Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Low achieving mathematics students' attitudinal and achievement changes as a result of using an integrated learning system

This paper reports on a study to measure the effectiveness of an integrated learning system (ILS) in improving mathematics achievement for low achieving Year 5 to 9 students. The study found that statistically significant gains on the integrated learning system were not supported by scores on standardised mathematics achievement tests. It also found that although student attitudes to computers decreased (significantly for some items), the students still liked the integrated learning system and felt that it had helped them to learn.

Year 6 students' idiosyncratic notions of unitising, reunitising and regrouping decimal number places

Having flexible notions of the unit (e.g., 26 ones can be thought of as 2.6 tens, 1 ten 16 ones, 260 tenths, etc.) should be a major focus of elementary mathematics education. However, often these powerful notions are relegated to computations where the major emphasis is on "getting the right answer" thus procedural knowledge rather than conceptual knowledge becomes the primary focus. This paper reports on 22 high-performing students' reunitising processes ascertained from individual interviews on tasks requiring unitising, reunitising and regrouping; errors were categorised to depict particular thinking strategies. The results show that, even for high-performing students, regrouping is a cognitively complex task. This paper analyses this complexity and draws inferences for teaching.

Understanding preservice teachers’ predispositions for teaching engineering education in Australian schools.

Engineering education is underrepresented in Australia at the primary, middle school and high school levels. Understanding preservice teachers’ preparedness to be involved in engineering will be important for developing an engineering curriculum. This study administered a literature-based survey to 36 preservice teachers, which gathered data about their perceptions of engineering and their predispositions for teaching engineering. Findings indicated that the four constructs associated with the survey had acceptable Cronbach alpha scores (i.e., personal professional attributes .88, student motivation .91, pedagogical knowledge .91, and fused curricula .89). However, there was no “disagree” or “strongly disagree” response greater than 22% for any of the 25 survey items. Generally, these preservice teachers indicated predispositions for teaching engineering in the middle school. Extensive scaffolding and support with education programs will assist preservice teachers to develop confidence in this field. Governments and education departments need to recognise the importance of engineering education, and universities must take a stronger role in developing engineering education curricula.

Employing the five-factor mentoring instrument : analysing mentoring practices for teaching primary science.

Primary science education is a concern around the world and quality mentoring within schools can develop preservice teachers’ practices. A five-factor model for mentoring has been identified, namely, personal attributes, system requirements, pedagogical knowledge, modelling, and feedback. Final-year preservice teachers (mentees, n=211) from three Turkish universities were administered a previously validated instrument to gather perceptions of their mentoring in primary science teaching. ANOVA indicated that each of these five factors was statistically significant (p<.001) with mean scale scores ranging from 3.36 to 4.12. Although mentees perceived their mentors to provide evaluation feedback (95%), model classroom management (88%), guide their preparation (96%), and outline the science curriculum (92%), the majority of mentors were perceived not to assist their mentees in 10 of the 34 survey items. Professional development programmes that target the specific needs of these mentors may further enhance mentoring practices for advancing primary science teaching.

Reading Squadron: Crossing borders in literacy experiences for preservice teachers.

Teaching literacy requires accurate and current knowledge in the field (Commonwealth of Australia, 2005). There have been persistent inquiries into what constitutes specialist knowledge and skills for teaching students to be literate. Preservice teacher education is fundamental to literacy development, which includes the approaches universities employ to prepare graduates for teaching literacy. Indeed, preservice teacher programs and literacy education also elicit insatiable media coverage. There is a continued push to improve literacy outcomes for school students across the nation and prepare the literacy knowledge and skills of Australian teachers. This study mainly focuses on 10 final-year preservice teachers attending a regional university campus who volunteered for further experiences to teach students to read traditional texts. These preservice teachers completed three university literacy units before commencing with practical applications. A literacy program, titled Reading Squadron, was developed in partnership between a local primary school and the university. Primary students were identified by the school as requiring literacy support. Preservice teachers attended a whole day training session run by school staff at the university and then visited the school for two one-hour sessions each week over a six-week period. Each preservice teacher was assigned two students and worked with each student for half an hour twice a week. The aim of this small-scale qualitative study was to investigate the perceptions of the preservice teachers and school staff as a result of their involvement in the Reading Squadron program. The preservice teachers completed a questionnaire to determine their views of the program and ascertain how it assisted their development. Further data were gathered from the preservice teachers through individual face-to-face interviews. Three school staff involved in the program also completed a questionnaire to determine the value of the program. Results indicated that the preservice teachers made links between theory and practice, and felt they gained knowledge about teaching reading. Three preservice teachers noted it was difficult to work around timetable commitments but gained from the experience and suggested embedding such experiences into university literacy units. Data gathered from school staff indicated that six-weeks was not sufficient time to measure improvements in the school students, however, they were supportive of such a program, particularly for its continuation. Collaborations between schools and universities can provide opportunities for preservice teachers to use theoretical knowledge gained from core university subjects with application to assist primary students’ literacy development in schools. Teachers in this study were supportive of the Reading Squadron program, however, more data needed to be collected to understand the literacy improvement of students. Longitudinal studies are required to ascertain specific knowledge and skills gained by preservice teachers to teach reading and how these programs enhance students’ literacy levels.

