Mathematics Education Research Group of Australasia, 2016
This study surveyed and analysed four secondary school students' writing about a square. Sfard's ... more This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally. This in turn helps refining the development of a geometric learning progression, with the accompaniment of a set of validated assessment tools and learning tasks that seeks to deepen teachers' understanding of geometric reasoning and support student learning.
This paper will report on the role of practitioners in a recent Australian study that developed e... more This paper will report on the role of practitioners in a recent Australian study that developed empirically based learning and assessment frameworks (i.e. learning trajectories) for algebraic, geometrical, and statistical reasoning in the middle years of schooling. To understand the nature of the teachers' role, the paper begins with a description of what is meant by 'curriculum' in Australia and the implications of this for teacher decision making and planning. We then provide a rationale for the study and a brief description of the methodology before illustrating how teachers were involved in the iterative research design through task development and the trial and refinement of partial credit scoring rubrics. The paper concludes by describing the development of targeted teaching advice and considering some of the challenges involved in dissemination.
The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skill... more The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum: Algebraic Reasoning, Geometrical and Spatial Reasoning, and Statistical Reasoning.
2013 IEEE 63rd Annual Conference International Council for Education Media (ICEM), 2013
Gaming has now been a part of educational practice for many years. The application of technology ... more Gaming has now been a part of educational practice for many years. The application of technology to gaming opened new doors to both complexity and sophistication of the interactions and dimensions of learning in a game environment. More recently online facilitation has enabled the globalisation of the gaming environment and extended the potential roles of the synthetic world in teaching and learning. An exploration of the nature and characteristics of multiplayer online games (MMOGS) suggests new and innovative learning opportunities from collaborative and learning community configurations to more competitive and advanced cognitive challenges through intricate, multilayered, multifaceted problem based scenarios. Single discipline, and interdisciplinary conformations lend themselves to both specific and generic learning, ranging from disciplinary content and concepts to social, emotional and advanced cognitive knowledge and application learning such as inquiry based learning (Kennedy-Clark, 2011). Moreover the learning environment can be local, national or international, offering unprecedented breadth and depth to interactions in both synchronous and asynchronous encounters. One aspect of online gaming or working in this complex learning environment (Paraskeva, Mysirlaki, & Papagianni, 2010) which has yet to be widely considered in the educational literature is the role of the academic and in particular the academic as a `game player' and the impact on their conceptualisations of learning and practice and the development of their experience and expertise in adapting, developing and weaving a learning design approaches and pedagogy into this predominantly entertainment based platform. Very simply the potential of online gaming for academic professional development is yet to be explored. This paper reports the story of an academic in the world of online gaming. The paper uses the narrative to illustrate the potential of the undertaking for education. Drawing on both contemporary literature and the immediate experiences of participation in the world of gaming, the paper explores the potential for the development of thinking, social learning, as well as the possible role of online gaming in cognitive learning and in particular problem solving in both real world and imaginary environments. Through an investigation of the various aspects of online gaming the paper draws on the experiences of the author, as a player and as an educator, in unpacking the key components and their possible relationships to learning. For example features such as avatars bring with them both conventions and opportunities for imagination and creativity, rules bring with them rights and responsibilities and the conceptualisation of communication requirements offers innumerable configurations which can incorporate learning relating to culture, nuance, literacy, diplomacy, specificity and the list goes on. The paper concludes with a suggestion for future adoption of gaming conventionality and innovation in education.
ABSTRACT For the last decade, international bodies have warned of a teacher shortage and sought t... more ABSTRACT For the last decade, international bodies have warned of a teacher shortage and sought to find ways of attracting more applicants to the profession. This article reports on a pilot study undertaken at one Australian university which asked why some applicants to preservice teaching courses had given up existing careers in order to become teachers. It then asked if their career change had been successful. Using open-ended questions and interviews, this paper recorded the view of 35 teachers who had been in teaching for 2–5 years. The findings suggest that reasons for selecting teaching as a second career are more complex and nuanced than existing research suggests, combining pragmatic, deeply personal and spiritual elements. It also found a significant connection between career change teachers’ satisfaction with their new occupation and the status of their occupation, indicating that further study of career change teachers’ experiences and personal beliefs is warranted.
