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Full-Text Articles in Science and Mathematics Education

High School Students' Motivation To Learn Mathematics: The Role Of Multiple Goals [Accepted Manuscript], Clarence Ng Jan 2018

High School Students' Motivation To Learn Mathematics: The Role Of Multiple Goals [Accepted Manuscript], Clarence Ng

Faculty of Education and Arts Publications

Using a sample of 310 Year 10 Chinese students from Hong Kong, this survey study examined the effects of multiple goals in learning mathematics. Independent variables were mastery, performance-approach, performance-avoidance, and pro-social goals. Dependent variables included perceived classroom goal structures, teacher’s support, learning motives and strategies, attitudes, and grade aspiration. Based on regression and cluster analyses, this study found convergent evidence supporting the benefits of adopting additional adaptive goals alongside mastery goals. Regression analyses located significant interaction between pro-social goals and mastery goals in predicting higher levels of positive learning attitudes and lower levels of surface learning motives. Cluster ...


Extending The Notion Of Specialized Content Knowledge: Proposing Constructs For Sck, Mun Y. Lai, Julie Clark Jan 2018

Extending The Notion Of Specialized Content Knowledge: Proposing Constructs For Sck, Mun Y. Lai, Julie Clark

Faculty of Education and Arts Publications

While it is widely believed that Specialized Content Knowledge (SCK) is essential to effective and quality mathematics teaching, the specific constructs that compose SCK remain underspecified. This paper describes the development and use of a new framework that extends the notion of SCK. The framework was trialled with a cohort of 90 first year Bachelor of Education (Primary) pre-service teachers who enrolled in a regional Australian university. The pre-service teachers undertook a mathematics test, which required them to address school students’ misconceptions and to explain specific mathematical concepts. Resultant data (i.e., the pre-service teachers’ responses to the written test ...


Generating Ideas For Numeracy Tasks Across The Curriculum, Vince Geiger Jan 2018

Generating Ideas For Numeracy Tasks Across The Curriculum, Vince Geiger

Faculty of Education and Arts Publications

No abstract provided.


Mathematics Cognition Reconsidered: On Ascribing Meaning, Thorsten Scheiner Jan 2018

Mathematics Cognition Reconsidered: On Ascribing Meaning, Thorsten Scheiner

Faculty of Education and Arts Publications

In contrast to the common assumption that mathematics cognition involves the attempt to recognize a previously unnoticed meaning of a concept, here mathematics cognition is reconsidered as a process of ascribing meaning to the objects of one’s thinking. In this paper, the attention is focused on three processes that are convoluted in the complex dynamics involved when individuals ascribe meaning to higher mathematical objects: contextualizing, complementizing, and complexifying. The aim is to discuss emerging perspectives of these three processes in more detail that speak to the complex dynamics in mathematics cognition.


Sense-Making In Mathematics: Towards A Dialogical Framing, Thorsten Scheiner Jan 2018

Sense-Making In Mathematics: Towards A Dialogical Framing, Thorsten Scheiner

Faculty of Education and Arts Publications

This paper presents a new theoretical viewpoint blended from the perspectives that mathematical meaning is extracted (from objects falling under a particular concept) and that mathematical meaning is given (to objects that an individual interacts with). It is elaborated that neither uni-directional framing (whether involving extracting meaning or giving meaning) provides a comprehensive account of the complex emergence of evolving forms of meaning. It is argued for a framing that construes sense-making in mathematics as dialogical: where what meaning one extracts is a function of what meaning is given to, and vice versa.


Theoretical Advances In Mathematical Cognition, Thorsten Scheiner, Marcia M. F. Pinto Jan 2018

Theoretical Advances In Mathematical Cognition, Thorsten Scheiner, Marcia M. F. Pinto

Faculty of Education and Arts Publications

This paper articulates and explicates theoretical perspectives that emerged in accounting for the complex dynamic processes involved when individuals ascribe meaning to the mathematical objects of their thinking. Here the focus is on the following processes that are convoluted in the complex dynamics in mathematical concept formation: contextualizing, complementizing, and complexifying. The paper elaborates these three processes in detail, recognizing their epistemological, conceptual, and cognitive significance in mathematical knowing and learning.


