History in the Australian Curriculum F-10 : providing answers without asking questions

This paper examines the most recent version of the Australian Curriculum: History F-10. It does so in two ways. First, it explores some of the strengths and weaknesses of this curriculum with reference to the decision to frame aspects of Australian history within the context of a world history approach. Whilst the positioning of Indigenous Histories is applauded, the curriculum’s lack of attention to the significance of the recent history of Australia’s Asian neighbours, and Australia’s relationship with them, is critiqued. This part of the paper also emphasises the need for comparative approaches and calls for greater emphasis on providing students with opportunities to critique and contest the construction of narratives about the past. Second, the paper introduces four invited articles that examine different aspects of the Australian Curriculum: History. Collectively these papers reiterate the significance of the richness of integrated and child-centred approaches and the importance of developing historical thinking, empathy and the historical imagination in the classroom.

Time-dependent fractional advection–diffusion equations by an implicit MLS meshless method

Recently, many new applications in engineering and science are governed by a series of fractional partial differential equations (FPDEs). Unlike the normal partial differential equations (PDEs), the differential order in a FPDE is with a fractional order, which will lead to new challenges for numerical simulation, because most existing numerical simulation techniques are developed for the PDE with an integer differential order. The current dominant numerical method for FPDEs is Finite Difference Method (FDM), which is usually difficult to handle a complex problem domain, and also hard to use irregular nodal distribution. This paper aims to develop an implicit meshless approach based on the moving least squares (MLS) approximation for numerical simulation of fractional advection-diffusion equations (FADE), which is a typical FPDE. The discrete system of equations is obtained by using the MLS meshless shape functions and the meshless strong-forms. The stability and convergence related to the time discretization of this approach are then discussed and theoretically proven. Several numerical examples with different problem domains and different nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the FADE.

A transition program in first year law : adopting the First Year Curriculum Principles

The First Year Curriculum Principles espouse a student-focused consistent and explicit curriculum, acknowledging diversity and the need to scaffold skills and learning. Commencing law students are no different to other first year students in that they must deal with changes in teaching and learning approaches and expectations. As well as the generic issues of transition, law students must grapple with learning the skills which are necessary for the study of law from the very start of their degree. A transition program at the commencement of a law degree as part of a planned first year curriculum provides an opportunity to introduce students to the study of law, the requisite skills as well as assist with transition to tertiary education.

Scaffolding techniques : a teacher training for cooperative learning in Thailand primary education

In general, the benefits of using cooperative learning include academic achievement, communication skills, problem-solving, social skills and student motivation. Yet cooperative learning as a Western educational concept may be ineffective in a different learning system. The study aims to investigate scaffolding techniques for cooperative learning in Thailand primary education. The program was designed to foster Thai primary school teachers’ cooperative learning implementation that includes the basic tenets of cooperative learning and socio-cognitive based learning. Two teachers were invited to participate in this experimental teacher training program for one and a half weeks. Then the teachers implemented a cooperative learning in their mathematics class for six weeks. The data from teacher interview and classroom observation indicated that the both teachers are able to utilise questions to scaffold their students’ engagement in cooperative learning. This initiative study showed that difficulty or failure of implementing cooperative learning in Thailand education may not be derived from cultural difference. The paper discussed the techniques the participant teachers applied with proactive scaffolding, reactive scaffolding and scaffolding questions that can be used to facilitate the implementation of cooperative learning in Thai school.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

Assessing students in senior science: an analysis of questions in contextualised chemistry exams

This study explores the development of a coding system for analysing test questions in two context-based chemistry exams. We describe our unique analytical procedures before contrasting the data from both tests. Our findings indicate that when a new curriculum is developed such as a context-based curriculum, teachers are required to combine the previously separate domains of context and concept to develop contextualised assessment. We argue that constructing contextualised assessment items requires teachers to view concepts and context as interconnected rather than as separate entities that may polarise scientific endeavour. Implications for practice, curriculum and assessment-development in context-based courses are proposed.

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.

TAFE-horticulture teachers’ conceptions of curriculum changes in Queensland, 1990-2003

The period from 1990-2003 was one of unprecedented curriculum change in the Queensland TAFE sector in general and Horticulture in particular. While curriculum theory had been clear for many years that teachers should be involved deeply in the curriculum process, data collected at the end of that period reveals that TAFE Horticulture teachers felt excluded and manipulated by the curriculum developers. With the benefit of distance, this thesis examines TAFE teachers’ conceptions of curriculum change in Horticulture and considers whether events since then have justified their reservations. The research paradigm of this study was informed by the qualitative research orientation of phenomenography based on extended interviews. The study revealed that teachers held eight qualitatively different conceptions of curriculum development. Some viewed the changes as representing a reduction in the quality of education, some as a retreat from education and training while others saw it as a reduction in the quality of teaching delivery. There were teachers who saw it as a way of saving money and others as causing instability and uncertainty, as exploitation of staff and a cause of extra (often unnecessary) work. Most saw the changes as imposed from above with the changes experienced as destructive to staff morale. Despite the generally negative conceptions of curriculum change, the study confirms the importance of teachers being regarded as central in the curriculum change process.

