Scaffolding students’ thinking in mathematical investigations

This article describes some of the issues that teachers might encounter when scaffolding students’ thinking during mathematical investigations. It describes four episodes where a teacher’s scaffolding failed to support students’ mathematical thinking and explores the reasons why the scaffolding was ineffective. Understanding what is ineffective and why is one way to improve pedagogical practice. As a background to these episodes, we first provide an overview of the mathematical investigation. Our paper concludes with some recommendations for judicious scaffolding during investigations.

The role of fluency in a mathematics item with an embedded graphic: Interpreting a pie chart.

The purpose of this study was to identify the pedagogical knowledge relevant to the successful completion of a pie chart item. This purpose was achieved through the identification of the essential fluencies that 12–13-year-olds required for the successful solution of a pie chart item. Fluency relates to ease of solution and is particularly important in mathematics because it impacts on performance. Although the majority of students were successful on this multiple choice item, there was considerable divergence in the strategies they employed. Approximately two-thirds of the students employed efficient multiplicative strategies, which recognised and capitalised on the pie chart as a proportional representation. In contrast, the remaining one-third of students used a less efficient additive strategy that failed to capitalise on the representation of the pie chart. The results of our investigation of students’ performance on the pie chart item during individual interviews revealed that five distinct fluencies were involved in the solution process: conceptual (understanding the question), linguistic (keywords), retrieval (strategy selection), perceptual (orientation of a segment of the pie chart) and graphical (recognising the pie chart as a proportional representation). In addition, some students exhibited mild disfluencies corresponding to the five fluencies identified above. Three major outcomes emerged from the study. First, a model of knowledge of content and students for pie charts was developed. This model can be used to inform instruction about the pie chart and guide strategic support for students. Second, perceptual and graphical fluency were identified as two aspects of the curriculum, which should receive a greater emphasis in the primary years, due to their importance in interpreting pie charts. Finally, a working definition of fluency in mathematics was derived from students’ responses to the pie chart item.

Analysing preservice teachers' potential for implementing engineering education in the middle school

Engineering is pivotal to any country's development. Yet there are insufficient engineers to take up available positions in many countries, including Australia (Engineers Australia, 2008). Engineering education is limited in Australia at the primary, middle and high school levels. One of the starting points for addressing this shortfall lies in preservice teacher education. This study explores second-year preservice teachers' potential to teach engineering in middle school, following their engagement with engineering concepts in their science curriculum unit and their teaching of engineering activities to Year 7 students. Using a literature-based pretest-posttest survey, items were categorised into four constructs (ie. personal professional attributes, student motivation, pedagogical knowledge and fused curricula). Results indicated that the preservice teachers' responses had not changed for instilling positive attitudes (88%) and accepting advice from colleagues (94%). However, there was statistical significance with 9 of the 25 survey items (p<0.05) after the preservice teachers' involvement in engineering activities. Fusing engineering education with other subjects, such as mathematics and science, is an essential first step in promoting preservice teachers' potential to implement engineering education in the middle school.

A collaborative approach to reading workshop in the middle years

Reflection Questions • How does the collaborative reading workshop approach engage students in higher order thinking and deep engagement with text? • How does the collaborative reading workshop approach support students to be active citizens and critically literate? • How does the interaction and collaborative thinking in this approach contribute to the students’ intellectual engagement and the teacher’s pedagogical rigor? • How could this approach be implemented or adapted at your school?

Insights from ecological psychology and dynamical systems theory can underpin a philosophy of coaching

The aim of this paper is to show how principles of ecological psychology and dynamical systems theory can underpin a philosophy of coaching practice in a nonlinear pedagogy. Nonlinear pedagogy is based on a view of the human movement system as a nonlinear dynamical system. We demonstrate how this perspective of the human movement system can aid understanding of skill acquisition processes and underpin practice for sports coaches. We provide a description of nonlinear pedagogy followed by a consideration of some of the fundamental principles of ecological psychology and dynamical systems theory that underpin it as a coaching philosophy. We illustrate how each principle impacts on nonlinear pedagogical coaching practice, demonstrating how each principle can substantiate a framework for the coaching process.

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.

Intentional first year curriculum design as a means of facilitating student engagement: some exemplars

The importance of student engagement to higher education quality, making deep learning outcomes possible for students, and achieving student retention, is increasingly being understood. The issue of student engagement in the first year of tertiary study is of particular significance. This paper takes the position that the first year curriculum, and the pedagogical principles that inform its design, are critical influencers of student engagement in the first year learning environment. We use an analysis of case studies prepared for Kift’s ALTC Senior Fellowship to demonstrate ways in which student engagement in the first year of tertiary study can be successfully supported through intentional curriculum design that motivates students to learn, provides a positive learning climate, and encourages students to be active in their learning.