The Effect Of Interest And Engagement In Learning Science On Adults' Scientific Competency And Environmental Action, Yi-Ting Pan, Kuay-Keng Yang, Zuway-R Hong, Huann-Shyang Lin Jan 2018

The Effect Of Interest And Engagement In Learning Science On Adults' Scientific Competency And Environmental Action, Yi-Ting Pan, Kuay-Keng Yang, Zuway-R Hong, Huann-Shyang Lin

Faculty of Education and Arts Publications

Although existing research has documented the significant relationship among student interest, engagement, and learning outcome, limited studies have investigated how adults’ interest and engagement in learning science are related to their scientific competency and environmental action. This study used 2012 and 2015 national datasets which were collected from face-to-face interviews representing how the interest and engagement of Taiwan citizens in understanding and exposure to science in society synergistically interact with their scientific competency and environmental action. Results showed that engagement in learning is more predictive to scientific competency and environmental action than interest. In addition, engagement in visiting science museums ...


Conceptualisations Of Infinity By Primary Pre-Service Teachers, Elizabeth Date-Huxtable, Michael Cavanagh, Carmel Coady, Michael Easey Jan 2018

Conceptualisations Of Infinity By Primary Pre-Service Teachers, Elizabeth Date-Huxtable, Michael Cavanagh, Carmel Coady, Michael Easey

Faculty of Education and Arts Publications

As part of the Opening Real Science: Authentic Mathematics and Science Education for Australia project, an online mathematics learning module embedding conceptual thinking about infinity in science-based contexts, was designed and trialled with a cohort of 22 pre-service teachers during 1 week of intensive study. This research addressed the question: “How do pre-service teachers conceptualise infinity mathematically?” Participants argued the existence of infinity in a summative reflective task, using mathematical and empirical arguments that were coded according to five themes: definition, examples, application, philosophy and teaching; and 17 codes. Participants’ reflections were differentiated as to whether infinity was referred to ...


Learning From Lessons: Studying The Structure And Construction Of Mathematics Teacher Knowledge In Australia, China And Germany, Man Ching Esther Chan, David J. Clarke, Doug Clarke, Anne Roche, Yiming Cao, Andrea Peter-Koop Jan 2018

Learning From Lessons: Studying The Structure And Construction Of Mathematics Teacher Knowledge In Australia, China And Germany, Man Ching Esther Chan, David J. Clarke, Doug Clarke, Anne Roche, Yiming Cao, Andrea Peter-Koop

Faculty of Education and Arts Publications

The major premise of this project is that teachers learn from the act of teaching a lesson. Rather than asking “What must a teacher already know in order to practice effectively?”, this project asks “What might a teacher learn through their activities in the classroom and how might this learning be optimised?” In this project, controlled conditions are created utilising purposefully designed and trialled lesson plans to investigate the process of teacher knowledge construction, with teacher selective attention proposed as a key mediating variable. In order to investigate teacher learning through classroom practice, the project addresses the following questions: To ...


Emerging Insights From The Evolving Framework Of Structural Abstraction, Thorsten Scheiner, Márcia M. F. Pinto Jan 2017

Emerging Insights From The Evolving Framework Of Structural Abstraction, Thorsten Scheiner, Márcia M. F. Pinto

Faculty of Education and Arts Publications

Only recently ‘abstraction from objects’ has attracted attention in the literature as a form of abstraction that has the potential to take account of the complexity of students’ knowing and learning processes compatible with their strategy of giving meaning. This paper draws attention to several emerging insights from the evolving framework of structural abstraction in students’ knowing and learning of the limit concept of a sequence. Particular ideas are accentuated that we need to understand from a theoretical point of view since they reveal a new way of understanding knowing and learning advanced mathematical concepts.