Engaging middle school students in context-based science : One teacher's approach

In Australia, there is a crisis in science education with students becoming disengaged with canonical science in the middle years of schooling. One recent initiative that aims to improve student interest and motivation without diminishing conceptual understanding is the context-based approach. Contextual units that connect the canonical science with the students’ real world of their local community have been used in the senior years but are new in the middle years. This ethnographic study explored the learning transactions that occurred in one 9th grade science class studying an Environmental Science unit for 11 weeks. Data were derived from field notes, audio and video recorded conversations, interviews, student journals and classroom documents with a particular focus on two selected groups of students. Data were analysed qualitatively through coding for emergent themes. This paper presents an outline of the program and discussion of three assertions derived from the preliminary analysis of the data. Firstly, an integrated, coherent sequence of learning experiences that included weekly visits to a creek adjacent to the school enabled the teacher to contextualise the science in the students’ local community. Secondly, content was predominantly taught on a need-to-know basis and thirdly, the lesson sequence aligned with a model for context-based teaching. Research, teaching and policy implications of these results for promoting the context-based teaching of science in the middle years are discussed.

Hunters & gatherers : strategies for curriculum mapping and data collection for assurance of learning

Assurance of learning is a predominant feature in both quality enhancement and assurance in higher education. Assurance of learning is a process that articulates explicit program outcomes and standards, and systematically gathers evidence to determine the extent to which performance matches expectations. Benefits accrue to the institution through the systematic assessment of whole of program goals. Data may be used for continuous improvement, program development, and to inform external accreditation and evaluation bodies. Recent developments, including the introduction of the Tertiary Education and Quality Standards Agency (TEQSA) will require universities to review the methods they use to assure learning outcomes. This project investigates two critical elements of assurance of learning: 1. the mapping of graduate attributes throughout a program; and 2. the collection of assurance of learning data. An audit was conducted with 25 of the 39 Business Schools in Australian universities to identify current methods of mapping graduate attributes and for collecting assurance of learning data across degree programs, as well as a review of the key challenges faced in these areas. Our findings indicate that external drivers like professional body accreditation (for example: Association to Advance Collegiate Schools of Business (AACSB)) and TEQSA are important motivators for assuring learning, and those who were undertaking AACSB accreditation had more robust assurance of learning systems in place. It was reassuring to see that the majority of institutions (96%) had adopted an embedding approach to assuring learning rather than opting for independent standardised testing. The main challenges that were evident were the development of sustainable processes that were not considered a burden to academic staff, and obtainment of academic buy in to the benefits of assuring learning per se rather than assurance of learning being seen as a tick box exercise. This cultural change is the real challenge in assurance of learning practice.

Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

A visual description of early-number counting, addition and subtraction knowledge

Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain of knowledge. This visual language is based upon Piaget’s notion of reflective abstraction (Dubinsky, 1991; Piaget, 1977/2001), and thus captures the epistemological associations that link the problems, concepts and representations of the domain. The constructs of this visual language are introduced and then applied to the early-number domain. The introduction to this visual language may prompt reflection upon its suitability and significance to the description of other domains of knowledge. Through such a process of analysis and description, the visual language may serve as a scaffold for enhancing pedagogical content knowledge and thus ultimately improve learning outcomes.

A Popperian consilience : modelling mathematical knowledge and understanding

Goldin (2003) and McDonald, Yanchar, and Osguthorpe (2005) have called for mathematics learning theory that reconciles the chasm between ideologies, and which may advance mathematics teaching and learning practice. This paper discusses the theoretical underpinnings of a recently completed PhD study that draws upon Popper’s (1978) three-world model of knowledge as a lens through which to reconsider a variety of learning theories, including Piaget’s reflective abstraction. Based upon this consideration of theories, an alternative theoretical framework and complementary operational model was synthesised, the viability of which was demonstrated by its use to analyse the domain of early-number counting, addition and subtraction.

Young children's understandings about "square" in 3D virtual reality microworlds

This paper reports an investigation of primary school children’s understandings about "square". 12 students participated in a small group teaching experiment session, where they were interviewed and guided to construct a square in a 3D virtual reality learning environment (VRLE). Main findings include mixed levels of "quasi" geometrical understandings, misconceptions about length and angles, and ambiguous uses of geometrical language for location, direction, and movement. These have implications for future teaching and learning about 2D shapes with particular reference to VRLE.

Year 7 students’ approaches to understanding and solving NAPLAN numeracy problems

This study investigated how the interpretation of mathematical problems by Year 7 students impacted on their ability to demonstrate what they can do in NAPLAN numeracy testing. In the study, mathematics is viewed as a culturally and socially determined system of signs and signifiers that establish the meaning, origins and importance of mathematics. The study hypothesises that students are unable to succeed in NAPLAN numeracy tests because they cannot interpret the questions, even though they may be able to perform the necessary calculations. To investigate this, the study applied contemporary theories of literacy to the context of mathematical problem solving. A case study design with multiple methods was used. The study used a correlation design to explore the connections between NAPLAN literacy and numeracy outcomes of 198 Year 7 students in a Queensland school. Additionally, qualitative methods provided a rich description of the effect of the various forms of NAPLAN numeracy questions on the success of ten Year 7 students in the same school. The study argues that there is a quantitative link between reading and numeracy. It illustrates that interpretation (literacy) errors are the most common error type in the selected NAPLAN questions, made by students of all abilities. In contrast, conceptual (mathematical) errors are less frequent amongst more capable students. This has important implications in preparing students for NAPLAN numeracy tests. The study concluded by recommending that increased focus on the literacies of mathematics would be effective in improving NAPLAN results.