Faculty of Education - Research Publications

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End date: 2010 × Start date: 2003 × Type: Conference Paper ×

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    Student inclination to work with unfamiliar challenging problems: The role of resilience
    WILLIAMS, G (The Mathematical Association of Victoria, 2003)
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    Teacher Research can Enrich Teaching Practice: An Example
    WILLIAMS, G ; CAVALLIN, N (The Mathematical Association of Victoria, 2004)
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    Teaching and Learning in the Middle Years of Schooling: Having Faith in Students
    TADICH, B ; WILLIAMS, G (The Mathematical Association of Victoria, 2004)
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    The Nature of Spontaneity in High Quality Learning Situations
    WILLIAMS, G (Bergen University College, 2004)
    Spontaneity has been linked to high quality learning experiences in mathematics (Csikszentmihalyi & Csikszentmihalyi, 1992; Williams, 2002).This paper shows how spontaneity can be identified by attending to the nature of social elements in the process of abstracting (Dreyfus, Hershkowitz, & Schwarz, 2001). This process is elaborated through an illustrative example—a Year 8 Australian male student who scaffolded his learning by attending to images in the classroom that were intended for other purposes. Leon’s cognitive processing was not ‘observable’ (Dreyfus et al., 2001) in classroom dialogue because Leon ‘thought alone’. Post-lesson videostimulated reconstructive interviews facilitated study of Leon’s thought processes and extended methodological techniques available to study thinking in classrooms..
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    Abstracting by Constructing and Revising a 'Partially Correct Construct': A Case Study
    Williams, GW (Mathematics Education Research Group of Australasia, 2010)
    This study draws on data from a broader video-stimulated interview study of the role of optimism in collaborative problem solving. It examines the activity of a Grade 5 student, Tom, whose initial constructing activity resulted in a ‘Partially Correct Construct’. Insistent questioning from another group member pressuring for clarification led to Tom developing a ‘more correct construct’ with further potential for revision. This paper raises questions about influences that can stimulate or inhibit construct refinement.
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    Symbiosis between creative mathematical thinking accompanied by high positive affect, and optimism
    Williams, G ; Pinto, MMF ; Kawasaki, TF (The International Group for the Psychology of Mathematics Education (PME), 2010-01-01)
    Video-stimulated post-lesson interviews captured changes in a Grade 5 elementary school student, Tom's, orientation to problem solving. Whilst participating in small group problem solving including reports to the class ('Engaged to Learn' pedagogy), Tom changed from self-focused (Task 1), to group focused (Task 2), and taskfocused (Task 3). He experienced surprise as complexities became apparent in what had appeared to be simple (Task 2), and displayed positive affect during his creative thinking leading to insight (Task 3). Consistent with Seligman's (1995) findings, 'flow' (Csikszentmihalyi, 1992), a state of high positive affect accompanying creative activity was associated with optimism building. Instead of needing to be valued by others to feel successfol, Tom began to internalise his successes as attributes of self.
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    Leading Female Teachers in Boys’ Schools.
    Acquaro, D (ACEL, 2008)
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    Evaluating automated processes for revealing students’ mathematical thinking
    Stacey, K ; Steinle, V ; Wu, M ; PIERCE, R ; Giri, J (AARE, 2010)
    Understanding student thinking is key to planning effective teaching. Research over three decades has established good knowledge of stages of development and common misunderstandings in many school topics. However, in order for teachers to make formative assessment a normal part of their practice, mapping of student understanding needs to be available for a greater proportion of the school curriculum. Online testing of students is beginning to create substantial databases which could provide relevant information. The aim of this symposium is to present and discuss methods which move towards automation of data analysis.
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    SMART Assessment for Learning
    STACEY, K ; PRICE, E ; STEINLE, V ; CHICK, H ; GVOZDENKO, E (International Society for Design and Development in Education, 2009)
    “Specific Mathematics Assessments that Reveal Thinking,” which we abbreviate to “smart tests,” provide teachers with a quick and easy way to conduct assessment for learning. Using the internet, students in Years 7, 8, and 9 undertake a short test that is focused strongly on a topic selected by their teacher. Students’ stages of development are diagnosed, and sent to the teacher immediately. Where available, on-line teaching resources are linked to each diagnosis, to guide teachers in moving students to the next stage. Many smart tests are now being trialled in schools and their impact on students’ and teachers’ learning is being evaluated. Design issues are discussed.