Students' perceptions of the relevance of mathematics in engineering

In this paper, we report on the findings of an exploratory study into the experience of students as they learn first year engineering mathematics. Here we define engineering as the application of mathematics and sciences to the building and design of projects for the use of society (Kirschenman and Brenner 2010)d. Qualitative and quantitative data on students' views of the relevance of their mathematics study to their engineering studies and future careers in engineering was collected. The students described using a range of mathematics techniques (mathematics skills developed, mathematics concepts applied to engineering and skills developed relevant for engineering) for various usages (as a subject of study, a tool for other subjects or a tool for real world problems). We found a number of themes relating to the design of mathematics engineering curriculum emerged from the data. These included the relevance of mathematics within different engineering majors, the relevance of mathematics to future studies, the relevance of learning mathematical rigour, and the effectiveness of problem solving tasks in conveying the relevance of mathematics more effectively than other forms of assessment. We make recommendations for the design of engineering mathematics curriculum based on our findings.

Recognising Torres Strait Islander women’s knowledges in their children’s mathematics education

This paper discusses women’s involvement in their children’s mathematics education. It does, where possible, focus Torres Strait Islander women who share the aspirations of Aborginal communities around Australia. That is, they are keen for their children to receive an education that provides them with opportunities for their present and future lives. They are also keen to have their cultures’ child learning practices recognised and respected within mainstream education. This recognition has some way to go with the language of instruction in schools written to English conventions, decontextualised and disconnected to the students’ culture, Community and home language.

Teacher change and professional development in mathematics education

It is generally agreed that if authentic teacher change is to occur then the tacit knowledge about how and why they act in certain ways in the classroom be accessed and reflected upon. While critical reflection can and often is an individual experience there is evidence to suggest that teachers are more likely to engage in the process when it is approached in a collegial manner; that is, when other teachers are involved in and engaged with the same process. Teachers do not enact their profession in isolation but rather exist within a wider community of teachers. An outside facilitator can also play an active and important role in achieving lasting teacher change. According to Stein and Brown (1997) “an important ingredient in socially based learning is that graduations of expertise and experience exist when teachers collaborate with each other or outside experts” (p. 155). To assist in the effective professional development of teachers, outside facilitators, when used, need to provide “a dynamic energy producing interactive experience in which participants examine and explore the complex components of teaching” (Bolster, 1995, p. 193). They also need to establish rapport with the participating teachers that is built on trust and competence (Hyde, Ormiston, & Hyde, 1994). For this to occur, professional development involving teachers and outside facilitators or researchers should not be a one-off event but an ongoing process of engagement that enables both the energy and trust required to develop. Successful professional development activities are therefore collaborative, relevant and provide individual, specialised attention to the teachers concerned. The project reported here aimed to provide professional development to two Year 3 teachers to enhance their teaching of a new mathematics content area, mental computation. This was achieved through the teachers collaborating with a researcher to design an instructional program for mental computation that drew on theory and research in the field.

Library and information science education 2.0 : guiding principles and models of best practice ALTC Fellowship Report