Examining Mathematical Sophistications In Collaborative Problem Solving, Dung Tran, Man Ching Esther Chan Jan 2017

Examining Mathematical Sophistications In Collaborative Problem Solving, Dung Tran, Man Ching Esther Chan

Faculty of Education and Arts Publications

This paper reports on efforts to characterise levels of mathematical sophistication for students in collaborative mathematics problem solving. Using a laboratory classroom in Australia, data were captured with multiple cameras and audio inputs. Students worked individually, in pairs, and in small groups (4 to 6 students). We focused on investigating collaborative work, with the goal of studying the mathematical sophistications of students’ reasoning when solving problems. Drawing from two analytical frameworks to document the mathematical sophistication in students’ exchange, levels of cognitive demands and mathematical practices, this research highlights different aspects of students’ reasoning in solving these tasks.


Conception To Concept Or Concept To Conception? From Being To Becoming, Thorsten Scheiner Jan 2017

Conception To Concept Or Concept To Conception? From Being To Becoming, Thorsten Scheiner

Faculty of Education and Arts Publications

Previous approaches to mathematics knowing and learning have attempted to account for the complexity of students’ individual conceptions of a mathematical concept. Those approaches primarily focused on students’ conceptual development when a mathematical concept comes into being. Recent research insights indicate that some students give meaning not only to states/objects that have a being but also to states/objects that are yet to become. In those cases, conceptual development is not meant to reflect an actual concept (conception-to-concept fit), but rather to create a concept (concept-to-conception fit). It is argued that the process of generating a concept-to-conception fit, in ...


Building Cognitive Bridges In Mathematics: Exploring The Role Of Screencasting In Scaffolding Flexible Learning And Engagement, Catherine Mcloughlin, Birgit Loch Jan 2016

Building Cognitive Bridges In Mathematics: Exploring The Role Of Screencasting In Scaffolding Flexible Learning And Engagement, Catherine Mcloughlin, Birgit Loch

Faculty of Education and Arts Publications

Conceptual learning in mathematics can be made more accessible with mathscasts, which are dynamic, digitally recorded playbacks of worked examples and mathematical problem-solving on a computer screen, accompanied by audio narration. Mathscasts aim to enable students to develop deeper understanding of key foundational concepts in order to equip them to undertake degrees in Science, technology, engineering and mathematics (STEM). Previous research has indicated the success of maths screencasts to provide explanations of complex concepts and reinforcement of concepts previously learnt. The project presented here extends current research by demonstrating the value of visual, interactive screencasts for learning of mathematics, and ...


Images Of Abstraction In Mathematics Education: Contradictions, Controversies, And Convergences, Thorsten Scheiner, Márcia M. F. Pinto Jan 2016

Images Of Abstraction In Mathematics Education: Contradictions, Controversies, And Convergences, Thorsten Scheiner, Márcia M. F. Pinto

Faculty of Education and Arts Publications

In this paper we offer a critical reflection of the mathematics education literature on abstraction. We explore several explicit or implicit basic orientations, or what we call images, about abstraction in knowing and learning mathematics. Our reflection is intended to provide readers with an organized way to discern the contradictions, controversies, and convergences concerning the many images of abstraction. Given the complexity and multidimensionality of the notion of abstraction, we argue that seemingly conflicting views become alternatives to be explored rather than competitors to be eliminated. We suggest considering abstraction as a constructive process that characterizes the development of mathematical ...


Making Sense Of Students' Sense Making Through The Lens Of The Structural Abstraction Framework, Márcia M. F. Pinto, Thorsten Scheiner Jan 2016

Making Sense Of Students' Sense Making Through The Lens Of The Structural Abstraction Framework, Márcia M. F. Pinto, Thorsten Scheiner

Faculty of Education and Arts Publications

In this paper we use the evolving framework of structural abstraction as a theoretical lens to investigate how mathematics major university students understand the limit concept of a sequence. To this aim the theoretical framework is outlined and previous empirical data on one individual’s partial (re-)construction of a convergent sequence is revisited. In doing so, we provide insights in how students, who consider the formal definition of a mathematical concept as one of the components of their concept image, involve it into their overall mathematical discourse when building new knowledge. Deeper analysis also reveals unsettled issues about structural ...


