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    Collaborative learning and peer-tutoring in mathematics : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies (Mathematics), Massey University
    (Massey University, 2002) Rowe, Kathryn Joy
    This study sought to promote learning by enhancing the level of higher order cognitive talk among collaborative groups engaged on mathematical tasks. An intervention, designed to utilise structures such as listening, multiple retelling, questioning, elaboration, and justification to promote high-level discourse, was trialled and refined using an action research classroom study. The collaborative skills training programme was based on Medcalf's peer-tutoring model (1997) and adapted to incorporate features of Lyman's Think-Pair-Share collaborative model (1992). The teacher's role was seen as crucial to the development of collaborative group practices which establish the structures for high-level discourse. Collaborative group practices were reinforced in follow-up class discussions where the teacher facilitated student reflection on the mathematical strategies and the collaborative group strategies. It was also seen as important for the teacher to select appropriately levelled tasks which maintained the learner in his/her Zone of Proximal Development. Findings indicated that the structured intervention enhanced the level of higher order discourse between students and that it was an effective procedure to mediate learning. Several patterns of discourse were also identified that could provide useful indicators of higher level discourse to teachers during daily classroom observations.
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    Driving force? : motivations of senior mathematics students enrolled in National Certificate of Educational Achievement (NCEA) Level III Statistics & Modelling
    (Massey University, 2013) Fraser Webb, Jackie
    The objective of this study was to explore how senior mathematical students made sense of their mathematical experience through the New Zealand National Certificate of Educational Achievement (NCEA) qualifications system, and from that exploration to understand what factors motivated these students and to which factors these students attributed their mathematical success. The research is based on Constructivist Theory, with ethnomethodology as the methodological approach. The methodological tool utilised in the study was an online questionnaire. The students who completed the questionnaire attended an urban, co-educational, decile 8 secondary school in New Zealand. The participants were students aged 16 years old and over, enrolled in a full year NCEA Level 3 Statistics and Modelling Achievement Standards programme in 2013. The students in the sample were aware that there were set criteria within each grade for NCEA Level 3 Statistics and Modelling assessment tasks. The students were mindful that achievement was measured in discrete units. Evidence from the research suggests that to maximise student learning within the NCEA qualifications system, Level 3 Statistics and Modelling needs to be taught as a collective, cohesive statistics curriculum. The students in the sample attributed their highest mathematical outcomes to ability, effort and the teacher and their lowest mathematical outcomes to lack of ability, lack of effort and the level of difficulty of the assessment. The findings highlighted the importance of prioritising the teacher and student relationship. In the study, only 12% of students were convinced that their teacher was interested in them at an individual level. NCEA Level 3 Statistics and Modelling teachers need to be aware of the influence of the teacher and student relationship on student achievement. The findings from the research have implications for teaching and learning. The research evidence indicates a need for NCEA Level 3 Statistics and Modelling students to be aware of the nonnumerical content and grade criteria expectations of the Statistics and Modelling Achievement Standards prior to committing to the course.
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    Student perspectives and roles in an inquiry mathematics classroom : 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, 2013) Leach, Generosa
    This study examines the perspectives and roles of students aged 9-10 years old learning mathematics in an inquiry classroom. It builds on previous work which has advocated students learning mathematics through collaborative interaction as opposed to passive transmission of knowledge and skills. In this study the students’ beliefs about what they consider to be important in learning mathematics is compared to the ways in which they engage in mathematics activity. The varying roles students assume while learning mathematics and how this affects their agency are considered. This investigation is situated in an inquiry classroom. A sociocultural perspective provides the framework for the classroom context. Relevant literature is examined to provide a rationale for how students engaged in mathematical reasoning within this environment. The pedagogic approach of the teacher in developing effective student participation in mathematical reasoning by facilitating the even distribution of authority in the classroom is offered as an alternate to customary practice. Active student engagement in mathematical discussion and debate are all viewed as highly important for the enhancement of mathematical understanding. A qualitative research approach was implemented. The case study supported a classroom based investigation. Data were collected through individual interviews, participant and video-recorded observations and classroom artefacts. To develop the findings as one classroom case study, on-going and retrospective analyses of data were made. Significant changes were revealed in the relationship between the students’ espoused beliefs about learning mathematics and their enacted beliefs. The investigation illustrated that students were able to develop positive positional identities through active engagement in mathematical reasoning. The interaction patterns created in the classroom explicitly affected the construction of mathematical knowledge. From these findings insights are made into the type of environment which supports enhanced mathematics learning.