This ALTC Teaching Fellowship aimed to establish Guiding Principles for Library and Information Science Education 2.0. The aim was achieved by (i) identifying the current and anticipated skills and knowledge required by successful library and information science (LIS) professionals in the age of web 2.0 (and beyond), (ii) establishing the current state of LIS education in Australia in supporting the development of librarian 2.0, and in doing so, identify models of best practice. The fellowship has contributed to curriculum renewal in the LIS profession. It has helped to ensure that LIS education in Australia continues to meet the changing skills and knowledge requirements of the profession it supports. It has also provided a vehicle through which LIS professionals and LIS educators may find opportunities for greater collaboration and more open communication. This will help bridge the gap between LIS theory and practice and will foster more authentic engagement between LIS education and other parts of the LIS industry in the education of the next generation of professionals. Through this fellowship the LIS discipline has become a role model for other disciplines who will be facing similar issues in the coming years. Eighty-one members of the Australian LIS profession participated in a series of focus groups exploring the current and anticipated skills and knowledge needed by the LIS professional in the web 2.0 world and beyond. Whilst each focus group tended to draw on specific themes of interest to that particular group of people, there was a great deal of common ground. Eight key themes emerged: technology, learning and education, research or evidence-based practice, communication, collaboration and team work, user focus, business savvy and personal traits. It was acknowledged that the need for successful LIS professionals to possess transferable skills and interpersonal attributes was not new. It was noted however that the speed with which things are changing in the web 2.0 world was having a significant impact and that this faster pace is placing a new and unexpected emphasis on the transferable skills and knowledge. It was also acknowledged that all librarians need to possess these skills, knowledge and attributes and not just the one or two role models who lead the way. The most interesting finding however was that web 2.0, library 2.0 and librarian 2.0 represented a ‘watershed’ for the LIS profession. Almost all the focus groups spoke about how they are seeing and experiencing a culture change in the profession. Librarian 2.0 requires a ‘different mindset or attitude’. The Levels of Perspective model by Daniel Kim provides one lens by which to view this finding. The focus group findings suggest that we are witnessing a re-awaking of the Australian LIS profession as it begins to move towards the higher levels of Kim’s model (ie mental models, vision). Thirty-six LIS educators participated in telephone interviews aimed at exploring the current state of LIS education in supporting the development of librarian 2.0. Skills and knowledge of LIS professionals in a web 2.0 world that were identified and discussed by the LIS educators mirrored those highlighted in the focus group discussions with LIS professionals. Similarly it was noted that librarian 2.0 needed a focus less on skills and knowledge and more on attitude. However, whilst LIS professionals felt that there was a paradigm shift within the profession. LIS educators did not speak with one voice on this matter with quite a number of the educators suggesting that this might be ‘overstating it a bit’. This study provides evidence for “disparate viewpoints” (Hallam, 2007) between LIS educators and LIS professionals that can have a significant implications for the future of not just LIS professional education specifically but for the profession generally. Library and information science education 2.0: guiding principles and models of best practice 1 Inviting the LIS academics to discuss how their teaching and learning activities support the development of librarian 2.0 was a core part of the interviews conducted. The strategies used and the challenges faced by LIS educators in developing their teaching and learning approaches to support the formation of librarian 2.0 are identified and discussed. A core part of the fellowship was the identification of best practice examples on how LIS educators were developing librarian 2.0. Twelve best practice examples were identified. Each educator was recorded discussing his or her approach to teaching and learning. Videos of these interviews are available via the Fellowship blog at .The LIS educators involved in making the videos felt uncomfortable with the term ‘best practice’. Many acknowledged that there simply seeking to do the best by their students and that there was always room for improvement. For this reason these videos are offered as examples of “great practice”. The videos are a tool for other educators to use, regardless of discipline, in developing their teaching and learning approaches to supporting web 2.0 professionals. It has been argued that the main purpose of professional education is transformation (Dall’ Alba, 2009; Dall’Alba & Barnacle, 2007). As such professional education should focus not just on skills and knowledge acquisition but also on helping students to develop ways of being the professionals in question (ie LIS professionals, teachers, lawyers, engineers).The aim of this fellowship was to establish Guidelines for Library and Information Science Education 2.0 it has however become apparent that at this point in time it is not yet possible to fulfil this aim. The fellowship has clearly identified skills and knowledge needed by the LIS professional in web 2.0 world (and beyond). It has also identified examples of ‘great practice’ by LIS educators as they endeavour to develop LIS professionals who will be successful in a web 20 world. The fellowship however has also shown that the LIS profession is currently undergoing significant attitudinal and conceptual change. Consequently, before a philosophy of LIS education 2.0 can be expressed, the Australian LIS profession must first explore and articulate what it means to be an LIS professional in the 21st century (ie a world of web 2.0 and beyond). In short, the LIS profession in Australia must take stock not of “what we know and can do” but on “who we are becoming” (Dall’Alba, 2009, p 34).