Mathematical Applications And Modelling In The Teaching And Learning Of Mathematics, Jill Brown, Toshikazu Ikeda Jan 2015

Mathematical Applications And Modelling In The Teaching And Learning Of Mathematics, Jill Brown, Toshikazu Ikeda

Faculty of Education and Arts Publications

Applications and modelling have been an important theme in mathematics education during the last 40 years; in particular, through ICMEs regular working/topic groups and lectures on applications and modelling, and the series of International Community on the Teaching of Mathematical Modelling and Applications (ICTMA) conferences, held biennially since 1983. Relations between the real world and mathematics are particularly topical. One reason for learning mathematics is to understand and make sense of the world. The mathematics education community was invited to submit proposals addressing one of six themes and related issues. The focus could be at any level of education ...


"I Was In Year 5 And I Failed Maths": Identifying The Range And Causes Of Maths Anxiety In First Year Pre-Service Teachers, Sue Wilson Jan 2015

"I Was In Year 5 And I Failed Maths": Identifying The Range And Causes Of Maths Anxiety In First Year Pre-Service Teachers, Sue Wilson

Faculty of Education and Arts Publications

Mathematics anxiety affects primary pre-service teachers' engagement with and future teaching of mathematics. The study aimed to assess the level and range of mathematics anxiety in first year pre-service teachers entering their teacher education course, and to investigate the sources of this anxiety as perceived and identified by them. Data collection methods included the RMARS survey, and Critical Incident Technique. The results indicate that the most common negative impacts on pre-service teacher mathematical self-concept involved experiences with teachers. However, their current mathematics anxiety is most commonly aroused under testing or evaluation situations.


Using Transactional Distance Theory To Redesign An Online Mathematics Education Course For Pre-Service Primary Teachers, Kevin Larkin, Romina Jamieson-Proctor Jan 2015

Using Transactional Distance Theory To Redesign An Online Mathematics Education Course For Pre-Service Primary Teachers, Kevin Larkin, Romina Jamieson-Proctor

Faculty of Education and Arts Publications

This paper examines the impact of a series of design changes to an online mathematics education course in terms of transactional distance between learner and teachers, pre-service education students' attitudes towards mathematics, and their development of mathematical pedagogical knowledge. Transactional distance theory (TDT) was utilised to investigate and describe the interactions among course structure, course dialogue and student autonomy in an online course over a two-year period. Findings indicate that Web 2.0 technologies, when used thoughtfully by teachers, can afford high levels of structure and dialogue. Feedback from pre-service teachers indicated an improved attitude towards mathematics and an increase ...


The Impact Of Let’S Count On Children’S Mathematics Learning, Ann Gervasoni, Bob Perry, Linda Parish Jan 2015

The Impact Of Let’S Count On Children’S Mathematics Learning, Ann Gervasoni, Bob Perry, Linda Parish

Faculty of Education and Arts Publications

Let’s Count is an early mathematics program that has been designed by The Smith Family and the authors to assist educators in early childhood contexts in socially disadvantaged areas of Australia to work in partnership with parents and other family members to promote positive mathematical experiences for young children (3-5 years). A longitudinal evaluation of Let’s Count was undertaken in 2012-2014 involving 337 children in two treatment groups and 125 children in a comparison group. This paper shares preliminary results from the evaluation. Overall the findings demonstrate that Let’s Count was effective.


Lessons We Have (Not) Learned From Past And Current Conceptualizations Of Mathematics Teachers' Knowledge, Thorsten Scheiner Jan 2015

Lessons We Have (Not) Learned From Past And Current Conceptualizations Of Mathematics Teachers' Knowledge, Thorsten Scheiner

Faculty of Education and Arts Publications

This paper attempts to capture some of the breath of frameworks and models on mathematics teachers’ knowledge in order to identify central lessons we have (not yet) learned from past and current approaches in theorizing and conceptualizing a knowledge base for teaching mathematics: there are accounts of the complex and multidimensional nature of teachers’ knowledge but no accounts as to the reorganization of dimensions of teachers’ knowledge in order to be more consistent with a constructivist view on learning and teaching; there are accounts of what teachers’ knowledge is about but no accounts as to a structural description of teachers ...


