p < 0.001) than those scores obtained before the period of instruction. Further examination of the data for each of the dependent measures by means of three-way analyses of variance and covariance was carried out. Although these procedures provided further evidence, certain limitations in the study and in the instruments qualified the findings.
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    Professional development in mathematics for primary teachers : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies in Mathematics at Massey University
    (Massey University, 2003) Wood, Johanna Julene
    The purpose of this study was to describe teachers and principal perceptions about professional development in primary schools, and in particular mathematics professional development. A survey of primary teachers examined teachers' recent professional development experiences and related issues of access, needs assessment, effective and sustainable professional development, and accountability. These issues were further explored in relation to four case study schools in which both teachers and principals were interviewed. The study identified that there are a number of issues to confront when developing professional development programmes if individual and school needs are to be addressed. In particular, the need to obtain a balance between individual needs and school needs, the ideal and the reality, short-term and long-term needs, and curriculum demands and subject needs of individual teachers was an ever present challenge. The questionnaire results showed that mathematics professional development was not accessed regularly by all teachers, and in a few cases teachers reported purposely avoiding mathematics professional development because of a lack of confidence or entrenched beliefs. Issues of time for professional development and competing curriculum demands for primary teachers was a common concern of both principals and teachers. Professional development should be valued as an integral part of teaching and learning. In the case of mathematics this integration could well include the need to address teacher attitudes and beliefs about mathematics. Case studies suggest that school culture impacts on the value and integration of professional development and that the success or otherwise of any professional development initiatives is strongly related to the leadership and support structures within a school.
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    Teachers developing communities of mathematical inquiry : a dissertation presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Education at Massey University, Auckland, New Zealand
    (Massey University, 2007) Hunter, Roberta Kathleen
    This study explores how teachers develop communities of mathematical inquiry which facilitate student access to, and use of, proficient mathematical practices as reasoned collective activity. Under consideration are the pathways teachers take to change classroom communication and participation patterns and the mathematical practices which emerge and evolve, as a result. Sociocultural theories of learning underpin the focus of the study. A synthesis of the literature reveals the importance of considering the social and cultural nature of students' learning and doing mathematics in intellectual learning communities—communities in which shared intellectual space creates many potential learning situations. A collaborative classroom-based qualitative approach—design research—falls naturally from the sociocultural frame taken in the study. The design approach supported construction of a communication and participation framework used to map out pathways to constitute inquiry communities. Study group meetings, participant and video observations, interviews, and teacher recorded reflections in three phases over one year supported data collection. Retrospective data analysis used a grounded approach and sociocultural activity theory to present the results as two teacher case studies. Managing the complexities and challenges inherent in constituting communication and participation patterns each teacher in this study successfully developed communities of mathematical inquiry within their own classrooms. Important tools that the teachers used to mediate gradual transformation of classroom communication and participation patterns from those of conventional learning situations included the communication and participation framework and the questions and prompts framework. Significant changes were revealed as the teachers enacted progressive shifts in the sociocultural and mathematical norms which validated collective inquiry and argumentation as learning tools. Higher levels of student involvement in mathematical dialogue resulted in increased intellectual agency and verbalised reasoning. Mathematical practices were shown to be interrelated social practices which evolved within reasoned discourse. The research findings provide insights into ways teachers can be assisted to develop a range of pedagogical practices which support the constitution of inquiry communities. For New Zealand teachers, in particular, models for ways teachers can draw on and use their Maori and Pasifika students' ethnic socialisation to constitute mathematical inquiry communities are represented in the case study exemplars.
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    The impact of the mathematical identity of school leaders on professional development in mathematics education in NZ primary schools : a case study of two New Zealand primary sector schools : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education at Massey University, Albany, New Zealand
    (Massey University, 2010) Kendall-Jones, Stephen; Kendall-Jones, Stephen
    This study draws on psychoanalytical theory and research data to explore the experiences and impacts of different educational leadership approaches to improving teacher practice in primary sector mathematics education. Under consideration are the behaviours exhibited by Principals in response to their personal relationship with mathematics. Specifically, it examines how the mathematical identity of a Principal may influence their educational leadership of mathematics, how that may affect the provision of professional development for teachers who teach mathematics, and how that, in turn, affects the mathematical identity of those teachers. A review of the research literature reveals the importance of considering both the social and intrapersonal nature of mathematical identity and the interpersonal relationships of leadership and has led to this study being placed in the constructive philosophical approach from a Lacanian psychoanalytic context. The study also acknowledges the indeterminate nature of what the future holds, including the aim of school achievement, and defines this study as embedded in the postmodern system of ideas as a means of viewing social and cultural phenomena. The study is a comparison between two contrasting school environments. Consistent with an interpretive approach, data collection and analysis have complementary roles with each activity informing the other. Data collection instruments used for this study were the questionnaire, personal interviews, focus group interviews, and the researcher. The investigation revealed that a Principal who consistently addresses their mathematical identity, through direct participation in professional development, is more likely to correctly identify strategic development needs and to provide appropriate professional development in mathematics. This provision addresses the mathematical identity of teachers by improving mathematical content and pedagogical knowledge. The study found that many Principals were educated through a behaviourist pedagogy and that participation in current professional development allowed them to better understand the constructivist approach of contemporary mathematics education and best practice in classroom practice. The Principal!s personal participation also builds relational trust with the teaching team, enabling the conditions for a learning culture within their school. From these findings, recommendations are made for Principals to reflect upon the effective provision of professional development in mathematics whilst considering how psychological influences might affect their educational leadership of mathematics and teacher practice.