Young children’s experience of visual displays of their artwork

The practice of displaying children's artwork in early childhood classrooms poses a number of questions about the child and his or her visual artwork. This paper focuses on young children’s experiences with the display of their own visual artwork. Following Giorgi's (1985a; 1985b) approach to conducting phenomenological psychological research, 13 children between the ages of 4 and 6 years attending an independent school outside metropolitan Detroit, Michigan (USA) participated in semi-structured interviews as a way of uncovering their lived experiences of seeing their artwork displayed. The study yielded 12 essential themes and from these three key issues and their implications for early childhood art education are explored.

Re-imagining and re-imaging the nation through the history curriculum.

Nationalism is not a naturally occurring sentiment, but rather needs to be carefully nurtured and sustained in the social imaginary through the production and circulation of unifying narratives that invoke the nation’s imagined community. The school curriculum is crucial in this process, legitimating and disseminating selected narratives while de-legitimating and marginalising other accounts and their voices. Certain watershed events in nations’ histories have always posed political problems in history curricula (Cajani & Ross, 2007) –however the pressures and concerns of current times now suggest political solutions in history curricula. This paper briefly examines recent political debates in Australia to argue that the school history curriculum has become a site of increasing interest for the exercise of official forms of nationalism and the production of a nostalgic, celebratory national biography. The public debates around school history curriculum are theorised as nostalgic re-nationalising efforts in response to the march of cultural globalisation and its attendant uncertainties.

Naming trouble in online internationalized education

This paper offers an analysis of cultural politics that emerged around naming practices in an ethnographic study of the interactions within an online MBA unit, offered by an Australian university to both ‘local’ Australian students and international students enrolled through a Malaysian partner institution. It became evident that names were doing important identity, textual and pedagogical work in these interactions and considerable interactive trouble arose over the social practices surrounding names. The analysis uses sociolinguistic concepts to analyse selected slices of the online texts and participants' interview accounts. The analysis shows how ethnocentric default settings in the courseware served to heighten and exacerbate cultural difference as a pedagogical problem. These events are related to the larger problematic of theorising the context of culture in times of globalisation and increasingly entangled educational routes, with implications for the enterprise of online internationalised education.

The appeal of the International Baccalaureate in Australia’s educational market: A curriculum of choice for mobile futures

In Australia there is growing interest in a national curriculum to replace the variety of matriculation credentials managed by State Education departments, ostensibly to address increasing population mobility. Meanwhile, the International Baccalaureate (IB) is attracting increasing interest and enrolments in State and private schools in Australia, and has been considered as one possible model for a proposed Australian Certificate of Education. This paper will review the construction of this curriculum in Australian public discourse as an alternative frame for producing citizens, and ask why this design appeals now, to whom, and how the phenomenon of its growing appeal might inform national curricular debates. The IB’s emergence is understood with reference to the larger context of neo-liberal marketization policies, neo-conservative claims on the curriculum and middle class strategy. The paper draws on public domain documents from the IB Organisation and newspaper reportage to demonstrate how the IB is constructed for public consumption in Australia.

Planning mobile futures : the border artistry of International Baccalaureate Diploma choosers

This paper reports on a study of students choosing the International Baccalaureate Diploma (IBD) over state-based curricula in Australian schools. The IBD was initially designed as a matriculation certificate to facilitate international mobility. While first envisaged as a lifestyle agenda for cultural elites, such mobility is now widespread with more people living ‘beyond the nation’ through choice or circumstance. Beck (2007) and others highlight how the capacity to cross national borders offers a competitive edge with which to strategically pursue economic and cultural capital. Beck’s ‘border artistes’ are those who use national borders to their individual advantage through reflexive strategy. The study explored the rationales and strategy behind the choice of the IBD curriculum expressed by students in a focus group interview and an online survey. This paper reports on their imagined transnational routes and mobile orientations, and how a localised curriculum limits their imagined mobile futures.

