Faculty of Education - Theses
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ItemTeacher questioning practices across a sequence of consecutive mathematics lessons: a multiple-case study of junior secondary teachers in Australia and mainland China( 2017)Question asking is one of the most common strategies used by teachers in their everyday classroom instructional practice. Over recent decades, many attempts have been made to categorise teacher questions asked during classroom instruction and to report on teachers’ skilful questioning strategies. These categorisations consider the context where the questions are asked, the appropriate use of different types of questions, the learning opportunities created in the sequences of teacher-student interactions and so on. This study was designed to extend our understanding of teachers' questioning practices in classrooms through a fine-grained analysis of mathematics lessons taught by four competent junior secondary teachers from mainland China and Australia. The study demonstrates the importance of examining teaching strategies over a sequence of lessons, the power of the IRF (Initiation-Response-Follow-up) framework as a basic structure for investigating classroom interactions, and the complexity of teaching practices, made evident through the focused investigation of the ubiquitous practice of teacher questioning. Based on the IRF framework, a comprehensive coding system was developed to analyse what kinds of verbal questions were initiated by the teachers to elicit mathematical information and in what ways the teachers made use of students’ verbal contributions in order to facilitate student construction and acquisition of mathematical knowledge. In particular, a distinction was made between Q&A question pairs, IRF (single) sequences, and IRF (multiple) sequences. Classification systems were developed for question types within each interactive category. Within IRF (multiple) sequences, the categories: initiating and follow-up represented a fundamental distinction, each category having its own suite of sub-categories. For each participating teacher, a whole unit of consecutive lessons was examined (from 6 to 10 lessons per unit). Analysis of the data suggested that: (1) Across the professional practice of the four teachers, two each in mainland China and in Australia, similarities and differences in the ways in which teachers employ questioning strategies were observed. The differences regarding questioning strategies across the consecutive lessons include: (i) number/frequency of questions asked in each lesson; (ii) the proportions of questions in IRF (multiple) sequences and the proportions of the questions in Q&A question pairs and IRF (single) sequences; and, (iii) the use of subcategories for initiation questions in each lesson. And the similarities are as follows: (i) the proportion of initiation questions in IRF (multiple) sequences out of all questions in each lesson; and, (ii) the use of subcategories for follow-up questions in each lesson. The essential point suggested by the comparison of similarities and differences regarding teacher questioning practices in this study is that the Chinese teachers and Australian teachers employed questioning strategies with similar forms but with distinctly different functions. (2) Regardless of the geographical location of the classroom, teachers’ questioning strategy choice is made rationally based on such contexts as the nature of instructional tasks and the constraints facing the teachers at the time. Those constraints might involve time limit and overemphasis on procedural fluency caused by the need to prepare students for high-stakes examinations, the demands of catering to students’ individual differences, the need for coherent delivery and explanation of sophisticated mathematics and the need to elicit information about student existing understanding. Unlike the two Chinese teachers who valued the achievement of lesson goals above any other factors, both Australian teachers placed greatest emphasis equally on students’ demands and lesson content. (3) In the case of the use of the three kinds of IRF (multiple) sequences (leading, facilitating/probing, orchestrating), the nature of teacher lesson planning – collaborative and institutionalised in the case of mainland China, and individually done in the case of Australia – affects how teachers make use of questions in class. These local educational contexts pose culturally-situated challenges, even though the teacher questioning strategies that are chosen and performed may reflect rational professional decisions by all four teachers, predicated on similar pedagogical goals. Teachers’ adjustment of their questioning routines in response to competing tensions in their classroom practices provided some of the most interesting features of the research. In addition, this study also suggests that teacher professional development program designers should ensure that novice teachers are given an opportunity to observe the teaching of a sequence of lessons and to observe closely how one expert teacher’s questioning strategies are strategically employed according to the demands of the particular lesson and its place in the topic sequence. Such strategic variation of questioning practice cannot be fully or correctly understood without the examination of the teaching of consecutive lessons.
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ItemQuality interactions for mathematics learning: how early childhood teachers enact a suite of play-based mathematics activities with children aged from three to five years( 2013)The Early Years Learning Framework for Australia (EYLF; DEEWR, 2009) requires early childhood educators to implement a play-based curriculum to teach children mathematical ideas in the years before school. Many early childhood educators report anxiety about their own mathematical knowledge and uncertainty about how to go about meeting this requirement of the framework. This implementation study used a mixed-methods, multiple case study approach to investigate how different early childhood educators implemented a packaged suite of play-based mathematics activities with 122 children aged from three to five years. Six early childhood educators agreed to present one activity from the provided suite of activities each day to a small group of children. Data were derived from educators’ self-reported implementation records, semi-structured interviews with participants at three points over a seven-month period, and video-recordings of educators presenting a play-based mathematics activity. Video-recordings were transcribed and analysed using Conversation Analysis. Assessments of pedagogical quality were made at room level and at group level at the start and end of the study. Children were assessed using selected tests of cognitive ability and achievement from the Woodcock-Johnson III at the start and end of the implementation phase. Findings demonstrate that systematic and repeated use of the suite of play-based mathematics activities is associated with teachers’ increased mathematics confidence, and higher quality emotional support and instructional support. Woodcock-Johnson III Concept Formation W scores obtained at the start and end of the seven month-implementation phase show that frequent use of the play-based activities was also associated with a significant increase in children’s learning outcomes. In addition, the systematic and purposeful use of a curriculum (activities, pedagogical strategies and mathematical language) supports the sequential and child-appropriate incorporation of mathematical concepts in an early childhood program. Consistency across settings in quality and frequency of mathematics teaching facilitates a positive and more equitable learning trajectory for all children.
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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.