Faculty of Education - Theses
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ItemAn insight into student understanding of functions in a graphing calculator environment( 2003)The introduction of graphing calculators into senior secondary schools and mandating of their use in high stakes assessment makes student expertise in finding a complete graph of a function essential. This thesis investigated the cognitive, metacognitive, mathematical, and technological processes senior secondary students used in seeking a complete graph of a difficult cubic function. A pretest of function knowledge was administered to two mixed ability classes in their final two years of secondary school. Five pairs of experienced users of TI-83 or 82 graphing calculators from these classes were audio and videotaped solving a problem task. Protocols were constructed and subjected to intensive qualitative macroanalysis and microanalysis using tools developed by the researcher from Schoenfeld’s work. The findings were: (1)all students demonstrated understanding of the local and global nature of functions and the synthesis of these in determining a complete graph; (2) a range of mathematical and graphing calculator knowledge was applied in seeking a global view of the function with their combined application being more efficient and effective; (3) an understanding of automatic range scaling features facilitated efficient finding of a global view; (4) all pairs demonstrated having a clear mental image of the function sought and the possible positions of the calculator output relative to this; (5) students were able to resolve situations involving unexpected views of the graph to determine a global view; (6) students displayed understanding of local linearity of a function; (7) when working in the graphical representation, students used the algebraic but not the numerical representation to facilitate and support their solution; (8) scale marks were used to produce more elegant solutions and facilitate identification of key function features to produce a sketch but some students misunderstood the effect of altering these; (9) pairs differed in the proportion of cognitive and metacognitive behaviours demonstrated with question asking during evaluation supporting decision making; (10) correct selection of xxi an extensive range of graphing calculator features and use of dedicated features facilitated efficient and accurate identification of coordinates of key function features.
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ItemAssessing metacognition( 2000)Researchers, educators and curriculum documents promote the importance of metacognition for student learning but much confusion in the field continues to exist about what the term 'metacognition' means. This lack of clarity creates obstacles for researchers and educators. It is difficult to teach and assess what has not been clearly defined. Because of the importance attached to assessed curriculum, a likely implication is that metacognition will not be widely embraced as a worthwhile part of the curriculum unless metacognition is clearly defined and is included as part of assessment practices. This thesis investigated the assessment of metacognition within the curriculum domain of mathematics. The study involved Year 6 students from three different schools. Conventional techniques used for monitoring metacognition are criticised in terms of their validity and reliability. The need for practical assessment tasks was identified to minimise limitations of individual techniques and attend to questions of rigor. A new multi-method approach was developed and trialled for the assessment of three key metacognitive functions: Awareness, Evaluation and Regulation. The main features of this approach were a hands-on card sorting task and a video replay used within the context of a problem based clinical interview. This thesis sets out the consequences of implementing a new method for the assessment of meta cognition. The data generated provides a detailed endorsement of a theoretical model for metacognition developed in the course of this thesis. The findings of the study call into question previous research into metacognition (both methodologically and in terms of actual findings) and shed significant light on the nature of metacognition and its use by Year 6 students in the solution of mathematical problems. The results consistently show that student metacognitive behaviour is predictable regardless of school, class or task. The study also provides a technique for assessing and researching metacognition that could be adapted for other purposes and in other contexts.
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ItemThinking, small group interactions, and interdisciplinary project work( 2008)Interdisciplinary Project Work (PW) was introduced as an educational initiative in Singapore schools from primary to pre-university levels in 2000. PW was posited to (a) enhance perceptions and use of inter-subject connections in real-world problems, (b) promote knowledge application, and (c) provide a platform for the use of thinking skills. The main goal of this thesis is to explore how these objectives are inter-related with factors influencing the quality of group collaborative mathematical thinking processes and mathematical outcomes during a mathematically-based interdisciplinary project. In this study, high quality mathematical thinking processes occur when the flow of group interactions is purposefully directed towards the enhancement of mathematically accurate, logical, and reasonable outcomes. A Sequential Explanatory Mixed Methods Design consisting of consecutive quantitative and qualitative data collection and analysis procedures was used to answer the seven research questions in the study. A researcher-designed mathematically-based interdisciplinary project was implemented over 14-15 weeks with 16 classes of students (aged 13-14) belonging to two educational streams (higher and average-ability) in three Singapore government secondary schools. No teaching intervention was administered. Six scales were developed for pre- and post-project measurements of students’ mathematical confidence, perception of the value of mathematics, and perception of the interconnectedness of mathematics (N = 398). Ten student-group cases (n = 38) were selected for further in-depth qualitative data collection procedures pertaining to the nature of mathematical knowledge application, use of metacognitive monitoring and regulatory strategies, and core thinking skills application during three tasks in the interdisciplinary project. The findings of this study clearly demonstrate the complexities of using PW to promote holistic and connected use of knowledge. Five substantial contributions to research on interdisciplinary learning arise from the thesis:1. An empirical framework synthesising factors influencing the quality of group collaborative mathematical knowledge application processes and outcomes was developed.2. The social influence of the group member activating applications of core thinking skills and metacognitive monitoring and regulatory strategies is a mediating factor influencing the flow of cognitive-metacognitive group interactions, and therefore, the quality of collaborative mathematical knowledge application processes and outcomes.3. Leaders of high-stream groups who were socially non-dominant but mathematically active were more likely to apply a higher frequency of core thinking skills than group members in other roles (i.e., questioner, recorder, and encourager) during a mathematically-based interdisciplinary project.4. The types and complexities of mathematical knowledge and skills applied during a mathematically-based interdisciplinary project did not correspond with stream.5. Whilst students were more able to appreciate the use of mathematics for inter-subject learning after participating in a mathematically-based interdisciplinary project, their beliefs about inter-subject connections and efforts at making these connections only marginally changed.These outcomes enhance our understanding of the challenges involved in the successful use of interdisciplinary tasks with middle school students and provide focuses for future teacher facilitation of mathematical learning during interdisciplinary education.