Open Access. Powered by Scholars. Published by Universities.®

Education Commons

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 30 of 65

Full-Text Articles in Education

The Murky Distinction Between Self-Concept And Self-Efficacy: Beware Of Lurking Jingle-Jangle Fallacies [Accepted Manuscript], Herbert W. Marsh, Reinhard Pekrun, Philip D. Parker, Kou Murayama, Jiesi Guo, Theresa Dicke, A. Katrin Arens Jan 2019

The Murky Distinction Between Self-Concept And Self-Efficacy: Beware Of Lurking Jingle-Jangle Fallacies [Accepted Manuscript], Herbert W. Marsh, Reinhard Pekrun, Philip D. Parker, Kou Murayama, Jiesi Guo, Theresa Dicke, A. Katrin Arens

Faculty of Health Sciences Publications

This study extends the classic constructive dialogue/debate between self-concept and self-efficacy researchers (Marsh, Roche, Pajares, & Miller, 1997) regarding the distinctions between these 2 constructs. The study is a substantive-methodological synergy, bringing together new substantive, theoretical, and statistical models and developing new tests of the classic jingle-jangle fallacy. We demonstrate that in a representative sample of 3,350 students from math classes in 43 German schools, generalized math self-efficacy and math outcome expectancies were indistinguishable from math self-concept, but were distinct from test-related and functional measures of self-efficacy. This is consistent with the jingle-jangle fallacies that are proposed. On the basis of pretest variables, we demonstrate negative frame-of-reference effects in social (big-fish-little-pond effect) and dimensional (internal/external frame-of-reference effect) comparisons for three self-concept-like constructs in each of the first 4 years of secondary school. In contrast, none of the frame-of-reference effects were significantly negative for either of the two self-efficacy-like constructs in any of the 4 years of testing. After controlling for pretest variables, each of the 3 self-concept-like constructs (math self-concept, outcome expectancy, and generalized math self-efficacy) in each of the 4 years of secondary school was more strongly related to posttest outcomes (school grades, test scores, future aspirations) than were the corresponding 2 self-efficacy-like factors. Extending discussion by Marsh et al. (1997), we clarify distinctions between self-efficacy and self-concept; the role of evaluation, worthiness, and outcome expectancy in self-efficacy measures; and complications in generalized and global measures of self-efficacy. (PsycINFO Database Record (c) 2019 APA, all rights reserved)


The Intersection Of Gender, Social Class, And Cultural Context: A Meta-Analysis [Accepted Manuscript], Philip D. Parker, Brooke Van Zanden, Herbert W. Marsh, Katherine Owen, Jasper J. Duineveld, Michael Noetel Jan 2019

The Intersection Of Gender, Social Class, And Cultural Context: A Meta-Analysis [Accepted Manuscript], Philip D. Parker, Brooke Van Zanden, Herbert W. Marsh, Katherine Owen, Jasper J. Duineveld, Michael Noetel

Faculty of Health Sciences Publications

Expectancy value theory is often evoked by educational psychologists to explain gender differences in Science, Technology, Engineering, and Mathematics (STEM) variables. Yet gender does not operate in isolation. Nor are gender effects likely to be context free. In the current meta-analysis, we explore gender differences in STEM-related expectancy for success, and the task values of intrinsic, utility, attainment, and cost. We find that gender differences were generally small in size. Invoking the concept of intersectionality, we find that heterogeneity in gender effect sizes are large and gender differences are moderated, primarily, by socioeconomic status, ethnic diversity, and somewhat by national ...


Value Beliefs About Math: A Bifactor-Esem Representation [Accepted Manuscript], Daniela Fadda, L. Francesca Scalas, Alexandre J. S. Morin, Herbert W. Marsh, Hanna Gaspard Jan 2019

Value Beliefs About Math: A Bifactor-Esem Representation [Accepted Manuscript], Daniela Fadda, L. Francesca Scalas, Alexandre J. S. Morin, Herbert W. Marsh, Hanna Gaspard

Faculty of Health Sciences Publications

This study proposed an improved representation of the factor structure of the Gaspard et al. (2015) value beliefs about math scale relying on bifactor exploratory structural equation modeling (B-ESEM). Using a convenience sample of 537 Italian students (327 males; Mage = 18.2), our results supported the superiority of a B-ESEM solution including nine specific factors (intrinsic, importance of achievement, personal importance, utility for school/job, utility for life, social utility, effort required, opportunity cost, and emotional cost) and one global value factor. The results further revealed that the specific factors (with the exception of personal importance) retained meaning over and ...


