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.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Nursing students’ knowledge and practice of infection control precautions : an educational intervention

Aim. This paper is a report of the effectiveness of a purpose-designed education program in improving undergraduate nursing students’ understanding and practice of infection control precautions. Background. The severe acute respiratory syndrome outbreak in 2003 highlighted that healthcare workers were under-prepared for such an epidemic. While many in-service education sessions were arranged by institutions in response to the outbreak, preservice nursing education has overlooked preparation for handling such infectious disease epidemics. Method. A quasi-experimental design was used and a 16-hour, purpose-designed infection control education programme was implemented for preservice nursing students in southern Taiwan. Self-administered questionnaires were distributed at three time points during the period September 2005 to April 2006 to examine the sustainability and effectiveness of the intervention. Results. A total of 175 preservice nursing students participated in the study. Following the education programme, students in the intervention group showed a statistically significant improvement across time in their knowledge of these precautions [F(2, 180) = 13Æ53, P < 0Æ001] and confidence in resolving infectionrelated issues [F(1Æ79, 168Æ95) = 3Æ24] when compared with those in the control group. Conclusion. To improve nursing students’ capacity in responding to infectious epidemics, an educational programme that integrates the theme of infection precautions, learning theory and teaching strategies is recommended for all nursing institutes.

Mixing colours: An ICT tool based on a semiotic framework for mathematical meaning-makng about ratio and fractions

This paper reports on the research and development of an ICT tool to facilitate the learning of ratio and fractions by adult prisoners. The design of the ICT tool was informed by a semiotic framework for mathematical meaning-making. The ICT tool thus employed multiple semiotic resources including topological, typological, and social-actional resources. The results showed that individual semiotic resource could only represent part of the mathematical concept, while at the same time it might signify something else to create a misconception. When multiple semiotic resources were utilised the mathematical ideas could be better learnt.

Providing innovative planning education experience : teaching regional planning in an international context

Rapidly changing economic, social, and environmental conditions have created a need for urban and regional planning practitioners who are resilient, innovative, and able to cope with the increasingly complex and cosmopolitan nature of major metropolitan areas. This need should be reflected in planning education that allows students to experience a diverse range of approaches to problems and challenges, and that exposes students to the diverse array of perspectives on planning issues. This paper investigates the outcomes of a collaborative regional planning exercise organised jointly by planning academics from both Queensland University of Technology and the International Islamic University of Malaysia, and involving planning students from both universities. The regional planning exercise consisted of a regional appraisal and report topics of the area under investigation, Klang Valley – Kuala Lumpur, Malaysia. It culminated with the presentation of regional development strategies for the area, with a field trip to Malaysia being the cornerstone of the project. The collaborative exercise involved a series of workshops and seminars organised locally, in which both Australian and Malaysian planning students participated, as well as meetings with local and federal planning officials, and also a forum for Young Planners of Australian and Malaysian Planning Institutes. The experience attempted to bridge the teaching of theoretical concepts of regional planning and development and the regional, more professional knowledge of planning practice, as it relates to specific political, institutional and cultural contexts. A survey of participating students, from both Queensland University of Technology and the International Islamic University of Malaysia, highlights the benefits of such project in terms of leaning experience and exposure to different cultural contexts.

How current pedagogy methods in games teaching in the UK, Australia and the US have been shaped by historical, socio cultural, environmental and political constraints

Crucial to enhancing the status and quality of games teaching in schools is a developed understanding of the teaching strategies adopted by practitioners. In this paper, we will demonstrate that contemporary games‟ teaching is a product of individual, task and environmental constraints (Newell, 1986). More specifically, we will show that current pedagogy in the U.K., Australia and the United States is strongly influenced by historical, socio-cultural environmental and political constraints. In summary, we will aim to answer the question „why do teachers teach games the way they do.‟ In answering this question, we conclude that teacher educators, who are trying to influence pedagogical practice, must understand these potential constraints and provide appropriate pre-service experiences to give future physical education teachers the knowledge, confidence and ability to adopt a range of teaching styles when they become fully fledged teachers. Essential to this process is the need to enable future practitioners to base their pedagogical practice on a sound understanding of contemporary learning theories of skill acquisition.

Blogs, wikis and podcasts : collaborative knowledge building tools in a design and technology course

Design and Technology has become an important part of the school curriculum. In Queensland, Australia, Technology (which encompasses Design) is one of the Key Learning Areas (KLAs) for students in the first ten years of schooling. This KLA adopts a student-centred, hands-on constructivist approach to teaching and learning. The ability to conceptualise and implement appropriate learning experiences, however, has been a challenge for some early career teachers. This paper describes how Design and Technology is being taught to pre-service primary teachers at an Australian University through their involvement in a range of authentic problem-solving activities supported by social learning tools such as wikis and blogs. An interview with a sample from this group (N=5) provides an insight into how these social software tools enhanced their knowledge and learning. This paper will describe how these social learning tools impact on the agency of learning.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Year 8, 9 and 10 students’ understanding and access of percent knowledge

This paper reports on Years 8, 9 and 10 students’ knowledge of percent problem types, use of diagrams, and type of solution strategy. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema based methods.

Place value, multiplicativity, reunitizing and effective classroom teaching of decimal numeration

Student understanding of decimal number is poor (e.g., Baturo, 1998; Behr, Harel, Post & Lesh, 1992). This paper reports on a study which set out to determine the cognitive complexities inherent in decimal-number numeration and what teaching experiences need to be provided in order to facilitate an understanding of decimal-number numeration. The study gave rise to a theoretical model which incorporated three levels of knowledge. Interview tasks were developed from the model to probe 45 students’ understanding of these levels, and intervention episodes undertaken to help students construct the baseline knowledge of position and order (Level 1 knowledge) and an understanding of multiplicative structure (Level 3 knowledge). This paper describes the two interventions and reports on the results which suggest that helping students construct appropriate mental models is an efficient and effective teaching strategy.

Interdisciplinarity vs disciplinarity : developing knowledge for problem solving in middle years of schooling

Interdisciplinary studies are fundamental to the signature practices for the middle years of schooling. Middle years researchers claim that interdisciplinarity in teaching appropriately meets the needs of early adolescents by tying concepts together, providing frameworks for the relevance of knowledge, and demonstrating the linking of disparate information for solution of novel problems. Cognitive research is not wholeheartedly supportive of this position. Learning theorists assert that application of knowledge in novel situations for the solution of problems is actually dependent on deep discipline based understandings. The present research contrasts the capabilities of early adolescent students from discipline based and interdisciplinary based curriculum schooling contexts to successfully solve multifaceted real world problems. This will inform the development of effective management of middle years of schooling curriculum.

Cultivating teachers’ beliefs, knowledge and skills for leading change in schools

Australian policy initiatives and state curriculum reform efforts affirm a commitment to address student disengagement through the development of inclusive school environments, curriculum, and pedagogy. This paper, drawing on critical social theory, describes three Australian projects that support the cultivation of teachers’ beliefs, knowledge and skills for critical reflection and leading change in schools. The first project reports on the valued ethics that emerged in pre-service teacher reflections about a Service-learning Program at a university in Queensland. The second project reports on a school-based collaborative inquiry approach to professional development with a focus on literacy practices. The final project reports on an initiative in another university in Victoria, to operationalise pedagogical change and curriculum renewal in Victoria, through the Principles of Learning and Teaching (PoLT). These case studies illustrate how critical reflection and development of beliefs, knowledge and skills can be acquired to better meet the needs of schools.