Problematising the mathematics curriculum : some examples from Australia and Japan

Problem solving is often seen as being the core of mathematics. While there are many examples of teaching for and about problem solving, there are relatively few examples of teaching mathematical content through problem solving. This paper uses data from three, apparently quite different, mathematics lessons from Australia and Japan to explore different ways in which mathematics can be taught successfully through problem solving and to analyse some of the characteristics of such lessons. It also attempts to identify some of the supports and constraints for adopting a problem solving approach to the teaching of mathematics that exist in the quite different contexts of Japan and Australia.

Exploring creative music making as a vehicle for integrated teaching and learning

The arts have evolved with each society as a means of consolidating cultural and social identity and connecting past with future generations (Russell-Bowie, 2006, p3). Situating the arts within a broader interdisciplinary curriculum, we believe, allows students to discover and explore social issues and their relevance to students' contemporary lives. We argue that creative music making through composition promotes a deeper and more personally relevant teaching and learning experience for teacher education students, particularly when situated within an interdisciplinary framework.

The challenge for us as teacher educators' is to prepare pre-service teachers for both disciplinary and interdisciplinary learning as is required by the Victorian Essential Learning Standards (VELS). At Deakin University, in the Bachelor of Teaching (Primary/Secondary) Degree, the postgraduate unit called Humanities, Societies and Environments; Language and Music Education adopts an interdisciplinary pedagogy that encourages students to learn from each other, share content knowledge and make links between and across VELS domains.

In this paper we reflect on the possibilities exploring of creative music making to enhance the teaching and learning of social education, with particular reference to issues of environmental change. Specifically, we reflect on non-music specialist students' experiences in Semester 1, 2008 using Jeannie Baker's book Window (1991) as a platform to deliberate about the impact of urbanisation on the environment. Through dramatisation and a sonic environment students were able to both further conceptualise issues of social change and their understandings of the power of integrating music across other VELS domains.

Studies on dietary fibre : analysis, epidemiological and physiological aspects

This thesis involves an investigation in three areas; first, a study of an enzymatic-gravimetric method for the analysis of dietary fibre; second, a survey of dietary fibre intake in an area of a developing country, and finally, some observations on the functional aspects of gel-forming dietary fibre in the rat. A simple and rapid enzymatic-gravimetric assay for both soluble and insoluble dietary fibre has been critically investigated. Reference samples were also analysed by a more comprehensive, enzymatic gas chromatographic method to allow testing of the relative accuracy of the enzymatic-gravimetric method. The enzymatic-gravimetric method was found to be highly reproducible but gave a slightly higher value for total dietary fibre than the more comprehensive method. This discrepancy is probably due to the presence of small quantities of resistant starch and protein residue which are recovered in the enzymatic-gravimetric method. In the enzymatic-gas chromatographic method, protein residue is not measured, and resistant starch is estimated, but not counted as dietary fibre. The enzymatic-gravimetric method was applied to the analysis of foods commonly consumed in the Padang region of West Sumatra in Indonesia, in order to estimate dietary fibre intake in the region. Daily intakes of usual foods were estimated by use of a 24-hour recall procedure aided by food photographs to assist in the estimation of portion size. Samples of approximately 60 of the most commonly consumed foods were collected and analysed for dietary fibre. These appear to be the first data which report values for dietary fibre in Indonesion foods and they represent a significant improvement upon the existing data on crude fibre content. Knowledge of the amounts of foods usually consumed and their dietary fibre content allowed an estimation of usual intakes of dietary fibre. Fibre intake was found to be lower than in the developing countries of Africa and was comparable to intakes measured in the U.K. This is the first study to show that in this part of South East Asia, a developing country area using polished rice as a staple food, dietary fibre intakes are as low as in Western countries. Low intakes of fibre are believed to be related to the prevalence of a range of diseases and, in this study, preliminary data on the rates of non-infective, chronic diseases were collected from the two main hospitals in West Sumatra. Chronic, non-infectious diseases such as inguinal hernia, appendicitis, haemorrhoids, diabetes mellitus, hypertension and malignant neoplasms of the rectum are relatively frequent in West Sumatra. While no firm conclusions can be drawn from these data, they do show the possibility of a relationship between low intakes of dietary fibre and the prevalence of these diseases, and suggest that further investigation is necessary. Some observations were made of the effect of gel-forming dietary fibre on stomach emptying and intestinal transit rate in the rat. Xanthan gum was added to iso-osmotic solutions to produce increased viscosity and phenol sulphonphthalein (phenol red) was used as a non-absorbable marker. Gavage feeding of solutions with a range of viscosities was used to study the effect of viscosity on the rate of stomach emptying and intestinal transit. Increased viscosity was observed to slow gastro-intestinal transit and this provides one mechanism by which dietary fibre of the gel-forming type ray improve glucose tolerance.

