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Subject: search.filters.subject.390109 Mathematics and numeracy curriculum and pedagogy

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    Making it count : teacher actions to support the development of multiplicative reasoning through the use of choral counting conceptual starters : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education in Mathematics Education at Massey University, Albany, New Zealand
    (Massey University, 2024) Frazerhurst, Lauren Kaye
    Learning to think multiplicatively is one of the most challenging transitions primary aged students must make in their journey of mathematical learning. This study explores the development of multiplicative reasoning among Year Five to Eight students in Aotearoa New Zealand through a conceptual starter activity involving choral counting. Additionally, it examines the pedagogical actions used by teachers to support students in engaging in collaborative discourse and advance students’ multiplicative reasoning through the enactment of mathematical practices. Relevant literature is examined to illustrate how students develop multiplicative reasoning and what key mathematical concepts they must first understand. The literature review provides evidence of the important role of teacher pedagogical actions that support students’ multiplicative reasoning through facilitating their participation in investigating, noticing, conjecturing, explaining, justifying, and generalising. An interpretivist approach was taken for this qualitative classroom-based case study. A collaborative planning and reflective partnership was established with two teacher participants to support the lesson development. Teacher interviews, video recorded observations, and classroom artefacts made up the data collection. On-going and retrospective data analysis was used to form the findings of this study. The findings revealed important advances in students’ multiplicative reasoning as the teachers facilitated collaborative discourse. Students were provided with many opportunities to share and clarify their thinking while building on the ideas of others. This occurred as explicit counting, place value, and multiplicative concepts were explored. The research findings provide insights into ways teachers can support students to develop conjectures, explanations, justification, and generalisations as they engage with the choral count starter activities. The results of this study suggest that student participation in choral count starter activities where teachers emphasise the enactment of mathematical practices through collaborative discussion support their development of multiplicative thinking.
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    Developing 11-13 year old students’ conceptual understanding of rational numbers : a case study investigating effective teacher pedagogical actions in a mathematics classroom : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education in Mathematics Education at Massey University, Albany, New Zealand
    (Massey University, 2024) Sheppard, Kelly Ann
    Rational numbers, encompassing fractions, percentages, and decimals, are challenging for many students to understand. Research often focuses on the teaching and learning of these topics in isolation, rather than as part of the broader concept of rational numbers. However, there is limited research on the teaching practices that effectively support students’ overall understanding of rational numbers. This study explores the teacher actions that help students develop a conceptual understanding of rational numbers and examines how students demonstrate their growing understanding. A case study and qualitative methods were chosen for this research. The study involved one teacher and a class of 24 Year 7 and 8 students from an urban school in New Zealand. The teacher facilitated eight lessons focused on rational numbers, which included collaborative mathematical discussions. A variety of data were collected and analysed, including interviews, video recorded classroom observations, and examples of student work. The findings revealed that when teachers design lessons around real-world mathematical tasks, promote collaborative discourse, and encourage the use of mathematical practices, students develop a deeper understanding of rational numbers. Additionally, using visual representations and explicitly connecting different forms of rational number representations helped enhance students’ mathematical understanding. This study contributes to the literature on how primary school teachers can effectively support students in developing a strong understanding of rational number concepts. It highlights that teacher content knowledge, combined with purposeful teaching strategies, can provide greater opportunities for students to develop a deeper understanding of rational numbers.
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    Supporting 5 – 6 year old students to know and use mathematical practices : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education in Mathematics Education at Massey University, Albany, New Zealand
    (Massey University, 2024) Pearce, Emily Louisa
    Supporting students to be mathematically proficient at school, begins from their first formal mathematics lesson. For students in Aotearoa, the refreshed curriculum outlines the expectation that students engage in mathematical explanations, justification, argumentation, representations and generalizing. Whilst there is sufficient literature on these mathematical practices with older students, there is limited research focusing on how to enact mathematical practices with young learners. This study examines the teacher actions used within students first formal mathematics lessons and the ways in which the teacher engaged the young learners to explain, justify, argue mathematically, represent their thinking and generalise mathematical ideas. Drawing upon qualitative research methods within a single bounded case study this study was set within a semi-rural school in Aotearoa. One teacher was selected to participate with ten young students aged five years old and one student aged six years old. Data collection occurred during these students first seven formal mathematics lessons. A range of data were collected and analysed, including field notes, video recorded classroom observations, photographs of student work samples and a teacher questionnaire. Findings revealed the complex nature of engaging young learners in mathematical practices. However, when students are expected to and provided with opportunities to reason mathematically, young learners can succeed. Initially the teacher actions included specific questioning and conversational moves to draw out the thinking from the students. Over the duration of the study these teacher actions shifted to include open prompts requesting the students engage in a mathematical practice. This study provides insight to the progression of teacher actions used and offers a contribution to the literature regarding how young learners can mathematically reason. It is acknowledged that for such practices to occur teachers must value mathematical conversation and constantly provide opportunities for young learners to reason.