Young children learning for the environment: Researching a forest adventure

Field experiences for young children are an ideal medium for environmental education/education for sustainability because of opportunities for direct experience in nature, integrated learning, and high community involvement. This research documented the development - in 4-5 year old Prep children - of knowledge, attitudes and actions/advocacy in support of an endangered native Australian animal, the Greater Bilby. Data indicated that children gained new knowledge, changed attitudes and built a repertoire of action/ advocacy strategies in native animal conservation as a result of participating in a forest field adventure. The curriculum and pedagogical features that supported these young children’s learning include: active engagement in a natural environment, learning through curriculum integration at home and at school, anthropomorphic representations of natural elements, making connections with cultural practices, and intergenerational learning. The paper also highlights research strategies that can be usefully and ethically applied when conducting studies involving young children.

Transforming Queensland VET : Challenges and Opportunities (Volume 3)

The volume is the third in a series that addresses change and development in the delivery of VET programs in Queensland. The chapters address a breadth of issues that relate to the changing landscape for teaching and learning in VET programs through e-learning. Organisational change is a key focus of this volume. James Waterson examines business and pedagogical perspectives for SkillsTech Australia to create teaching and learning environments that will enrich the learning experience for staff and students. Kerry Emerson explores the ways in which printing teachers might change current practices in order to deliver their training to apprentices and trainees – off-the-job, onthe- job and online, through e-learning. The chapter by Erik Dodwell takes up issues of user-friendly RPL interviews and the challenges to develop a model that may be applied consistently across all industry areas using conversational interviews. The chapters by Linda Roberston, Nina Woodrow, and Anushka Weerackody discuss teaching and learning for specific groups of students. Linda Roberston proposes a vision for learning support teachers in which the learner is encouraged to be a self-directed and autonomous learner who is capable of utilising e-learning resources and is information literate. Nina Woodrow presents a case for the diminished sense of occupational identity by adult literacy teachers and the implications of this loss of expertise across the VET sector. Constructive strategies for change are outlined. The chapter by Anushka Weerackody explores ideas to enhance the practices of ESL teachers in TAFE Queensland through an online community of practice. The issues of on-the-job training through e-learning for various trades is considered by Anne-Louise Johnston and the benefits and challenges for SkillsTech Australia in developing training partnerships with industry to deliver these changes. These papers were completed by the authors as a part of their postgraduate studies at QUT. The views reported are those of the authors and should not be attributed to the Queensland Department of Education and Training. Donna Berthelsen and Lauren Vogel Faculty of Education Queensland University of Technology December 2009

A model of teacher professional development based on the principles of lesson study

The researcher’s professional role as an Education Officer was the impetus for this study. Designing and implementing professional development activities is a significant component of the researcher’s position description and as a result of reflection and feedback from participants and colleagues, the creation of a more effective model of professional development became the focus for this study. Few studies have examined all three links between the purposes of professional development that is, increasing teacher knowledge, improving teacher practice, and improving student outcomes. This study is significant in that it investigates the nature of the growth of teachers who participated in a model of professional development which was based upon the principles of Lesson Study. The research provides qualitative and empirical data to establish some links between teacher knowledge, teacher practice, and student learning outcomes. Teacher knowledge in this study refers to mathematics content knowledge as well as pedagogical-content knowledge. The outcomes for students include achievement outcomes, attitudinal outcomes, and behavioural outcomes. As the study was conducted at one school-site, existence proof research was the focus of the methodology and data collection. Developing over the 2007 school year, with five teacher-participants and approximately 160 students from Year Levels 6 to 9, the Lesson Study-principled model of professional development provided the teacher-participants with on-site, on-going, and reflective learning based on their classroom environment. The focus area for the professional development was strategising the engagement with and solution of worded mathematics problems. A design experiment was used to develop the professional development as an intervention of prevailing teacher practice for which data were collected prior to and after the period of intervention. A model of teacher change was developed as an underpinning framework for the development of the study, and was useful in making decisions about data collection and analyses. Data sources consisted of questionnaires, pre-tests and post-tests, interviews, and researcher observations and field notes. The data clearly showed that: content knowledge and pedagogical-content knowledge were increased among the teacher-participants; teacher practice changed in a positive manner; and that a majority of students demonstrated improved learning outcomes. The positive changes to teacher practice are described in this study as the demonstrated use of mixed pedagogical practices rather than a polarisation to either traditional pedagogical practices or contemporary pedagogical practices. The improvement in student learning outcomes was most significant as improved achievement outcomes as indicated by the comparison of pre-test and post-test scores. The effectiveness of the Lesson Study-principled model of professional development used in this study was evaluated using Guskey’s (2005) Five Levels of Professional Development Evaluation.