Shifting The Emphasis Toward A Structural Description Of (Mathematics) Teachers' Knowledge, Thorsten Scheiner Jan 2015

Shifting The Emphasis Toward A Structural Description Of (Mathematics) Teachers' Knowledge, Thorsten Scheiner

Faculty of Education and Arts Publications

Despite the wide range of various conceptualisations of (mathematics) teachers’ knowledge, the literature is restricted in two interrelated respects: (1) the focus is (almost always) limited to the subject matter content, and (2) the form and nature of teachers’ knowledge seem not to have been noticed by researchers working in the field. The paper seeks to address these gaps by (a) broadening the current perspective to include an epistemological, cognitive, and didactical lens on the knowledge base for teaching mathematics, and (b) going beyond what the teachers’ knowledge is about to take account of how the knowledge is structured and ...


Theorising About Mathematics Teachers' Professional Knowledge: The Content, Form, Nature, And Source Of Teachers' Knowledge, Thorsten Scheiner Jan 2015

Theorising About Mathematics Teachers' Professional Knowledge: The Content, Form, Nature, And Source Of Teachers' Knowledge, Thorsten Scheiner

Faculty of Education and Arts Publications

The guiding philosophy of this theoretical work lays in the argument that mathematics_teachers’ professional knowledge is the integration of various knowledge facets derived_from different sources including teaching experience and research. This paper goes beyond_past trends identifying what the teachers’ knowledge is about (content) by providing new_perspectives, in particular, on how the knowledge is structured and organised (form), on_what teachers’ draw on their knowledge (source), and whether the knowledge is stable and_coherent or contextually-sensitive and fluid (nature).


What Do Error Patterns Tell Us About Hong Kong Chinese And Australian Students: Understanding Of Decimal Numbers?, Mun Y. Lai, Sara Murray Jan 2014

What Do Error Patterns Tell Us About Hong Kong Chinese And Australian Students: Understanding Of Decimal Numbers?, Mun Y. Lai, Sara Murray

Faculty of Education and Arts Publications

Mathematics educators have had a long standing interest in students’ understanding of decimal numbers. Most studies of students’ understanding of decimals have been conducted within Western cultural settings. The present study sought to gain insight into Chinese Hong Kong students’ and regional Australian students’ general performance on a variety of decimals tasks and to investigate students’ error patterns.


"Change My Thinking Patterns Towards Maths": A Bibliotherapy Workshop For Pre-Service Teachers' Mathematics Anxiety, Sue Wilson, Monica Raven Jan 2014

"Change My Thinking Patterns Towards Maths": A Bibliotherapy Workshop For Pre-Service Teachers' Mathematics Anxiety, Sue Wilson, Monica Raven

Faculty of Education and Arts Publications

In small-group workshops, a joint initiative of the researcher and the student counsellor, primary (elementary) pre-service teachers (PSTs) wrote about critical incidents in their mathematics learning, and shared them with the group. Then, PSTs read extracts about mathematics anxiety (maths anxiety), and wrote and shared their reflections (bibliotherapy). Their experiences illuminated factors in their maths anxiety and helped them identify alternative conceptions. The discussion highlights the need for teacher educators’ awareness of perspectives of PSTs, verbalisation and sharing of emotions, and includes recommendations for further research.


School Mathematics Leaders' Perceptions Of Successes And Challenges Of Their Leadership Role Within A Mathematics Improvement Project, Matthew Sexton, Ann Downton Jan 2014

School Mathematics Leaders' Perceptions Of Successes And Challenges Of Their Leadership Role Within A Mathematics Improvement Project, Matthew Sexton, Ann Downton

Faculty of Education and Arts Publications

The mathematics curriculum leader plays an important role in leading the mathematics curriculum in primary schools. They experience successes and face challenges associated with this leadership role. The perceptions that 25 mathematics leaders held about the successes and challenges they experienced whilst participating in a school mathematics project are reported. Main successes included improved mathematics planning practices using key ideas, transformed cultures concerning mathematics education, and greater use of quality tasks. The main challenge related to sustaining improvements and maintaining the profile of mathematics in school improvement agendas after involvement in the project.