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    Primary school teachers' feelings about teaching mathematics using a problem-solving approach : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education at Massey University, Albany, New Zealand
    (Massey University, 2023) Kaur, Rajvir
    The importance of teaching the problem solving approach in the mathematics curriculum has been centralised for many years in both curriculum development and research. Yet there is still resistance from teachers to adopting the problem-solving approach when teaching mathematics. The existing literature identifies that teachers' beliefs, attitudes, mathematical knowledge, and previous experiences in learning mathematics effect their ability to implement the problem-solving approach in mathematics, but little is known about the emotional side of the experiences of adopting problem-solving approach by primary school teachers. Emotions have a pivotal role in learning and learning outcomes. Emotions affect learning and learning affects emotions, therefore, they are central to efficient teaching and learning processes. To understand and gain insights into teachers' emotions in teaching problem-solving approach in mathematics, the aim of this research is to explore New Zealand primary school teachers' feelings in the implementation of the problem-solving approach. Qualitative research methods were employed to collect the in-depth data from four primary school teachers using semi-structured interviews via Zoom. The cognitive theory of emotions 'The OCC theory' and thematic analysis was used to identify emotions and situations that elicit such emotions. Results show both positive and negative emotions and highlight that the main sources of teachers' emotions are students' participation and collaboration, teachers' self-held beliefs, job context, and classroom environment. The study outlines that it is crucially important to understand the eliciting situations leading to such emotions in order to increase the implementation of the problem-solving approach in primary school education. Furthermore, to support teachers with the shift towards the problem-solving approach, this study also outlines that there should be some level of emotional support for teachers alongside the material support (such as providing school wide PLD and resources).
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    Ethics of care in the mathematics classroom : a thesis presented in partial fulfilment of the requirements for the degree of Masters in Education (Māori Education) at Massey University, Palmerston North, New Zealand
    (Massey University, 2022) Stone, Melanie
    Ethics of care is a complex and critical element of educational theory and practice which is commonly misunderstood by teachers across all subject areas. Teachers understanding and mindset towards ethics of care is reflected in their utilisation of classroom practices of care. Whilst there are numerous indigenous voices championing various approaches to care for those working with Māori and Pāsifika students, implementation of these practices in the New Zealand educational context is inconsistent and there remains significant achievement gaps between different groups of ethnicities. One programme aiming to address the way in which care practices are utilised in mathematics is Developing Mathematics Inquiry Communities programme of professional learning and development. Through the lens of relational and critical race frameworks as influenced by feminist theory this study used a qualitative approach to examine the elements of teacher mindset toward ethics of care in mathematics and explored the impact which participation in professional learning and development has on these mindsets. Through semi-structured interviews, practices of care utilised in the classrooms of mathematics teachers of year five and six students were identified. In total three teachers at varying stages of their teaching careers and varying lengths of Developing Mathematics Inquiry Communities participation were interviewed. An examination of literature relating to ethics of care, Developing Mathematics Inquiry Communities professional learning and development, and current practices of care in the context of New Zealand mathematics classrooms was undertaken. This identified several practices of care currently used by New Zealand mathematics teachers working with Māori and Pāsifika students such as: use of mixed-ability grouping, student-centred learning practices, community and whānau involvement in mathematics learning, and place-based mathematics contexts. Utilisation of each of these practices was described by interview participants as a response to their participation in professional development. Through better understanding of the nature of ethics of care, how professional development impacts on teacher mindset toward ethics of care and identifying successful practices of care for teachers of Māori and Pāsifika students in mathematics classrooms, teachers engaging in professional development will be better equipped to implement and enhance practices of care in their own classrooms.