A communitarian theory of the education rights of students with disabilities

There is a lack of writing on the issue of the education rights of people with disabilities by authors of any theoretical persuasion. While the deficiency of theory may be explained by a variety of historical, philosophical and practical considerations, it is a deficiency which must be addressed. Otherwise, any statement of rights rings out as hollow rhetoric unsupported by sound reason and moral rectitude. This paper attempts to address this deficiency in education rights theory by postulating a communitarian theory of the education rights of people with disabilities. The theory is developed from communitarian writings on the role of education in democratic society. The communitarian school, like the community within which it nests, is inclusive. Schools both reflect and model the shape of communitarian society and have primary responsibility for teaching the knowledge and virtues which will allow citizens to belong to and function within society. Communitarians emphasise responsibilities, however, as the corollary of rights and require the individual good to yield to community good when the hard cases arise. The article not only explains the basis of the right to an inclusive education, therefore, but also engages with the difficult issue of when such a right may not be enforceable.

Making sense of mass education

Making Sense of Mass Education provides a comprehensive analysis of the field of mass education. The book presents new assessment of traditional issues associated with education – class, race, gender, discrimination and equity –to dispel myths and assumptions about the classroom. It examines the complex relationship between the media, popular culture and schooling, and places the expectations surrounding the modern teacher within ethical, legal and historical contexts. The book blurs some of the disciplinary boundaries within the field of education, drawing upon sociology, cultural studies, history, philosophy, ethics and jurisprudence to provide stronger analyses. The book reframes the sociology of education as a complex mosaic of cultural practices, forces and innovations. Engaging and contemporary, it is an invaluable resource for teacher education students, and anyone interested in a better understanding of mass education.

Theories of learning mathematics

According to Karl Popper, widely regarded as one of the greatest philosophers of science in the 20th century, falsifiability is the primary characteristic that distinguishes scientific theories from ideologies – or dogma. For example, for people who argue that schools should treat creationism as a scientific theory, comparable to modern theories of evolution, advocates of creationism would need to become engaged in the generation of falsifiable hypothesis, and would need to abandon the practice of discouraging questioning and inquiry. Ironically, scientific theories themselves are accepted or rejected based on a principle that might be called survival of the fittest. So, for healthy theories on development to occur, four Darwinian functions should function: (a) variation – avoid orthodoxy and encourage divergent thinking, (b) selection – submit all assumptions and innovations to rigorous testing, (c) diffusion – encourage the shareability of new and/or viable ways of thinking, and (d) accumulation – encourage the reuseability of viable aspects of productive innovations.

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.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.

Changing agendas in international research in mathematics education

Handbooks serve an important function for our research community in providing state-of-the-art summations, critiques, and extensions of existing trends in research. In the intervening years between the second and third editions of the Handbook of International Research in Mathematics Education, there have been stimulating developments in research, as well as new challenges in translating outcomes into practice. This third edition incorporates a number of new chapters representing areas of growth and challenge, in addition to substantially updated chapters from the second edition. As such, the Handbook addresses five core themes, namely, Priorities in International Mathematics Education Research, Democratic Access to Mathematics Learning, Transformations in Learning Contexts, Advances in Research Methodologies, and Influences of Advanced Technologies...

General practitioners learning qualitative research: A case study of postgraduate education

Background Qualitative research is increasingly being recognised as a vital aspect of primary healthcare research. Teaching and learning how to conduct qualitative research is especially important for general practitioners and other clinicians in the professional educational setting. This article examines a case study of postgraduate professional education in qualitative research for clinicians, for the purpose of enabling a robust discussion around teaching and learning in medicine and the health sciences. Method A series of three workshops was delivered for primary healthcare academics. The workshops were evaluated using a quantitative survey and qualitative free-text responses to enable descriptive analyses. Results Participants found qualitative philosophy and theory the most difficult areas to engage with, and learning qualitative coding and analysis was considered the easiest to learn. Discussion Key elements for successful teaching were identified, including the use of adult learning principles, the value of an experienced facilitator and an awareness of the impact of clinical subcultures on learning.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.