Theories of Mathematics Education : Seeking New Frontiers

This inaugural book in the new series Advances in Mathematics Education is the most up to date, comprehensive and avant garde treatment of Theories of Mathematics Education which use two highly acclaimed ZDM special issues on theories of mathematics education (issue 6/2005 and issue 1/2006), as a point of departure. Historically grounded in the Theories of Mathematics Education (TME group) revived by the book editors at the 29th Annual PME meeting in Melbourne and using the unique style of preface-chapter-commentary, this volume consist of contributions from leading thinkers in mathematics education who have worked on theory building. This book is as much summative and synthetic as well as forward-looking by highlighting theories from psychology, philosophy and social sciences that continue to influence theory building. In addition a significant portion of the book includes newer developments in areas within mathematics education such as complexity theory, neurosciences, modeling, critical theory, feminist theory, social justice theory and networking theories. The 19 parts, 17 prefaces and 23 commentaries synergize the efforts of over 50 contributing authors scattered across the globe that are active in the ongoing work on theory development in mathematics education.

Politicizing mathematics education : has politics gone too far? Or not far enough?

In this chapter we tackle increasingly sensitive questions in mathematics education, those that have polarized the community into distinct schools of thought as well as impacted reform efforts.

The intra-aortic balloon pump in heart failure management : implications for nursing practice

Management of acute heart failure is an important consideration in critical care. Mechanical support of the failing heart is crucial for improving health outcomes. The most common Australasian application of intraaortic balloon counterpulsation (IABP) is in the setting of cardiogenic shock. High end users of IABP (>37/annum) demonstrate significantly lower mortality for cardiogenic shock managed with IABP (p <0.001) in contrast to hospitals which employ limited IABP (<4/annum). This underscores the importance of proficiency in managing patient receiving IABP support. Nurses play a crucial role in carding for patients with acute heart failure. This paper summarises care considerations for management of the IABP.

Solving graphics tasks : gender differences in middle-school students

The capacity to solve tasks that contain high concentrations of visual-spatial information, including graphs, maps and diagrams, is becoming increasingly important in educational contexts as well as everyday life. This research examined gender differences in the performance of students solving graphics tasks from the Graphical Languages in Mathematics (GLIM) instrument that included number lines, graphs, maps and diagrams. The participants were 317 Australian students (169 males and 148 females) aged 9 to 12 years. Boys outperformed girls on graphical languages that required the interpretation of information represented on an axis and graphical languages that required movement between two- and three-dimensional representations (generally Map language).

The utilisation of skilled immigrants and skilled Refugees in countries of destination

about 82 million immigrants in the OECD area; and worldwide, there are about 191 million immigrants and displaced persons, and some 30-40 million unauthorised immigrants. Also according to recent OECD report, little in-depth research has been carried out to-date to help decision makers in government, business, and society at large, to better understand the complexities and wider consequences of future migration flows. Literatures have also indicated that the lack of a skilled population in muchneeded occupations in countries of destination have contributed to the need to bring in skilled foreign workers. Furthermore, despite current global financial crisis, some areas of occupation are in need of skilled workers such that in a job-scarce environment jobs become fewer and employers are more likely to demand skilled workers from both natives and immigrants. Global competition for labour is expected to intensify, especially for top talent, highly qualified and semi-skilled individuals. This exacerbate the problems faced by current skilled immigrants and skilled refugees, particularly those from non-main English speaking countries who are not employed at optimal skill level in countries of destination. The research study investigates whether skilled immigrants are being effectively utilised in their countries of destination, in the context of employment. In addition to skilled immigrants, data sampling will also include skilled refugees who, although arriving under the humanitarian program, possess formal qualifications from their country of origin. Underlying variables will be explored such as the strength of social capital or interpersonal ties; and human capital in terms of educational attainment and proficiency in the English Language. The aim of the study is to explain the relationship between the variables; and whether the variables influence the employment outcomes. A broad-ranging preliminary literature review has been undertaken to explore the substantial bodies of knowledge on skilled immigrants worldwide, including skilled refugees; and to investigate whether the utilisation issues are universal or specific to a country. In addition, preliminary empirical research and analysis has been undertaken, to set the research focus and to identify the problems beyond literature. Preliminary findings have indicated that immigrants and refugees from non-main English speaking countries are particularly impacted by employment issues regardless of their skills and qualifications acquired in their country of origins; compared with immigrants from main-English speaking countries. Preliminary findings from the literature review also indicate that gaps in knowledge still exist. Although the past two decades have witnessed a virtual explosion of theory and research on international migration, no in-depth research has been located that specifically links immigrants and refugees social and human capitals in terms of employment outcomes. This research study aims to fill these gaps in research; and subsequently contribute to contemporary body of knowledge in literatures on the utilisation of skilled immigrants and skilled refugees, specifically those from non-main English speaking countries. A mixed methods design will be used, which incorporates techniques from both quantitative and qualitative research traditions that will be triangulated at the end of the data collection stage.