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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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    Learning to participate in a mathematical community of inquiry : insights from cogenerative dialogues : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education at Massey University, Palmerston North, New Zealand
    (Massey University, 2019) Rice, Fiona Elizabeth
    Mathematics teaching and learning in New Zealand is currently in a state of change, with classroom learning environments transitioning from more traditional classrooms focused on individual performance outcomes towards more collaborative communities of mathematical inquiry. This study is set in the context of ongoing school-wide professional development initiative focused on developing mathematical inquiry communities (DMIC), with the overall aim of the study being to develop an understanding of how students experience learning mathematics as they learn to participate in a developing mathematical inquiry community. The study uses cogenerative dialogues (cogens) to generate student voice to explore students' experiences and perceptions within this new context for mathematical learning. Providing a forum for students to discuss their experiences and thoughts about their learning environment, the cogenerative dialogues (cogens) served to cogenerate understandings which would facilitate student and teacher learning within the emergent community of mathematical inquiry, allowing students to collaborate with their teacher and co-learners to co-construct their learning environment. The study examines students' perceptions of the collaborative learning environment and explores how students negotiate this change as they become part of a mathematical inquiry community. Findings revealed that students' social interactions and experiences within their groups have a significant influence on learning and that negotiating the collaborative learning environment is of primary concern for these students. The data offer a glimpse of how these students experience and work within groups, how they go about their learning in groups, and how they feel groups should be organised. Findings also considered to what extent students develop student agency through collaborative work and being able to share student voice.
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    How are teachers in intermediate schools catering for the diverse learning needs of their students in mathematics? : a thesis submitted to Massey University in partial fulfilment of the requirements for the degree of Master of Education (MEd), Institute of Education Te Kura o te Mātauranga
    (Massey University, 2020) Hatch, Jenna
    Increasingly teachers are finding that students within their classes represent a diverse range of abilities, experiences and backgrounds (Parsons et al., 2018; Tomlinson et al., 2003) Students in mathematics classes across New Zealand display diverse learning needs, and come to school with a vast range of prior knowledge, experiences, skills and understanding requiring teachers to find ways to cater for such differences within their programme. The Ministry of Education (2016) recognises the increasingly diverse population of New Zealand and calls for teachers to ensure that every child is provided with opportunities for educational success regardless of ethnic, cultural or economic background. Within New Zealand, intermediate schools play a valuable role in bridging the gap between primary and secondary education. In the two years that students attend, teachers focus on developing the skills of emerging adolescents and preparing them for secondary education. This study critically examines how teachers in intermediate schools cater for diverse learning needs of students in mathematics and explores the rationale for the methods they choose. At present there is little research in New Zealand intermediate schools that provides understanding of current beliefs and practices regarding catering for the diverse learners found in intermediate school classrooms. This study aims to provide further understanding, and to identify areas for further development. In order to examine the research question “how are teachers in intermediate schools catering for diverse learning needs in mathematics”, a qualitative multiple case study approach was used. Twelve teachers across three different intermediate schools were interviewed and each school was presented as a separate case, followed by a cross case analysis identifying common themes. Findings from the study showed that teachers primarily used different forms of grouping to cater for diverse learners in mathematics, rather than a focus on the content of lessons and tasks given to students. Concerns and pressures around assessment also played a big factor in shaping teacher attitudes towards grouping practices, and teacher capability and understanding around alternatives to ability grouping were also a common theme.
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    "It makes me feel proud of who I am" : developing functional thinking through culturally located tasks : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education in Mathematics Education at Massey University, Manawatū, New Zealand
    (Massey University, 2020) Gibbs, Bronwyn Elizabeth
    Success in algebra plays a major role in equity and lifelong opportunities well beyond the mathematics classroom. Nationally, and internationally, high failure rates in algebra see many non-dominant students excluded from equitable higher education, career, and economic opportunities. There appears to be limited research focused on non-dominant students and the development of algebraic thinking through culturally located tasks. This study examines the representations Māori and Pāsifika students use when engaging with contextual functional tasks, and the ways Māori and Pāsifika students generalise culturally located tasks involving functions. A design based research intervention and qualitative research methods, drawing on a Pāsifika research methodology, were selected as most appropriate for the study. Twelve 10-12 year old Māori and Pāsifika students from a low socio-economic, urban school in New Zealand participated. Students engaged in an intervention of eight lessons focused on developing functional thinking with growing patterns drawn from Māori and Pāsifika cultures. A range of data were collected and analysed, including interviews, field notes, video recorded classroom observations, and photographs of student work. Findings revealed that when Māori and Pāsifika students were given opportunities to draw on their cultures to make sense of functional relationships, they constructed increasingly sophisticated and abstract representations to identify, communicate, and justify generalisations. There was significant growth in their conceptual understanding of both contextualised and decontextualised growing patterns. Additionally, aligning tasks with non dominant students' traditions and experiences strengthened students' mathematical and cultural identities. This study offers a contribution to the literature regarding how culturally contextualised tasks support non-dominant students to engage in early algebra, in particular, the representation and generalisation of functions. To address disparities and structural inequities in mathematics education, educators must acknowledge that students bring their own cultural knowledge and strengths to the classroom, and provide opportunities for all students to learn mathematics in ways they see as relevant to their cultural identities and communities. Recognising that mathematics is inherently cultural is a key lever for equity.