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Item Attitudes and beliefs in mathematics education : a comparative study between New Zealand and Indonesia : a thesis presented in partial fulfilment of the requirements for the degree of Master of Educational Studies (MEd Studs) in Mathematics Education at Massey University(Massey University, 1996) Margono, GargukThis comparative study investigated the differences between New Zealand and Indonesian mathematics students and teachers, in attitudinal and beliefs aspects. Attitudes and beliefs about mathematics education were used as dependent variables; countries and gender were used as independent variables. A total of 191 Indonesian general secondary school students (92 males and 99 females) from grade II (year 11), 8 mathematics teachers (4 males and 4 females), and 47 New Zealand students (23 males and 24 females) from Form 6 and 7 (year 11 and 12) volunteered for the study. Students and teachers completed a researcher developed questionnaire which measured the attitudinal and beliefs about mathematics learning and teaching. A t-test procedure was used to compare the means of attitudinal and beliefs aspects. Analysis of the data suggested that: 1. Significant differences between countries existed with regard to students' enjoyment of mathematics, value (perceive usefulness) of mathematics, beliefs about mathematics, mathematics learning, and beliefs about home support. 2. Differences within New Zealand students by gender were due to students' beliefs about mathematics learning and beliefs about mathematics teaching. No significant differences were found within Indonesian students by gender for attitudinal and beliefs aspects. 3. Differences among subgroups gender (males and females for New Zealand and Indonesia) were found in students' value (perceive usefulness) of mathematics, beliefs about mathematics learning, beliefs about mathematics learning, and beliefs about mathematics teaching. 4. Differences in teachers' beliefs about learning and teaching mathematics were found. In Indonesian, mathematics teachers emphasized students listening to teacher explanations, note taking, reading text-books, doing written exercises from text-books, watching a teacher work through a problem, working out practical problems, and opportunities for students to practice exam/test questions. New Zealand mathematics teachers emphasized teacher led discussions, demonstrations, and explanations, as well as student discussions. These findings are restricted to the sample population of grade II (year 11) students at general secondary school Jakarta and Form 6 and 7 (year 11 and 12) coeducational secondary school in Palmerston North. However, it is felt that these schools are representative of schools at the senior level in their respective countries. This study indicates that there are differences in some aspects of attitudinal and beliefs about mathematics, but does not relate these findings to students' performance in mathematics. The effect of attitudinal and beliefs aspects on performance in mathematics, and in relation to curriculum reforms, should be explored in the future research.Item 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 KathleenThis 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.