ABSTRACT As part of a teacher professional learning project in mathematics education, university ... more ABSTRACT As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a “pre-brief, teaching, and debrief” process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the lesson, during the lesson, following the debrief, and several weeks later, data were collected on teachers’ intended and actual observation foci and any anticipated changes in their beliefs and practices arising from the experience. There were several common themes in teachers’ intended observations, including a focus on questioning, catering for individual differences, and building student engagement. As evident in other research, teachers’ intended and actual observations gave greater attention to teacher actions and decision making than to student learning and thinking. In this paper, we situate demonstration lessons within teacher professional learning models, describe the features of our model, summarise teacher data, and discuss issues arising from our work.
This work is copyright. It may be reproduced in whole or in part for study or training purposes s... more This work is copyright. It may be reproduced in whole or in part for study or training purposes subject to the inclusion of an acknowledgment of the source and no commercial usage or sale. Reproduction for purposes other than those indicated above, requires the prior ...
med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifie... more med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifiera viktiga tillväxtpunkter, som indikerar elevers matematikutveckling. Intresset ligger här på elever i åldern 5-8 år. Enskilda intervjuer av eleverna ger läraren möjlighet att finna varje elevs aktuella nivå för att kunna lägga upp en passande undervisning. F orskningsprojektet Early Numeracy, ENRP, är ett treårsprojekt där stat-liga och fristående skolor i Victoria, Australian Catholic University och Monash University är engagerade. Det syftar till att identifiera effektiva angreppssätt för matematikinlärning under de första tre skolåren. Projektets syf-ten var: • att stödja skolorna att införa nyckelfaktorer för skolutveckling som en del av skolans matematikprogram, • att utmana lärare att utforska insikter kring hur barn utvecklar sin matematiska förståelse och hur denna kan stödjas genom undervisningen, • att utvärdera effekten av kompetens-utvecklingsprogrammets inverkan på elevern...
med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifie... more med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifiera viktiga tillväxtpunkter, som indikerar elevers matematikutveckling. Intresset ligger här på elever i åldern 5-8 år. Enskilda intervjuer av eleverna ger läraren möjlighet att finna varje elevs aktuella nivå för att kunna lägga upp en passande undervisning. F orskningsprojektet Early Numeracy, ENRP, är ett treårsprojekt där stat-liga och fristående skolor i Victoria, Australian Catholic University och Monash University är engagerade. Det syftar till att identifiera effektiva angreppssätt för matematikinlärning under de första tre skolåren. Projektets syf-ten var: • att stödja skolorna att införa nyckelfaktorer för skolutveckling som en del av skolans matematikprogram, • att utmana lärare att utforska insikter kring hur barn utvecklar sin matematiska förståelse och hur denna kan stödjas genom undervisningen, • att utvärdera effekten av kompetens-utvecklingsprogrammets inverkan på elevern...
Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, interna... more Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice.
Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, interna... more Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice.
The relationship between research and practice has long been an area of interest for researchers,... more The relationship between research and practice has long been an area of interest for researchers, policy makers and practitioners alike. One obvious arena where mathematics education research can make a practical contribution is the design and implementation of school mathematics curricula. This requires research that is fine-grained and focused on individual student learning trajectories as well as large-scale research that explores how student populations engage with the big ideas of mathematics. This research forum brings together work from the United States and Australia on the development and use of evidence-based learning progressions/trajectories in mathematics. In particular, the forum will consider their basis in theory, their focus and scale, and the methods used to identify and validate learning progressions.
The concept of symmetry is vital for the study of science and developing spatial and geometric re... more The concept of symmetry is vital for the study of science and developing spatial and geometric relationships. Yet few studies have been conducted to examine how students learn this concept. This study investigates 757 Year 4 to 10 students ability to reason about symmetrical relationships. By analysing the semiotic processes through the lens of the theory of semiotic mediation and Sfards mathematical discourse framework, the results show the synergic relations between visualisation of artefacts, and the use of signs and keywords in the construction of knowledge.