Early years teachers’ attitudes towards mathematics

Worldwide, there is considerable attention to providing a supportive mathematics learning environment for young children because attitude formation and achievement in these early years of schooling have a lifelong impact. Key influences on young children during these early years are their teachers. Practising early years teachers‟ attitudes towards mathematics influence the teaching methods they employ, which in turn, affects young students‟ attitudes towards mathematics, and ultimately, their achievement. However, little is known about practising early years teachers‟ attitudes to mathematics or how these attitudes form, which is the focus of this study. The research questions were: 1. What attitudes do practising early years teachers hold towards mathematics? 2. How did the teachers‟ mathematics attitudes form? This study adopted an explanatory case study design (Yin, 2003) to investigate practising early years teachers‟ attitudes towards mathematics and the formation of these attitudes. The research took place in a Brisbane southside school situated in a middle socio-economic area. The site was chosen due to its accessibility to the researcher. The participant group consisted of 20 early years teachers. They each completed the Attitude Towards Mathematics Inventory (ATMI) (Schackow, 2005), which is a 40 item instrument that measures attitudes across the four dimensions of attitude, namely value, enjoyment, self-confidence and motivation. The teachers‟ total ATMI scores were classified according to five quintiles: strongly negative, negative, neutral, positive and strongly positive. The results of the survey revealed that these teachers‟ attitudes ranged across only three categories with one teacher classified as strongly positive, twelve teachers classified as positive and seven teachers classified as neutral. No teachers were identified as having negative or strongly negative attitudes. Subsequent to the surveys, six teachers with a breadth of attitudes were selected from the original cohort to participate in open-ended interviews to investigate the formation of their attitudes. The interview data were analysed according to the four dimensions of attitudes (value, enjoyment, self-confidence, motivation) and three stages of education (primary, secondary, tertiary). Highlighted in the findings is the critical impact of schooling experiences on the formation of student attitudes towards mathematics. Findings suggest that primary school experiences are a critical influence on the attitudes of adults who become early years teachers. These findings also indicate the vital role tertiary institutions play in altering the attitudes of preservice teachers who have had negative schooling experiences. Experiences that teachers indicated contributed to the formation of positive attitudes in their own education were games, group work, hands-on activities, positive feedback and perceived relevance. In contrast, negative experiences that teachers stated influenced their attitudes were insufficient help, rushed teaching, negative feedback and a lack of relevance of the content. These findings together with the literature on teachers‟ attitudes and mathematics education were synthesized in a model titled a Cycle of Early Years Teachers’ Attitudes Towards Mathematics. This model explains positive and negative influences on attitudes towards mathematics and how the attitudes of adults are passed on to children, who then as adults themselves, repeat the cycle by passing on attitudes to a new generation. The model can provide guidance for practising teachers and for preservice and inservice education about ways to foster positive influences to attitude formation in mathematics and inhibit negative influences. Two avenues for future research arise from the findings of this study both relating to attitudes and secondary school experiences. The first question relates to the resilience of attitudes, in particular, how an individual can maintain positive attitudes towards mathematics developed in primary school, despite secondary school experiences that typically have a negative influence on attitude. The second question relates to the relationship between attitudes and achievement, specifically, why secondary students achieve good grades in mathematics despite a lack of enjoyment, which is one of the dimensions of attitude.

Developing a model of embedding academic numeracy in university programs : a case study from nursing

