Faculty of Education - Research Publications
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ItemTechnology-supported classrooms: New opportunities for communication and development of mathematical understanding(Springer Spektrum, 2019-06-03)This chapter provides an overview of some themes which have emerged over two decades of Bärbel Barzel’s work related to the teaching and learning of school mathematics with technology. The themes which are discussed include technology supporting mathematical communication, technology supporting cognitive activities and technology supporting an open classroom. Overall, the focus is on the potential for technology-supported classrooms to promote students’ understanding in secondary school mathematics. Four papers are used to illustrate Barzel’s contribution.
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ItemEvolution over Two Decades of CAS-Active Senior Secondary Mathematics Curriculum and Assessment(MDPI, 2022-07)The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. This paper reports reflections on these developments over two decades from the perspectives of a researcher and the state mathematics manager (the authors) in consultation with four implementing teachers (the consultants). The authors critically examined the strategic design decisions that were made for the initiative over time. Then, with contributions from the four consultants, technical design issues relating to assessment and to teaching and the changes over a decade were investigated. A range of modifications have been made over the two decades, driven by changes in device capability and progressively increasing teaching expertise. The place of CAS in senior mathematics is now widely accepted, partly because an examination component not allowing any technology has been implemented. Examination questions have become more general, which may have added difficulty, but more questions involve setting up a real situation mathematically.
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ItemBeyond Accuracy: A Process for Analysis of Constructed Responses in Large(The Korean Society of Educational Studies in Mathematics, 2022-08-31)This article reports a detailed analysis of errors made by early algebra students who are learning equation solving. Whilst we aim to deepen the knowledge base that can be used by teachers and curriculum writers to plan instruction, the main goal of this article is to demonstrate a 5-step process that we have developed to analyse, summarize, visualize and grasp meaning from large numbers of short constructed responses to mathematics questions. This data-driven process is illustrated using responses from 3,010 students to an online test, which is intended to be highly diagnostic and used for formative purposes. The test consisted of 14 very carefully selected linear equations to solve. Students entered only the numerical answers. Although nearly all the errors identified have been previously reported in the literature, the study provides insights into their prevalence in this target population and demonstrates how they correspond to other characteristics of the students’ algebra, including the strategies that they use to solve these linear equations. It also provides a practical example of using short constructed responses as a window into students’ thinking.
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ItemMathematical Competencies of Chinese Students: An International Perspective(SPRINGER INTERNATIONAL PUBLISHING AG, 2021-01-01)This chapter identifies aspects of the study of mathematical competencies of Chinese students that are likely to be of special interest to international readers. Perhaps the most striking feature is the scale of the work. Within an overarching framework for conceptualizing mathematical competencies, there are detailed reviews of the treatment of each of these cognitive and non-cognitive competencies in the Chinese curriculum since 1902, and a comprehensive set of snapshots of the current performance of Grade 8 students on each. The assessment tools provide powerful base-line data for monitoring students’ mathematical competencies into the future. The detail in the studies will assist international researchers to more deeply understand some of the paradoxes in PISA results, such as Chinese students reporting low classroom exposure to “applied problems” while also demonstrating outstanding performance on items emphasizing PISA’s formulate process. The book gives insight into the strong Chinese tradition of mathematics education, changing over time in response to dramatic social and economic forces but retaining unique features and also becoming increasingly well integrated with international thought.
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ItemNo Preview AvailableTeaching Mathematics through Problem Solving(Sociedad Canaria Isaac Newton de Profesores de Matemáticas, 2018)This paper offers two ways to combine the teaching of mathematics and problem solving: teaching mathematics to solve problems or teaching mathematics through problem solving. By means of examples of activities, teaching through problem solving is proposed.
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ItemNo Preview AvailableScience and Mathematics Literacy: PISA for Better School Education(SPRINGER, 2018-08)
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ItemSMARTA—online-diagnostic to reveal students’ algebraic thinking and enhance teachers’ diagnostic competencies(Danish School of Education, Aarhus Unviersity, 2022)Individual, diagnosis-guided support for learners is one of the most important factors in understanding mathematics and learning efficiently. Especially in the field of algebra many students often still lack basic competencies to handle variables, algebraic expressions and equations in a proper way. Digitally supported diagnostic systems offer the possibility to perform a deep understanding-oriented diagnosis with little time. This is the aim of the Australian SMART-system (Specific Mathematics Assessments that Reveal Thinking (Stacey et al., 2018)), which is currently being adapted for use in German-speaking countries. SMARTA is a twofold project to investigate the effects on students’ understanding of algebra and on teachers’ insight into formative assessment in the field of algebra.
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ItemTeaching with new technology: four 'early majority' teachers(SPRINGER, 2013-10)
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ItemSpecific Mathematics Assessments that Reveal Thinking: An Online Tool to Build Teachers’ Diagnostic Competence and Support Teaching(Springer, 2018)In this chapter, we describe the design of an online system for the formative assessment of students’ understanding of mathematics and discuss how it develops diagnostic competence and influences teaching. The smart-test system covers many mathematics topics studied by students between about 10 and 16 years of age. It is programmed to provide teachers with an automated diagnosis of their own students’ stages of development in specific topics and to report on an individual’s errors and misconceptions, in order to inform teaching. Our claim is that teachers’ diagnostic competence increases when they have easy access to information about their own students’ thinking. In turn, this can further improve teaching, and hence learning. By drawing together evaluative data from four sources, we highlight aspects of teachers’ initial responses to formative assessment and the effect of using this system on their knowledge for teaching and the subsequent changes to teaching practice. Overall, teachers report that using the smart-tests has improved their knowledge of the thinking of individual students as well as of students in general (i.e., their pedagogical content knowledge), and that they can use this information in several ways to adjust their teaching. Paradoxically, using smart-tests reduces the demand for teachers to have specific knowledge for diagnosis and at the same time increases this knowledge and so improves their diagnostic competence.
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ItemTeachers' views of using an on-line, formative assessment system for mathematics(COEX, 2012)In this paper we discuss some issues arising from teachers’ use of an on-line system for formative assessment of their students’ understanding of mathematics. The ‘smart tests’ cover many topics in secondary school mathematics, and are programmed to provide an automated diagnosis of students’ stages of learning in specific topics, to inform teaching. In particular, we highlight teachers’ views about: the desirability of formative assessment; the use that they make of this information; the provision of feedback; and the effect of using the system on their pedagogical content knowledge and subsequent changes to their practice .Overall, teachers report that use of the tests improves their knowledge of the achievement of individual students and students in general, and that they can use this information in several ways to improve their teaching.