Young Women Face Disadvantage To Enrollment In University Stem Coursework Regardless Of Prior Achievement And Attitudes [Accepted Manuscript], Herbert W. Marsh, Brooke Van Zanden, Philip D. Parker, Jiesi Guo, James Conigrave, Marjorie Seaton Jan 2019

Young Women Face Disadvantage To Enrollment In University Stem Coursework Regardless Of Prior Achievement And Attitudes [Accepted Manuscript], Herbert W. Marsh, Brooke Van Zanden, Philip D. Parker, Jiesi Guo, James Conigrave, Marjorie Seaton

Faculty of Health Sciences Publications

We evaluated STEM (science, technology, engineering, and mathematics) coursework selection by women and men (representative longitudinal sample, 10,370 Australians) in senior high school and university, controlling achievement and expectancy-value variables. A near-zero total effect of gender on high school STEM enrollment reflected pathways favoring boys through achievement and expectancy-value variables, but a counteracting direct effect of gender favoring girls. In contrast, subsequent university STEM enrollment favored boys. In both high school and university, enrollments favored girls in life sciences and boys in physical sciences, but at university there was a leaky pipeline in which girls who qualified to pursue ...


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.


Enlightening Science: Addressing The Cognitive And Non-Cognitive Aspects Of Science Learning, Munirah Shaik Kadir Jan 2018

Enlightening Science: Addressing The Cognitive And Non-Cognitive Aspects Of Science Learning, Munirah Shaik Kadir

Theses

Physical science (or physics) is known to be one of the least popular school curriculum domains, mainly because of its complexity. When students encounter seemingly insurmountable difficulties when learning something, they lose the motivation to continue. It has been suggested that both the cognitive (e.g., students’ conceptual understanding and achievement) and non-cognitive (e.g., psychological aspects such as academic self-concept and motivation) factors of learning are essential for helping students achieve their optimal best in a curriculum domain. However, there has not been much research, if any, which uses a dual approach to investigate both aspects of science learning ...


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 ...


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 ...


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.


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 ...


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.


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 ...


Teaching And Learning Spatial Thinking With Young Students: The Use And Influence Of External Representations, Peta Spencer Oct 2017

Teaching And Learning Spatial Thinking With Young Students: The Use And Influence Of External Representations, Peta Spencer

Theses

Previous research suggests spatial thinking is fundamental to mathematics learning (Bronowski, 1947; Clements & Sarama, 2007, 2011), and acts as a predictor for future mathematical achievement levels (Battista, 1990; Gunderson et al., 2012). However, research with regard to spatial thinking is almost non-existent in early years mathematics classrooms (Bruce, Moss, & Ross, 2012; Clements & Sarama, 2011; Newcombe & Frick, 2010; Sarama & Clements, 2009, 2011; Stipek, 2013), and how to teach it in these contexts has received little attention. Fewer studies again have focused on the use of virtual manipulatives in influencing young students’ spatial thinking (Highfield & Mulligan, 2007; Ng & Sinclair, 2015). Despite a recent surge in studies exploring the influence of virtual manipulatives in mathematics classrooms, little is known about how these manipulatives compare to physical manipulatives, especially in regard to the changes that occur in the social interactions between teacher and students during the learning process. To date, there has been no comparative study conducted that explores the influence of different external representations (e.g., physical manipulatives and virtual manipulatives) on both the teaching and the learning aspects within mathematics classrooms. The purpose of this research is to explore the use of external representations (i.e., physical manipulatives as compared to virtual manipulatives) in the mathematics classroom and how these representations support young, disadvantaged students’ spatial thinking. The use of manipulatives is a common starting point for the teaching and learning of spatial thinking.

Previous research on manipulative use (both physical and virtual) in mathematics education has yielded positive results with regard to student learning (Clements, 1999; Heddens, 1997; Highfield & Mulligan, 2007; Riconscente, 2013; Siemon et al., 2011; Warren, 2006; Warren & Miller, 2013). Recent studies indicate that these newer digital technologies promote interactions between visual and kinaesthetic learning, which have been shown to support the teaching and learning of spatial thinking (Battista, 2008; Bruce, McPherson, Sabeti, & Flynn, 2011; Clements & Sarama, 2011; Highfield & Mulligan, 2007; Jorgensen & Lowrie, 2012; Sinclair, de Freitas, & Ferrara, 2013; Sinclair & Moss, 2012). However, results from comparative studies between physical manipulatives and virtual manipulatives have been varied (e.g., Brown, 2007; Olkum, 2003; Suh, 2005). It is proposed that ...


