Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Teachers and the emotional dimensions of class in resource-affected rural Australia

In recent years, a 'cultural turn' in the study of class has resulted in a rich body of work detailing the ways in which class advantage and disadvantage are emotionally inscribed and embodied in educational settings. To date, however, much of this literature has focused on the urban sphere. In order to address this gap in the literature, this paper focuses on the affective evaluations made by teachers employed in rural and remote Australian schools of students' families, bodies, expectations and practices. The central argument is that moral ascriptions of class by the teachers are powerfully shaped by dominant socio-cultural constructions of rurality that equate 'the rural' with agriculture.

If teams are so good.. : science teachers' conceptions of teams and teamwork

The focus of this study is the phenomenon of teams and teamwork. Currently the Professional Standards of Queensland’s teachers state that teams are critical to teachers’ work. This study uses a phenomenographic approach to investigate science teachers’ conceptions of teams and teamwork in the science departments of fifteen Queensland State secondary schools. The research identifies eight conceptions of teams and teamwork. The research findings suggest that the team represents a collective of science teachers bounded by the Science Department and their current timetabled subject. Collaboration was found in the study to be an activity that occurred between teachers in the same social space. The research recognises a new category of relationship between teachers, designated as ‘ask-and-receive’. The research identifies a lack of teamwork within the science department and the school. There appears to be no teaming with other subject departments. The research findings highlight the non-supportive team and teamwork policies, procedures and structures in the schools and identify the lack of recognition of the specialised skills of science teachers. The implications for the schools and science teachers are considerable, as the current Professional Standards of Education Queensland and the Queensland College of Teachers provide benchmarks of knowledge and practice of teams and teamwork for teachers. The research suggests that the professional standards relating to teams and teamwork cannot be achieved in the present school environment.

Scaffolding an EFL (English as a foreign language) ‘effective writing’ class in a hybrid learning community

This study sought to establish and develop innovative instructional procedures, in which scaffolding can be expanded and applied, in order to enhance learning of English as a Foreign Language (EFL) writing skills in an effective hybrid learning community (a combination of face-to-face and online modes of learning) at the university where the researcher is working. Many educational experts still believe that technology has not been harnessed to its potential to meet the new online characteristics and trends. There is also an urgency to reconsider the pedagogical perspectives involved in the utilisation of online learning systems in general and the social interactions within online courses in particular that have been neglected to date. An action research design, conducted in two cycles within a duration of four months, was utilised throughout this study. It was intended not only to achieve a paradigm shift from transmission-absorption to socio-constructivist teaching/learning methodologies but also to inform practice in these technology-rich environments. Five major findings emerged from the study. First, the scaffolding theory has been extended. Two new scaffolding types (i.e., quasi-transcendental scaffolding and transcendental scafolding), two scaffolding aspects (i.e., receptive and productive) and some scaffolding actions (e.g., providing a stimulus, awareness, reminder, or remedy) for EFL writing skills in an effective hybrid learning community have been identified and elaborated on. Second, the EFL ‘Effective Writing’ students used the scaffolds implemented in a hybrid environment to enhance and enrich their learning of writing of English essays. The online activities, conducted after the F2F sessions most of the time, gave students greater opportunities to both reinforce and expand the knowledge they had acquired in the F2F mode. Third, a variety of teaching techniques, different online tasks and discussion topics utilised in the two modes bolstered the students’ interests and engagement in their knowledge construction of how to compose English-language essays. Fourth, through the scaffolded activities, the students learned how to scaffold themselves and thus became independent learners in their future endeavours of constructing knowledge. Fifth, the scaffolding-to-scaffold activities provided the students with knowledge on how to effectively engage in transcendental scaffolding actions and facilitate the learning of English writing skills by less able peers within the learning community. Thus, the findings of this current study extended earlier understandings of scaffolding in an EFL hybrid learning environment and will contribute to the advancement of future ICT-mediated courses in terms of their scaffolding pedagogical aspects.

Researching Teachers for the Middle Years

The educational landscape around middle schooling reform is a contemporary focus of the Australian school education agenda. The University of Queensland Middle Years of Schooling pre-service teacher education program develops specialist teachers for this crucial phase of schooling. This program has become a national leader for middle school teacher education. This paper reports on aspects of a longitudinal study that began with the first cohort of students in the program in 2003. To date 234 students have been involved as participants in the study. The findings demonstrate that students: can articulate what is meant by the term middle years and can identify with a need for a philosophy of middle schooling; are aware that they are part of a reform movement which has swept the nation and which has implications for teaching in schools in the twenty first century; are confident the program is producing highly skilled professional teachers willing to take on the challenges of teaching in the middle years; can say how their training has helped them understand and account for the educational experiences of students in a time of transition; and hold quiet, yet firm beliefs about teaching in the middle years. Furthermore, using a measure of lexical density to analyze the verbs used by respondents, it seems that this quiet confidence has grown in the period from 2003 – 2006.