This is a study of the academic numeracy of nursing students. This study develops a theoretical model for the design and delivery of university courses in academic numeracy. The following objectives are addressed: 1. To investigate nursing students' current knowledge of academic numeracy; 2. To investigate how nursing students’ knowledge and skills in academic numeracy can be enhanced using a developmental psychology framework; and 3. To utilise data derived from meeting objectives 1 and 2 to develop a theoretical model to embed academic numeracy in university programs. This study draws from Valsiner’s Human Development Theory (Valsiner, 1997, 2007). It is a quasi-experimental intervention case study (Faltis, 1997) and takes a multimethod approach using pre- and post-tests; observation notes; and semi-structured teaching sessions to document a series of microgenetic studies of student numeracy. Each microgenetic study is centered on the lived experience of students becoming more numerate. The method for this section is based on Vygotsky’s double stimulation (Valsiner, 2000a; 2007). Data collection includes interviews on students’ past experience with mathematics; their present feelings and experiences and how these present feelings and experiences are transformed. The findings from this study have provided evidence that the course developed for nursing students, underpinned by an appropriate framework, does improve academic numeracy. More specifically, students improved their content knowledge of and confidence in mathematics in areas that were directly related to their degree. The study used Valsiner’s microgenetic approach to development to trace the course as it was being taught and two students’ personal academic numeracy journeys. It highlighted particularly troublesome concepts, then outlined scaffolding and pathways used to develop understanding. This approach to academic numeracy development was summarised into a four-faceted model at the university, program, course and individual level. This model can be applied successfully to similar contexts. Thus the thesis advances both theory and practice in this under-researched and under-theorised area.

Engineering-based modelling experiences in the elementary classroom

Introducing engineering-based model-eliciting experiences in the elementary curriculum is a new and increasingly important domain of research by mathematics, science, technology, and engineering educators. Recent research has raised questions about the context of engineering problems that are meaningful, engaging, and inspiring for young students. In the present study an environmental engineering activity was implemented in two classes of 11-year-old students in Cyprus. The problem required students to develop a procedure for selecting among alternative countries from which to buy water. Students created a range of models that adequately solved the problem although not all models took into account all of the data provided. The models varied in the number of problem factors taken into consideration and also in the different approaches adopted in dealing with the problem factors. At least two groups of students integrated into their models the environmental aspect of the problem (energy consumption, water pollution) and further refined their models. Results indicate that engineering model-eliciting activities can be introduced effectively into the elementary curriculum, providing rich opportunities for students to deal with engineering contexts and to apply their learning in mathematics and science to solving real-world engineering problems.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Making it creatively : building sustainable careers in the arts and creative industries

Many people aspire to careers in the arts and creative industries. However, it has long been known that it can be challenging to navigate a creative career: that competition for work can be intense, particularly for entry-level positions, and that success requires advanced skill sets in addition to a high degree of artistic talent and proficiency. In this article, Dr Ruth Bridgstock draws upon her doctoral and post-doctoral research to explore the challenges involved in building a creative career in Australia and suggest ways to support emerging creatives to build satisfying and sustainable careers.

Orals ain’t orals : the role of prepared oral presentations in the classroom and beyond. How do instruction and feedback practices guide delivery choices?

Despite an ostensibly technology-driven society, the ability to communicate orally continues to feature as an essential ability for students at school and university, as it is for graduates in the workplace. Pedagogically, one rationale is that the need to develop effective oral communication skills is tied to life-long learning which includes successful participation in future work-related tasks. One tangible way that educators have assessed proficiency in the area of communication is through prepared oral presentations. While much of the literature uses the terms 'oral communication' and 'oral presentation' interchangeably, some writers question the role more formal presentations play in the overall development of oral communication skills. However, such formal speaking tasks continue to be a recognised assessment practice in both the secondary school and academy, and, therefore, worthy of further investigation. Adding to the discussion, this thesis explores the knowledge and skills students bring into the academy from previous educational experiences. It examines some of the teaching and assessment methods used in secondary schools to develop oral communication skills through the use of formal oral presentations. Specifically, it investigates criterion-referenced assessment sheets and how these tools are used as a form of instruction, as well as their role and effectiveness in the evaluation of student ability. The focus is on the student's perspective and includes 12 semi-structured interviews with school students. The purpose of this thesis is to explore key thematics underpinning oral communication and to identify tensions between expectations and practice. While acknowledging the breadth and depth of material available under the heading of 'communication theory', this study specifically draws on an expanded view of the rhetorical tradition to fully interrogate the assumptions supporting the practice of assessing oral presentations. Finally, this thesis recommends reconnecting with an updated understanding of rhetoric as a way of assisting in the development of expressive, articulate and discerning communicators.

Jabberwocky : the complexities of mathematical English

Mathematical English is a unique language based on ordinary English, with the addition of highly stylised formal symbol systems. Some words have a redefined status. Mathematical English has its own lexicon, syntax, semantics and literature. It is more difficult to understand than ordinary English. Ability in basic interpersonal communication does not necessarily result in proficiency in the use of mathematical English. The complex nature of mathematical English may impact upon the ability of students to succeed in mathematical and numeracy assessment. This article presents a review of the literature about the complexities of mathematical English. It includes examples of more than fifty language features that have been shown to add to the challenge of interpreting mathematical texts. Awareness of the complexities of mathematical English is an essential skill needed by mathematics teachers when teaching and when designing assessment tasks.