Digital kids, analogue students : a mixed methods study of students' engagement with a school-based Web 2.0 learning innovation

The inquiry documented in this thesis is located at the nexus of technological innovation and traditional schooling. As we enter the second decade of a new century, few would argue against the increasingly urgent need to integrate digital literacies with traditional academic knowledge. Yet, despite substantial investments from governments and businesses, the adoption and diffusion of contemporary digital tools in formal schooling remain sluggish. To date, research on technology adoption in schools tends to take a deficit perspective of schools and teachers, with the lack of resources and teacher ‘technophobia’ most commonly cited as barriers to digital uptake. Corresponding interventions that focus on increasing funding and upskilling teachers, however, have made little difference to adoption trends in the last decade. Empirical evidence that explicates the cultural and pedagogical complexities of innovation diffusion within long-established conventions of mainstream schooling, particularly from the standpoint of students, is wanting. To address this knowledge gap, this thesis inquires into how students evaluate and account for the constraints and affordances of contemporary digital tools when they engage with them as part of their conventional schooling. It documents the attempted integration of a student-led Web 2.0 learning initiative, known as the Student Media Centre (SMC), into the schooling practices of a long-established, high-performing independent senior boys’ school in urban Australia. The study employed an ‘explanatory’ two-phase research design (Creswell, 2003) that combined complementary quantitative and qualitative methods to achieve both breadth of measurement and richness of characterisation. In the initial quantitative phase, a self-reported questionnaire was administered to the senior school student population to determine adoption trends and predictors of SMC usage (N=481). Measurement constructs included individual learning dispositions (learning and performance goals, cognitive playfulness and personal innovativeness), as well as social and technological variables (peer support, perceived usefulness and ease of use). Incremental predictive models of SMC usage were conducted using Classification and Regression Tree (CART) modelling: (i) individual-level predictors, (ii) individual and social predictors, and (iii) individual, social and technological predictors. Peer support emerged as the best predictor of SMC usage. Other salient predictors include perceived ease of use and usefulness, cognitive playfulness and learning goals. On the whole, an overwhelming proportion of students reported low usage levels, low perceived usefulness and a lack of peer support for engaging with the digital learning initiative. The small minority of frequent users reported having high levels of peer support and robust learning goal orientations, rather than being predominantly driven by performance goals. These findings indicate that tensions around social validation, digital learning and academic performance pressures influence students’ engagement with the Web 2.0 learning initiative. The qualitative phase that followed provided insights into these tensions by shifting the analytics from individual attitudes and behaviours to shared social and cultural reasoning practices that explain students’ engagement with the innovation. Six indepth focus groups, comprising 60 students with different levels of SMC usage, were conducted, audio-recorded and transcribed. Textual data were analysed using Membership Categorisation Analysis. Students’ accounts converged around a key proposition. The Web 2.0 learning initiative was useful-in-principle but useless-in-practice. While students endorsed the usefulness of the SMC for enhancing multimodal engagement, extending peer-topeer networks and acquiring real-world skills, they also called attention to a number of constraints that obfuscated the realisation of these design affordances in practice. These constraints were cast in terms of three binary formulations of social and cultural imperatives at play within the school: (i) ‘cool/uncool’, (ii) ‘dominant staff/compliant student’, and (iii) ‘digital learning/academic performance’. The first formulation foregrounds the social stigma of the SMC among peers and its resultant lack of positive network benefits. The second relates to students’ perception of the school culture as authoritarian and punitive with adverse effects on the very student agency required to drive the innovation. The third points to academic performance pressures in a crowded curriculum with tight timelines. Taken together, findings from both phases of the study provide the following key insights. First, students endorsed the learning affordances of contemporary digital tools such as the SMC for enhancing their current schooling practices. For the majority of students, however, these learning affordances were overshadowed by the performative demands of schooling, both social and academic. The student participants saw engagement with the SMC in-school as distinct from, even oppositional to, the conventional social and academic performance indicators of schooling, namely (i) being ‘cool’ (or at least ‘not uncool’), (ii) sufficiently ‘compliant’, and (iii) achieving good academic grades. Their reasoned response therefore, was simply to resist engagement with the digital learning innovation. Second, a small minority of students seemed dispositionally inclined to negotiate the learning affordances and performance constraints of digital learning and traditional schooling more effectively than others. These students were able to engage more frequently and meaningfully with the SMC in school. Their ability to adapt and traverse seemingly incommensurate social and institutional identities and norms is theorised as cultural agility – a dispositional construct that comprises personal innovativeness, cognitive playfulness and learning goals orientation. The logic then is ‘both and’ rather than ‘either or’ for these individuals with a capacity to accommodate both learning and performance in school, whether in terms of digital engagement and academic excellence, or successful brokerage across multiple social identities and institutional affiliations within the school. In sum, this study takes us beyond the familiar terrain of deficit discourses that tend to blame institutional conservatism, lack of resourcing and teacher resistance for low uptake of digital technologies in schools. It does so by providing an empirical base for the development of a ‘third way’ of theorising technological and pedagogical innovation in schools, one which is more informed by students as critical stakeholders and thus more relevant to the lived culture within the school, and its complex relationship to students’ lives outside of school. It is in this relationship that we find an explanation for how these individuals can, at the one time, be digital kids and analogue students.