Mathematics Education Research Group of Australasia, 2016
This study surveyed and analysed four secondary school students' writing about a square. Sfard's ... more This study surveyed and analysed four secondary school students' writing about a square. Sfard's discursive approach to understanding mathematical discourse was used to analyse the responses collected from 214 Australian secondary school students. The results showed that geometric knowledge was developed experientially and not developmentally. This in turn helps refining the development of a geometric learning progression, with the accompaniment of a set of validated assessment tools and learning tasks that seeks to deepen teachers' understanding of geometric reasoning and support student learning.
This paper will report on the role of practitioners in a recent Australian study that developed e... more This paper will report on the role of practitioners in a recent Australian study that developed empirically based learning and assessment frameworks (i.e. learning trajectories) for algebraic, geometrical, and statistical reasoning in the middle years of schooling. To understand the nature of the teachers' role, the paper begins with a description of what is meant by 'curriculum' in Australia and the implications of this for teacher decision making and planning. We then provide a rationale for the study and a brief description of the methodology before illustrating how teachers were involved in the iterative research design through task development and the trial and refinement of partial credit scoring rubrics. The paper concludes by describing the development of targeted teaching advice and considering some of the challenges involved in dissemination.
The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skill... more The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum: Algebraic Reasoning, Geometrical and Spatial Reasoning, and Statistical Reasoning.
2013 IEEE 63rd Annual Conference International Council for Education Media (ICEM), 2013
Gaming has now been a part of educational practice for many years. The application of technology ... more Gaming has now been a part of educational practice for many years. The application of technology to gaming opened new doors to both complexity and sophistication of the interactions and dimensions of learning in a game environment. More recently online facilitation has enabled the globalisation of the gaming environment and extended the potential roles of the synthetic world in teaching and learning. An exploration of the nature and characteristics of multiplayer online games (MMOGS) suggests new and innovative learning opportunities from collaborative and learning community configurations to more competitive and advanced cognitive challenges through intricate, multilayered, multifaceted problem based scenarios. Single discipline, and interdisciplinary conformations lend themselves to both specific and generic learning, ranging from disciplinary content and concepts to social, emotional and advanced cognitive knowledge and application learning such as inquiry based learning (Kennedy-Clark, 2011). Moreover the learning environment can be local, national or international, offering unprecedented breadth and depth to interactions in both synchronous and asynchronous encounters. One aspect of online gaming or working in this complex learning environment (Paraskeva, Mysirlaki, & Papagianni, 2010) which has yet to be widely considered in the educational literature is the role of the academic and in particular the academic as a `game player' and the impact on their conceptualisations of learning and practice and the development of their experience and expertise in adapting, developing and weaving a learning design approaches and pedagogy into this predominantly entertainment based platform. Very simply the potential of online gaming for academic professional development is yet to be explored. This paper reports the story of an academic in the world of online gaming. The paper uses the narrative to illustrate the potential of the undertaking for education. Drawing on both contemporary literature and the immediate experiences of participation in the world of gaming, the paper explores the potential for the development of thinking, social learning, as well as the possible role of online gaming in cognitive learning and in particular problem solving in both real world and imaginary environments. Through an investigation of the various aspects of online gaming the paper draws on the experiences of the author, as a player and as an educator, in unpacking the key components and their possible relationships to learning. For example features such as avatars bring with them both conventions and opportunities for imagination and creativity, rules bring with them rights and responsibilities and the conceptualisation of communication requirements offers innumerable configurations which can incorporate learning relating to culture, nuance, literacy, diplomacy, specificity and the list goes on. The paper concludes with a suggestion for future adoption of gaming conventionality and innovation in education.
ABSTRACT For the last decade, international bodies have warned of a teacher shortage and sought t... more ABSTRACT For the last decade, international bodies have warned of a teacher shortage and sought to find ways of attracting more applicants to the profession. This article reports on a pilot study undertaken at one Australian university which asked why some applicants to preservice teaching courses had given up existing careers in order to become teachers. It then asked if their career change had been successful. Using open-ended questions and interviews, this paper recorded the view of 35 teachers who had been in teaching for 2–5 years. The findings suggest that reasons for selecting teaching as a second career are more complex and nuanced than existing research suggests, combining pragmatic, deeply personal and spiritual elements. It also found a significant connection between career change teachers’ satisfaction with their new occupation and the status of their occupation, indicating that further study of career change teachers’ experiences and personal beliefs is warranted.