Culture counts in making Chinese maths-smart

Chinese Australians consistently outperform their peers in mathematics and according to QUT researcher Michael Mu this is not only because of pushy parents or motivated students.

Negotiating teacher identities : dialogic reflections on classroom interaction in a transnational context

This study investigates the development of teacher identity in a transnational context through an analysis of the voices of sixteen preservice teachers from Hong Kong who engage in interaction with primary students in an Australian classroom. The context for this research is the school-based experience undertaken by these preservice English as a second language teachers as part of their short language immersion (SLIM) program in Brisbane, Australia. Such SLIM programs are a genre of study abroad programs which have been gaining in popularity within teacher education in Australia, attended by preservice and inservice teachers from China, Hong Kong, Korea, and other Asian countries. This research is conducted at a time when the imperative to globalise higher education provision is a strategic factor in the educational policies of both Australia and Hong Kong. In Australia, international educational services now constitute the country’s third largest export with more than 400,000 students coming to Australia to study annually. In order to maintain Australia’s current global position as the third most popular Englishspeaking study destination, the government is now focusing on sustainability and the quality of the study experience being offered to international students (Bradley Review, 2008). In Hong Kong, the government sponsors both preservice and inservice English as a second language (ESL) teachers to undertake SLIM programs in Australia and other English-speaking countries, as part of their policy of promoting high levels of English proficiency in Hong Kong classrooms. Transnational teacher education is an important issue to which this study contributes insights into the affordances and constraints of a school-based experience in the transnational context. Second language teacher education has been defined as interventions designed to develop participants’ professional knowledge. In this study, it is argued that participation in a different community of practice helps to foreground tacit theories of second language pedagogy, making them visible and open to review. Questions of pedagogy are also seen as questions of teacher identity, constituting the way that one is in the classroom. I take up a sociocultural and poststructural framework, drawing on the work of James Gee and Mikhail Bakhtin, to theorise the construction of teacher identity as emerging through dialogic relations and socially situated discursive practices. From this perspective, this study investigates whether these teachers engage with different ways of representing themselves through appropriating, adapting or rejecting Discourses prevailing in the Australian classroom. Research suggests that reflecting on dilemmas encountered as lived experiences can extend professional understandings. In this study, the participants engage in a process of dialogic reflection on their intercultural classroom interactions, examining with their peers and their lecturer/researcher selected moments of dissonance that they have faced in the unfamiliar context of an Australian primary classroom. It is argued that the recursive and multivoiced nature of this process of reflection on practice allows participants opportunities to negotiate new understandings of second language teacher identity. Dialogic learning, based on the theories of Bakhtin and Vygotsky, provides the theoretic framing not only for the process of reflection instantiated in this study, but also features in the analysis of the participants’ second language classroom practices. The research design uses a combined discourse analytic and ethnographic approach as a logic-of-inquiry to explore the dialogic relationships which these second language teachers negotiate with their students and their peers in the transnational context. In this way, through discourse analysis of their classroom talk and reflective dialogues, assisted by the analytic tools of speech genres and discourse formats, I explore the participants’ ways of doing and being second language teachers. Thus, this analysis traces the process of ideological becoming of these beginner teachers as shifts in their understandings of teacher and student identities. This study also demonstrates the potential for a nontraditional stimulated recall interview to provide dialogic scaffolding for beginner teachers to reflect productively on their practice.

Assessing the potential of mathematics textbooks to promote deep learning

Curriculum documents for mathematics emphasise the importance of promoting depth of knowledge rather than shallow coverage of the curriculum. In this paper, we report on a study that explored the analysis of junior secondary mathematics textbooks to assess their potential to assist in teaching and learning aimed at building and applying deep mathematical knowledge. The method of analysis involved the establishment of a set of specific curriculum goals and associated indicators, based on research into the teaching and learning of a particular field within the mathematics curriculum, namely proportion and proportional reasoning. Topic selection was due to its pervasive nature throughout the school mathematics curriculum at this level. As a result of this study, it was found that the five textbook series examined provided limited support for the development of multiplicative structures required for proportional reasoning, and hence would not serve well the development of deep learning of mathematics. The study demonstrated a method that could be applied to the analysis of junior secondary mathematics in many parts of the world.