Online professional communities : understanding the effects of membership on teacher practice

Online communities offer teachers a forum to discuss ideas, seek support, engage in professional discussions and network with a wider peer group. The popularity of online communities for teachers is self-evident by the quantity that has emerged in recent years and they present as opportunities to engage in continued pedagogical growth. The study presented in this paper has focused on the electronic discussions of three online communities for teachers, two Australian-based communities and one UK-based community. The aim was to analyse the content of the messages, via content analysis using the Practical Inquiry Model (Garrison, Anderson & Archer, 2001) in an attempt to determine if membership had an impact pedagogy. This study will present findings that support the conclusion that membership to online communities provides genuine opportunities for continued pedagogical growth for teachers. It will also show that they are being used as a problem solving resource, provide opportunities for professional discourse and professional support.

The development and evaluation of an innovative nursing practice model to improve undergraduate nursing students' competence in paediatric physical assessment

Introduction The purpose of this study was to develop, implement and evaluate the impact of an educational intervention, comprising an innovative model of clinical decisionmaking and educational delivery strategy for facilitating nursing students‘ learning and development of competence in paediatric physical assessment practices. Background of the study Nursing students have an undergraduate education that aims to produce graduates of a generalist nature who demonstrate entry level competence for providing nursing care in a variety of health settings. Consistent with population morbidity and health care roles, paediatric nursing concepts typically form a comparatively small part of undergraduate curricula and students‘ exposure to paediatric physical assessment concepts and principles are brief. However, the nursing shortage has changed traditional nursing employment patterns and new graduates form the majority of the recruitment pool for paediatric nursing speciality staff. Paediatric nursing is a popular career choice for graduates and anecdotal evidence suggests that nursing students who select a clinical placement in their final year intend to seek employment in paediatrics upon graduation. Although concepts of paediatric nursing are included within undergraduate curriculum, students‘ ability to develop the required habits of mind to practice in what is still regarded as a speciality area of practice is somewhat limited. One of the areas of practice where this particularly impacts is in paediatric nursing physical assessment. Physical assessment is a fundamental component of nursing practice and competence in this area of practice is central to nursing students‘ development of clinical capability for practice as a registered nurse. Timely recognition of physiologic deterioration of patients is a key outcome of nurses‘ competent use of physical assessment strategies, regardless of the practice context. In paediatric nursing contexts children‘s physical assessment practices must specifically accommodate the child‘s different physiological composition, function and pattern of clinical deterioration (Hockenberry & Barrera, 2007). Thus, to effectively manage physical assessment of patients within the paediatric practice setting nursing students need to integrate paediatric nursing theory into their practice. This requires significant information processing and it is in this process where students are frequently challenged. The provision of rules or models can guide practice and assist novice-level nurses to develop their capabilities (Benner, 1984; Benner, Hooper-Kyriakidis & Stannard, 1999). Nursing practice models are cognitive tools that represent simplified patterns of expert analysis employing concepts that suit the limited reasoning of the inexperienced, and can represent the =rules‘ referred to by Benner (1984). Without a practice model of physical assessment students are likely to be uncertain about how to proceed with data collection, the interpretation of paediatric clinical findings and the appraisal of findings. These circumstances can result in ad hoc and unreliable nursing physical assessment that forms a poor basis for nursing decisions. The educational intervention developed as part of this study sought to resolve this problem and support nursing students‘ development of competence in paediatric physical assessment. Methods This study utilised the Context Input Process Product (CIPP) Model by Stufflebeam (2004) as the theoretical framework that underpinned the research design and evaluation methodology. Each of the four elements in the CIPP model were utilised to guide discrete stages of this study. The Context element informed design of the clinical decision-making process, the Paediatric Nursing Physical Assessment model. The Input element was utilised in appraising relevant literature, identifying an appropriate instructional methodology to facilitate learning and educational intervention delivery to undergraduate nursing students, and development of program content (the CD-ROM kit). Study One employed the Process element and used expert panel approaches to review and refine instructional methods, identifying potential barriers to obtaining an effective evaluation outcome. The Product element guided design and implementation of Study Two, which was conducted in two phases. Phase One employed a quasiexperimental between-subjects methodology to evaluate the impact of the educational intervention on nursing students‘ clinical performance and selfappraisal of practices in paediatric physical assessment. Phase Two employed a thematic analysis and explored the experiences and perspectives of a sample subgroup of nursing students who used the PNPA CD-ROM kit as preparation for paediatric clinical placement. Results Results from the Process review in Study One indicated that the prototype CDROM kit containing the PNPA model met the predetermined benchmarks for face validity and the impact evaluation instrumentation had adequate content validity in comparison with predetermined benchmarks. In the first phase of Study Two the educational intervention did not result in statistically significant differences in measures of student performance or self-appraisal of practice. However, in Phase Two qualitative commentary from students, and from the expert panel who reviewed the prototype CD-ROM kit (Study One, Phase One), strongly endorsed the quality of the intervention and its potential for supporting learning. This raises questions regarding transfer of learning and it is likely that, within this study, several factors have influenced students‘ transfer of learning from the educational intervention to the clinical practice environment, where outcomes were measured. Conclusion In summary, the educational intervention employed in this study provides insights into the potential e-learning approaches offer for delivering authentic learning experiences to undergraduate nursing students. Findings in this study raise important questions regarding possible pedagogical influences on learning outcomes, issues within the transfer of theory to practice and factors that may have influenced findings within the context of this study. This study makes a unique contribution to nursing education, specifically with respect to progressing an understanding of the challenges faced in employing instructive methods to impact upon nursing students‘ development of competence. The important contribution transfer of learning processes make to students‘ transition into the professional practice context and to their development of competence within the context of speciality practice is also highlighted. This study contributes to a greater awareness of the complexity of translating theoretical learning at undergraduate level into clinical practice, particularly within speciality contexts.