Potency in professional development for teachers

There has been significant research into the impact of professional development (PD) on professional organisation and behaviour. PD has emerged in a diversity of forms in schools. Programs range form one hit seminars provided by an external consultant, through to a broad range of programmed development plans that integrate seminars; school based planning groups, action research, collaborative projects across schools, clusters and with critical friends, and mentoring. PD has been delivered to prompt school and teacher professional transformation or to support an ongoing development plan. PD is not uni-lateral and exists to support a very wide range of school and teacher development needs. The relevance and effectiveness of PD design and delivery is tied to the nature of the PD need and the context of provision. This paper reports an investigation into efficacy of various approaches to PD in Queensland schools. The research drew on responses to an online survey tool, focus groups and semi-structured interviews with PD coordinators, teachers, and school and district administrators to develop a model for effective PD planning that considers strategies for addressing current and future PD need and amelioration of barriers to PD effectiveness.

Critical social theory and transformative learning : evidence in pre-service teachers' service-learning reflection logs

This paper reports on the opportunities for transformational learning experienced by a group of pre-service teachers who were engaged in service-learning as a pedagogical process with a focus on reflection. Critical social theory informed the design of the reflection process as it enabled a move away from knowledge transmission toward knowledge transformation. The structured reflection log was designed to illustrate the critical social theory expectations of quality learning that teach students to think critically: ideology critique and utopian critique. Butin's lenses and a reflection framework informed by the work of Bain, Ballantyne, Mills and Lester were used in the design of the service-learning reflection log. Reported data provide evidence of transformational learning and highlight how the students critique their world and imagine how they could contribute to a better world in their work as a beginning teacher.

Trailblazers

A recent study in the United Kingdom (Ofsted Report 2008) provides strong evidence that well-organized activities outside the classroom contribute significantly to the quality and depth of children's learning, including their personal, social, and emotional development. Outdoor math trails supply further evidence of such enhanced learning: They are meaningful, stimulating, challenging, and exciting for children. Most important, these trails invite all students, irrespective of their classroom achievement level, to participate successfully in the problem activities and gain a sense of pride in the mathematics they create. Additionally, Math trails empower lifelong learning. Integrating "outside" mathematics with "inside" classroom mathematics can sow the seeds to develop flexible, creative, future-oriented mathematical thinkers and problem solvers. Here, English et al discuss how to design and implement math trails to promote active, meaningful, real-world mathematical learning beyond the classroom walls.

Adventures in pedagogy : the trials and tribulations of teaching common law in China

China is now seen as arguably, the next economic giant of the 21st century. From a country closed in the past to the external world, the Chinese market now presents as one of the most lucrative in the world economy. One area that has drawn increasing international interest is education - it has been estimated that by 2020 there will be 25 million excess demands for higher education places that the Chinese tertiary educational system cannot meet. Many overseas institutions have developed programs to cater for this immense potential market. In 2000 the Law Faculty of the University of Technology, Sydney (UTS)introduced a new postgraduate program specifically targeting the Chinese market. This paper is a brief assessment of the program - it examines general issues in the pedagogical delivery of programs in LOTE (Language Other Than English) and the use of 'proxies' in the delivery of LOTE programs. The paper concludes that while the UTS program demonstrates that it is feasible to use proxy lecturers or interpreters in the delivery of programs in LOTE, the exercise entails significant problems that can undermine the integrity of such programs.

Teachers' attitudes towards the gifted : the importance of professional development and school culture

Given that teachers have one of the most significant influences on the educational development of gifted students, reports of negative attitudes and beliefs in popular myths about giftedness are cause for concern. It is important to understand teachers’ attitudes and beliefs to implement effective training and educational practices to improve education for gifted students. This study explored the attitudes of Australian primary school teachers (N = 126) towards intellectually gifted children and their education at eight schools. These schools could be categorised into four different classifications in regards to their involvement in gifted education. Key findings include significant associations between teachers’ attitudes and their school classifications (p < .001), and their participation in gifted and talented education inservice training (p < .001). Findings from this study suggest that further teacher training and school-wide involvement in gifted education may assist in improving attitudes towards intellectually gifted children and their education.