Mathematical Modeling In School Education: Mathematical, Cognitive, Curricular, Instructional And Teacher Educational Perspectives, Jinfa Cai, Michelle Cirillo, John Pelesko, Rita Bommero Ferri, Marcelo Borba, Vincent Geiger, Gloria Stillman, Lyn English, Geoff Wake, Gabriele Kaiser Jan 2014

Mathematical Modeling In School Education: Mathematical, Cognitive, Curricular, Instructional And Teacher Educational Perspectives, Jinfa Cai, Michelle Cirillo, John Pelesko, Rita Bommero Ferri, Marcelo Borba, Vincent Geiger, Gloria Stillman, Lyn English, Geoff Wake, Gabriele Kaiser

Faculty of Education and Arts Publications

No abstract provided.


Teaching Strategies For Building Student Persistence On Challenging Tasks : Insights Emerging From Two Approaches To Teacher Professional Learning, Doug Clarke, Jill Cheeseman, Anne Roche, Stephanie Van Der Schans Jan 2014

Teaching Strategies For Building Student Persistence On Challenging Tasks : Insights Emerging From Two Approaches To Teacher Professional Learning, Doug Clarke, Jill Cheeseman, Anne Roche, Stephanie Van Der Schans

Faculty of Education and Arts Publications

In recent years, the mathematics education research community has given increased focus to the use of cognitively demanding, challenging tasks and the demands placed on students and teachers by their use. In particular, there is evidence that a major issue is students' lack of persistence when working on such tasks. In this article, we report on two approaches to teacher professional learning in which the use of challenging tasks was the focus. In the first case, two full days of professional learning were followed by the opportunity to teach up to ten challenging tasks. In the second case, teachers observed ...


Cognitive Processes Underlying Mathematical Concept Construction: The Missing Process Of Structural Abstraction, Thorsten Scheiner, Márcia M. F. Pinto Jan 2014

Cognitive Processes Underlying Mathematical Concept Construction: The Missing Process Of Structural Abstraction, Thorsten Scheiner, Márcia M. F. Pinto

Faculty of Education and Arts Publications

The purpose of this paper is twofold: On the one hand, this work frames a variety of considerations on cognitive processes underlying mathematical concept construction in two research strands, namely an actions-first strand and an objects-first strand, that mainly shapes past and current approaches on abstraction in learning mathematics. This classification provides the identification of an often overlooked fundamental cognitive process, namely structural abstraction. On the other hand, this work shows a theory-driven and research-based approach illuminating the hidden architecture of cognitive processes involved in structural abstraction that gives new insights into an integrated framework on abstraction in learning mathematics ...


Constructing Meanings Of Mathematical Registers Using Metaphorical Reasoning And Models, Mun Y. Lai Jan 2013

Constructing Meanings Of Mathematical Registers Using Metaphorical Reasoning And Models, Mun Y. Lai

Faculty of Education and Arts Publications

Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This paper investigates how a mathematics teacher made use of models and metaphors to construct mathematical meanings within a transformational shift between less- and more-mathematical language. The Peircian model of semiosis was employed to identify the conceptual relationships in the metaphors and to analyse possible discrepancies between the literal meaning of metaphors, the ...


Designing Mathematical Modelling Tasks In A Technology Rich Secondary School Context, Vincent Geiger, Trevor Redmond Jan 2013

Designing Mathematical Modelling Tasks In A Technology Rich Secondary School Context, Vincent Geiger, Trevor Redmond

Faculty of Education and Arts Publications

The potential of digital tools to enhance student learning is well researched, however, the potential of technology to promote students’ engagement with mathematical modelling tasks has received limited consideration. This paper draws on a research study that aimed to investigate the possibilities that exist for student learning when teachers from six secondary schools designed tasks that anticipated for the use of digital tools within mathematical modelling tasks. The paper describes and analyses the collaboration which took place in identifying principles of design for such tasks.