Do-it-yourself textbook review report card (Checklist)

It is argued that teachers will encounter many changes in teaching approaches and possibly in teaching materials resulting from the development and implementation of the national curriculum. With the new national curriculum, there will be new textbooks which will be 'new' as textbooks, but not necessarily new in mathematical content or instructional approaches. Two critical questions for these textbooks (or any textbooks) are: How good are these textbooks, as textbooks? How well do these textbooks fit whatever the 'new' curriculum is? Other questions to consider are: Is the content 'new' and/or substantial? Is the material 'fair' and representative? Elements of a good textbook are discussed including that it should have good design and provide good definitions, worked examples and counter-examples.

Judgement, reflexivitiy and interdisiciplinarity : reframing construction management education

A core skill of the construction management professional is decision making. Disciplinary content knowledge provides the basis for effective decision making, but is largely insufficient in contexts where projects demand a responsive and flexible approach to scenarios as they evolve and change. As Beckett and Hager suggest, ‘professional practice requires a much richer set of phenomena – a capacity to make judgements, sensitivity to intuition and an awareness of the purposes of the actions are all involved ‘(2002: 12). This paper begins by exploring judgement to develop a conceptual model for initiating and developing decision making skills for construction management professionals. The capacity to respond to change in a structured and self aware manner is examined through the concept of reflexivity, a concept borrowed from sociology. Reflexivity is an individual’s capacity to be aware, responsive and adaptability to constant changing and evolving environments. Coupled with this is the challenge for all built environment professionals in the need to integrate knowledge and processes from various specialist knowledge domains, particularly design domains. The conceptual model is then refined by synthesising concepts from interdisciplinary research.

The aim of this paper is to describe a framework to analyse and review current undergraduate and postgraduate coursework programs offerings from Deakin University in the School of Architecture and Building. Following Boud and Falchikov (2007) this framework starts with practice, that is, the actual ‘doing’ of construction management as the basis for shaping curriculum development.

Why educators should bring an end to pedagogy

As Australia is moving towards a national curriculum there are also activities to nationalise teacher education. This involves various departments of state and federal governments, third-party bodies funded by government such as the Curriculum Corporation and Teaching Australia, and non-government organisations such as the Business Council of Australia. These agencies are producing models and principles which aim on establishing standards of best practice for how they want teachers to teach. Within all of this activity the term ‘pedagogy’ is often employed to represent aspects of these best practices. Examples include ‘productive pedagogies’, ‘new pedagogies’, ‘pedagogical content knowledge’ and ‘pedagogical strategies’. However these are all means only without any end purposes which identify them as being valuable for education. In this paper I will argue that in order to have educative value teachers themselves must exercise a degree of professional autonomy to bring their own end purposes to their choice of pedagogy.

Preparing pre-service physical education teachers for uncertain future(s) : a scenario-based learning case study from Australia

Background: A key aim of a physical education teacher education (PETE) program is to promote wide and deep knowledge, enabling students to establish connections and understand contexts within and beyond education, physical education and their life worlds. Most often PETE programs equip students with content knowledge and pedagogical strategies that help them address current challenges, but less attention is directed to helping the students anticipate future challenges and engage with opportunities they may face as teachers.
Purpose: This paper presents a case study of scenario-based learning as it was implemented in a final year PETE program in an Australian university, as a means of preparing students for their future teaching careers.
Participants and setting: Twenty-five final year pre-service physical education teachers enrolled in the culminating unit of their physical education degree.
Data collection: Scenario-based learning was introduced to the students via class discussion and assigned tasks. Examples of student-written scenarios and reflection on the experience from the lecturer and student perspectives are analysed.
Findings: Although the cohort found the process of scenario-based learning daunting the post-unit questionnaires revealed that it was a valued and valuable means of exploring professional issues they will face in the future. Scenario-based learning was a powerful tool of learning as well as modelling a pedagogy students could use in the upper levels of secondary school.
Conclusion: This paper argues that scenario-based learning should be a key component of forward-looking PETE programs that encourage their graduates to solve problems about issues they may face as beginning teachers.

Leadership to improve mathematics outcomes in low SES schools and school networks

Instructional and transformational leadership is reportedly required to improve the mathematics outcomes of students in low socio-economic status school communities. This study of 43 schools in two networks of schools in rural Victoria explored leadership practices and found evidence to support both these leadership approaches along with distributed leadership practice. School leaders established network and school structures and relationships at various levels of the network and school organisation to enable and support ongoing improvement in teachers’ pedagogical content knowledge and teaching practice and to build the leadership capacity of teachers within their schools. The leaders’ knowledge of effective mathematics teaching practice enabled them to mentor teachers in their school or team and to support the practices of professional learning teams within their school.