ABSTRACT As part of a teacher professional learning project in mathematics education, university ... more ABSTRACT As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a “pre-brief, teaching, and debrief” process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the lesson, during the lesson, following the debrief, and several weeks later, data were collected on teachers’ intended and actual observation foci and any anticipated changes in their beliefs and practices arising from the experience. There were several common themes in teachers’ intended observations, including a focus on questioning, catering for individual differences, and building student engagement. As evident in other research, teachers’ intended and actual observations gave greater attention to teacher actions and decision making than to student learning and thinking. In this paper, we situate demonstration lessons within teacher professional learning models, describe the features of our model, summarise teacher data, and discuss issues arising from our work.
This work is copyright. It may be reproduced in whole or in part for study or training purposes s... more This work is copyright. It may be reproduced in whole or in part for study or training purposes subject to the inclusion of an acknowledgment of the source and no commercial usage or sale. Reproduction for purposes other than those indicated above, requires the prior ...
med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifie... more med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifiera viktiga tillväxtpunkter, som indikerar elevers matematikutveckling. Intresset ligger här på elever i åldern 5-8 år. Enskilda intervjuer av eleverna ger läraren möjlighet att finna varje elevs aktuella nivå för att kunna lägga upp en passande undervisning. F orskningsprojektet Early Numeracy, ENRP, är ett treårsprojekt där stat-liga och fristående skolor i Victoria, Australian Catholic University och Monash University är engagerade. Det syftar till att identifiera effektiva angreppssätt för matematikinlärning under de första tre skolåren. Projektets syf-ten var: • att stödja skolorna att införa nyckelfaktorer för skolutveckling som en del av skolans matematikprogram, • att utmana lärare att utforska insikter kring hur barn utvecklar sin matematiska förståelse och hur denna kan stödjas genom undervisningen, • att utvärdera effekten av kompetens-utvecklingsprogrammets inverkan på elevern...
med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifie... more med bättre kunskaper om elever I ett australiensiskt forskningsprojekt, ENRP, ingår att identifiera viktiga tillväxtpunkter, som indikerar elevers matematikutveckling. Intresset ligger här på elever i åldern 5-8 år. Enskilda intervjuer av eleverna ger läraren möjlighet att finna varje elevs aktuella nivå för att kunna lägga upp en passande undervisning. F orskningsprojektet Early Numeracy, ENRP, är ett treårsprojekt där stat-liga och fristående skolor i Victoria, Australian Catholic University och Monash University är engagerade. Det syftar till att identifiera effektiva angreppssätt för matematikinlärning under de första tre skolåren. Projektets syf-ten var: • att stödja skolorna att införa nyckelfaktorer för skolutveckling som en del av skolans matematikprogram, • att utmana lärare att utforska insikter kring hur barn utvecklar sin matematiska förståelse och hur denna kan stödjas genom undervisningen, • att utvärdera effekten av kompetens-utvecklingsprogrammets inverkan på elevern...
Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, interna... more Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice.
Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, interna... more Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice.
The relationship between research and practice has long been an area of interest for researchers,... more The relationship between research and practice has long been an area of interest for researchers, policy makers and practitioners alike. One obvious arena where mathematics education research can make a practical contribution is the design and implementation of school mathematics curricula. This requires research that is fine-grained and focused on individual student learning trajectories as well as large-scale research that explores how student populations engage with the big ideas of mathematics. This research forum brings together work from the United States and Australia on the development and use of evidence-based learning progressions/trajectories in mathematics. In particular, the forum will consider their basis in theory, their focus and scale, and the methods used to identify and validate learning progressions.
The concept of symmetry is vital for the study of science and developing spatial and geometric re... more The concept of symmetry is vital for the study of science and developing spatial and geometric relationships. Yet few studies have been conducted to examine how students learn this concept. This study investigates 757 Year 4 to 10 students ability to reason about symmetrical relationships. By analysing the semiotic processes through the lens of the theory of semiotic mediation and Sfards mathematical discourse framework, the results show the synergic relations between visualisation of artefacts, and the use of signs and keywords in the construction of knowledge.
Uploads
Papers by Marj Horne