Provoking critical awareness and intersubjectivity through "transformative storytelling"

Theories that inform pedagogical practices have positioned young children as innocent, pre-political and egocentric. This paper draws from an action research study that investigates the impact of “transformative storytelling”, where stories purposefully crafted to counter metanarratives, revealed the impact of human greed with one class of children aged five to six years of age. Derrida’s notion of “cinders” provided a concept for investigating the traces or imprints the language of story left behind, amidst the children’s comments and actions, enabling the possibilities of the history of these “cinders” (that is what informed these comments and actions) to be noticed. Readings of some of the children’s responses suggest that children aged five and six years can engage in political discourse through the provocation of “transformative storytelling”, and that their engagement demonstrated the consideration of others through critical awareness and intersubjectivity. These early readings raise questions regarding curriculum content and pedagogical practices in early years education and the validity of ongoing educational goals that incorporate critical awareness and intersubjectivity to equip students with communitarian strategies to counter the individualistic outlook of neoliberalist societies.

Identifying effective leadership practices for implementing a new mathematics curriculum in Taipei

This study explores successful junior high school principals’ leadership practices for implementing the reformed mathematics curriculum in Taipei. Avolio and Bass’s (2002) full range leadership theory was used to record data through interviews and observations of five Taipei “Grade A” junior high school principals. Findings revealed that specific leadership practices linked to management by exception-active and contingent reward (transaction leadership), and individualised consideration and idealised influence (transformational) were considered effective for implementing reform measures. Ensuring principals are aware of effective measures may further assist reform agendas.

Research productivity levels of Chinese TEFL academics

Since China’s Economic Reform and its Open Door Policy, China has entered a new era of education (Adamson, 2002; Hu, 2005a). English has gained status as a language for international relations (Graddol, 1997) and international trade (Qu, 2007). Hence, in 2001, China’s Ministry of Education (MOE) required universities to offer 5-10% of their course units in English, particularly in the fields of information technology, biotechnology, finance and law (Jen, 2001; MOE, 2001). However, “the upgrading of national English proficiency, then, is predicted largely on the professional competence of the teaching force” (Hu, 2005b, p. 655). For TEFL academics, one component of this competence is the capacity to conduct research (Day, 1991; Shu, 2002). Indeed, research productivity has become essential for university success, and academics’ employment and promotional prospects. This study aims to investigate 182 Chinese TEFL academics’ research outputs across three Chinese higher education institutions through the research question: What are the research productivity levels of Chinese TEFL academics? A survey instrument was devised to gather TEFL academics’ calculations of research productivity and, in particular, the quality and quantity of research outputs over a five-year period (2004-2008). Descriptive statistics through SPSS were used to analyse data across research output fields (e.g., journal articles, conference papers). Academic status varied (n=182; teaching assistants 23.6%, lecturers 47.3%, associate professors 22.5%, and professors 6.6%) as did years of teaching (1-5 years 27.4%, 6-10 years 24.7%, 11-15 18.1%, 16-20 years 13.7%, > 21 years 15.9%). Results (n=182, male=27%, females=73%) indicated 18% had not produced any research in the five-year period. Indeed, more than 70% had produced no research in all categories except non-core journal articles and provincial projects. An overwhelming majority of TEFL academics had zero productivity in 10 of the 12 categories. Nevertheless, there were highly-productive TEFL academics, who had produced five or more pieces of research across the 12 categories. In addition, there was not much difference between sole and co-authored research outputs, except non-core journal articles where sole authored work was 20% higher than co-authored work. China’s desire for international competitiveness in education will require measures that facilitate higher levels of research productivity. These measures must include professional development, support and mentoring programs, and employment of personnel who can guide these processes. Research performance is an outcome, hence there is a need to understand Chinese TEFL academics’ perceptions about research, and experiences that may hinder and facilitate higher research productivity.

Gender and the Australian parliament : putting the political scientist into the picture

This paper draws on a study of gender and politics in the Australian parliament in order to make a contribution to methodological debates in feminist political science. The paper begins by outlining the different dimensions of feminist political science methodology that have been identified in the literature. According to this literature five key principles can be seen to constitute feminist approaches to political science. These are: a focus on gender, a deconstruction of the public/private divide, giving voice to women, using research as a basis for transformation, and using reflexivity to critique researcher positionality. The next part of the paper focuses more specifically on reflexivity tracing arguments about its definition, usefulness and the criticisms it has attracted from researchers. Following this, I explore how my background as a member of the Australian House of Representatives from 1987 to 1996 provided an important academic resource in my doctoral study of gender and politics in the national parliament. Through this process I highlight the value of a reflexive approach to research.