Math Self-Concept, Grades, And Achievement Test Scores: Long-Term Reciprocal Effects Across Five Waves And Three Achievement Tracks [Accepted Manuscript], A. Katrin Arens, Herbert W. Marsh, Reinhard Pekrun, Stephanie Lichtenfeld, Kou Murayama, Rudolf Vom Hofe Jan 2017

Math Self-Concept, Grades, And Achievement Test Scores: Long-Term Reciprocal Effects Across Five Waves And Three Achievement Tracks [Accepted Manuscript], A. Katrin Arens, Herbert W. Marsh, Reinhard Pekrun, Stephanie Lichtenfeld, Kou Murayama, Rudolf Vom Hofe

Faculty of Health Sciences Publications

This study examines reciprocal effects between self-concept and achievement by considering a long time span covering grades 5 through 9. Extending previous research on the reciprocal effects model (REM), this study tests (1) the assumption of developmental equilibrium as time-invariant cross-lagged paths from self-concept to achievement and from achievement to self-concept, (2) the generalizability of reciprocal relations when using school grades and standardized achievement test scores as achievement indicators, and (3) the invariance of findings across secondary school achievement tracks. Math self-concept, school grades in math, and math achievement test scores were measured once each school year with a representative ...


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 ...


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.


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 ...


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.


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.


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).


Problem Solving, Thinking And Group Work In Mathematics: Developing An Effective Pedagogy, Gary R. Thomas Aug 2014

Problem Solving, Thinking And Group Work In Mathematics: Developing An Effective Pedagogy, Gary R. Thomas

Theses

This research investigates the use of heuristics and thinking routines while problem solving in mathematics in a collaborative setting of small groups. The educational setting and context of this study is a year 2 classroom in a Victorian school. The study began in response to first; that a thinking classroom is an active, reflective and learning environment that promotes ideas and rich thoughts. Ron Ritchhart is [sic] his book, Intellectual Character (2002) discusses intelligence, being smart and developing intellectual character, secondly; that mathematical problem solving requires students to have a starting point. Polya’s model of understand the problem, make ...


Young Indigenous Students' Experiences In Mathematics: An Exploration In Pattern Generalisation, Jodie Miller Jun 2014

Young Indigenous Students' Experiences In Mathematics: An Exploration In Pattern Generalisation, Jodie Miller

Theses

There is limited research that focuses on young Australian Indigenous students learning specific mathematical concepts (Meaney, McMurchy-Pilkington, & Trinick, 2012). To date, there has been no study conducted within an Australian context that considers how young Australian Indigenous students engage in mathematical generalisation of growing patterns. Mathematical growing patterns are a sequence of shapes or numbers characterised by the relationship between elements, which can increase or decrease by a constant difference (linear growing pattern). Additionally, growing patterns can also exhibit quadratic and exponential growth. The purpose of this study is to explore how young Australian Indigenous students generalise growing patterns. Patterns are a common route for young students to engage with in early algebraic thinking. Algebra has been labelled as a mathematical gatekeeper for all students, having the potential to provide both economic opportunity and equal citizenship (Satz, 2007). It has been proposed that algebra is one link in reducing the exacerbated inequalities between ethnicity and socioeconomic groups (Greenes, 2008). Concerns about students’ poor understanding of algebra in secondary school have contributed to early algebra becoming a focal point for mathematics education. Early algebra is its own unique subject, and is not to be confused with the teaching of algebra early. Rather, the concept of early algebra is integrated with other early mathematical concepts as students engage in the gradual introduction to formal notation (Carraher, Schliemann, & Schwartz, 2008). In addition, early algebraic thinking leads to a deeper understanding of mathematical structures (Blanton & Kaput, 2011; Carraher, Schliemann, Brizuela & Ernest, 2006; Cooper & Warren, 2011). Recent studies indicate that young students are capable of engaging with early algebraic concepts (e.g., Blanton & Kaput, 2011; Cooper & Warren, 2011; Cooper & Warren, 2008; Radford, 2010a; Rivera, 2006)...


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.