Teaching out-of-field : factors shaping identities of secondary science and mathematics

It is widely recognised that many teachers work 'out of field', taking subjects outside their specialities. Studies undertaken by the author and by other researchers shed light on how teachers themselves experience and understand out-of-field teaching. The article discusses the issue in relation to junior secondary science and mathematics. Evidence is drawn from the 2009 Teacher Identity In and Across Subjects (TIIAS) study. The article also includes a table summarising the findings of eight major research reports relevant to this issue. The author draws a range of conclusions. Teachers' experience and understanding of out-of-field teaching is determined not only by their subject content knowledge and their pedagogical content knowledge, but also by their context and by the personal resources available to them. Rural teachers often accept the need to teach across a number of subject areas, as part of their professional identity, despite the fact that they often lack easy access to subject specialists. Teachers tend to be more positive about out-of-field teaching when they themselves have had input into which subjects they will teach, and when they have an interest in or informal knowledge of the subject area. Teachers' interest in professional development to support their out-of-field teaching is influenced by whether they see themselves as simply filling in for someone, making the most of an opportunity, or pursuing an interest. Professional learning should ideally be initiated by or negotiated with the teachers, and should be provided at the point of need. School leaderships should maximise teachers' input into subject allocation and provision of professional learning opportunities. Teacher education courses need to prepare pre-service teachers to cope with out-of-field teaching.

Teaching and learning history in primary schools : pedagogical shifts, complexities and opportunities

From 2011 the teaching and learning of History will be expanded into all primary schools (Kindergarten – Year 6) throughout Australia under a National Curriculum, including the formal preschool/kindergarten year. History as one of four core subjects will replace current studies of society and environment curriculum taught in primary schools across. The curriculum implementation process will involve a cultural and pedagogical shift as primary teachers make adjustments to the discipline of History. This article begins with an outline of the current curriculum context. An analysis of the New South Wales Human Society and Its Environment and the Australian Curriculum: History Draft Consultation documents follows. The findings indicate that the History Draft Consultation lacks clear guidance for teachers and has a number of shortcomings compared to the NSW HSIE syllabus. There are opportunities, however, for primary teachers because of the broad similarities of content knowledge in both documents and the embedded historical concepts in the NSW syllabus document.

Information communication technology in secondary science education in Sri Lanka

This study researched the instruction of pre-service science teachers in Sri Lanka in the use of information communication technologies. It examined the use of a framework called the Technological Pedagogical Content Knowledge model that was found to assist the pre-service teachers in the effective use of technologies in their teaching.

Teaching primary science : emotions, identity and the use of practical activities

This paper uses cultural historical activity theory to examine the interactions between the choices primary teachers make in the use of practical activities in their teaching of science and the purposes they attribute to these; their emotions, background and beliefs; and the construction of their identities as teachers of science. It draws on four case studies of science lessons taught over a term by four exemplary teachers of primary science. The data collected includes video recordings of science lessons, interviews with each teacher and some of their students, student work, teachers’ planning documents and observation notes. In this paper, we examine the reflexive relationship between emotion and identity, and the teachers’ objectives for their students’ learning; the purposes (scientific and social) the teachers attributed to practical activities; and the ways in which the teachers incorporated practical activities into their lessons. The findings suggest that it is not enough to address content knowledge, pedagogy and pedagogical content knowledge in teacher education, but that efforts also need to be made to influence prospective primary teachers’ identities as scientific thinkers and their emotional commitment to their students’ learning of science.

Digital oral feedback written assignments as professional learning for teacher educators : a collaborative self-study.

Allan Luke (2008) uses a “pedagogical economy where literacy education is taken as a cultural gift”. This paper reports on the digital oral feedback provided to pre-service teachers in a literacy unit and explores the pedagogical gift this feedback is to the teacher educators marking this work. Rather than mark their written work as individual lecturers, we collaboratively read the assignment and recorded the sound file of the conversation around each assignment. We then participated in another conversation with a critical friend, which enabled us to explore the impact of this form of assessment on our professional identities as teacher educators. We found these conversations provided a rich context for our professional learning about ourselves as teacher educators, as well as specific content knowledge we both brought to the teaching of this unit. We found we were working as a team to provide more in-depth feedback of the assessment criteria for each assignment than we did with written feedback. Through this dialogical feedback we were able to construct the pre-service teachers' assignments as an important textual gift in our collaborative professional learning about assessment, and in exploring our beliefs and practices as teacher educators.

Simplified or erroneous? It’s a fine line

Novice learners need to have simplified explanations because they are unable to understand fuller, more-involved explanations. However, there is a dangerously thin line between simplified explanations and over-simplified erroneous explanations, which lead to later misunderstandings and misconceptions. It is harder to unlearn misunderstandings and misconceptions, than to learn something new ab initio.

It is virtually impossible for any teacher to know everything that students will need for future study and careers, as each subject will lead to a myriad of pathways. For example, in my undergraduate 1st year class, students will go into numerous majors across more than 16 degree programs ranging from arts to zoology and from engineering to food-and-nutrition.