E-learning and access : getting behind the hype

Rapid advances in information and communications technology (ICT) - particularly the development of online technologies -have transformed the nature of economic, social and cultural relations across the globe. In the context of higher education in post-industrial societies, technological change has had a significant impact on university operating environments. In a broad sense, technological advancement has contributed significantly to the increasing complexity of global economies and societies, which is reflected in the rise of lifelong learning discourses with which universities are engaging. More specifically, the ever-expanding array of ICT available within the university sector has generated new management and pedagogical imperatives for higher education in the information age.

Teaching and learning in a context-based chemistry classroom

Many current chemistry programs privilege de-contextualised conceptual learning, often limited by a narrow selection of pedagogies that too often ignore the realities of studentse own lives and interests (e.g., Tytler, 2007). One new approach that offers hope for improving studentse engagement in learning chemistry and perceived relevance of chemistry is the context-based approach. This study investigated how teaching and learning occurred in one year 11 context-based chemistry classroom. Through an interpretive methodology using a case study design, the teaching and learning that occurred during one term (ten weeks) of a unit on Water Quality are described. The researcher was a participant observer in the study who co-designed the unit of work with the teacher. The research questions explored the structure and implementation of the context-based approach, the circumstances by which students connected concepts and context in the context-based classroom and the outcome of the approach for the students and the teacher. A dialectical sociocultural theoretical framework using the dialectics of structure | agency and agency | passivity was used as a lens to explore the interactions between learners in different fields, such as the field of the classroom and the field of the local community. The findings of this study highlight the difficulties teachers face when implementing a new pedagogical approach. Time constraints and opportunities for students to demonstrate a level of conceptual understanding that satisfied the teacher, hindered a full implementation of the approach. The study found that for high (above average) and sound (average) achieving students, connections between sanctioned science content of school curriculum and the studentse out-of-school worlds were realised when students actively engaged in fields that contextualised inquiry and gave them purpose for learning. Fluid transitions or the toing and froing between concepts and contexts occurred when structures in the classroom afforded students the agency to connect concepts and contexts. The implications for teaching by a context-based approach suggest that keeping the context central, by teaching content on a "need-to-know" basis, contextualises the chemistry for students. Also, if teachers provide opportunities for student-student interactions and written work student learning can improve.