Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Homework for refugee middle school students with backgrounds marked by low levels of engagement with English school literacy

Homework presents many challenges for refugees from Africa who are arriving in Australian schools with histories of little, no or severely interrupted schooling. This is evident in the emergence of school- and community-based homework help, clubs and tutoring programs for the students. The aim of this article is to describe the homework support options accessed by eight students from Burundi, Rwanda, Eritrea and Sudan who participated in a study of pedagogy for middle school-aged African refugees, and the views on homework of their parents and teachers. The article shows some tensions between family and school expectations and the dilemmas that arise for teachers in a broader context of public concern about and official policy statement on excessive and repetitive homework. It is argued that application of policy guidelines needs to account for disadvantages that potentially accrue to students who cannot design their own independent study programs. Further, it is suggested that integration of skills and meaning-based pedagogy inherent in recent approaches to literacy education has potential for ensuring that students receive the forms of homework they require.

Exercise and secondary lymphedema : safety, potential benefits, and research issues

Participating in regular physical activity is encouraged following breast cancer (BC) treatment, except for those who have subsequently developed lymphoedema. We designed a randomised controlled trial to investigate the effect of participating in a supervised, mixed-type, moderate-intensity exercise program among women with lymphoedema following breast cancer. Women <76 years who had completed BC treatment at least six months prior and subsequently developed unilateral, upper-limb lymphoedema were randomly allocated to an intervention (n=16) or control (n=16) group. The intervention group (IG) participated in 20 supervised group exercise sessions over 12 weeks, while the control group (CG) was instructed to continue habitual activities. Lymphoedema status was assessed by bioimpedance spectroscopy (impedance ratio between limbs) and perometry (volume difference between limbs). Mean baseline measures were similar for the IG (1.13+0.15 and 337+307ml, respectively) and CG (1.13+0.15 and 377+416ml, respectively) and no changes were observed over time. However, 2 women in the IG no longer had evidence of lymphoedema by study end. Average attendance was over 70% of supervised sessions, and there were no withdrawals. The results indicate that, at worst, exercise does not exacerbate secondary lymphoedema. Women with secondary lymphoedema should be encouraged to be physically active, optimising their physical and psychosocial recovery.

Teamwork resources to support students and teachers at QUT

The educational advantage of students working cooperatively in teams has been acknowledged in the higher education sector as being profitable in the world of work and other post-university experiences.

The Student Success Project : Helping students at-risk of failing or leaving a unit - a work in progress

In Semester 1 2007, a Monitoring Student Engagement study, conducted as part of the Enhancing Transition at Queensland University of Technology (ET@QUT) Project and extending earlier work in the Project by Arora (2006), aimed at mapping the processes and resources used at that time to identify, monitor and manage students in their first year who were at risk of leaving QUT (Shaw, 2007). This identified a lack of documentation of the processes and resources used and revealed an ad-hoc rather than holistic and systematic approach to monitoring student engagement. One of Shaw’s recommendations was to: “To introduce a centralised case management approach to student engagement” (p. 14). That provided the genesis for the Student Success Project that is being reported on here. The aim of the Student Success Project is to trial, evaluate and ultimately establish holistic and systematic ways of helping students who appear to be at-risk of failing or withdrawing from a unit to persist and succeed. Students are profiled as being at-risk if they are absent from more than 2 tutorials in a row without contacting their tutor or if they fail to submit their first assignment. A Project Officer makes personal contact with these students to suggest ways they can get further assistance depending on their situation.

Getting skilled for education, training and employment : Indigenous Cultural Knowledges and mainstream knowledges of mathematics

This abstract is a preliminary discussion of the importance of blending of Indigenous cultural knowledges with mainstream knowledges of mathematics for supporting Indigenous young people. This import is emphasised in the documents Preparing the Ground for Partnership (Priest, 2005), The Indigenous Education Strategic Directions 2008–2011 (Department of Education, Training and the Arts, 2007) and the National Goals for Indigenous Education (Department of Education, Employment and Work Relations, 2008). These documents highlight the contextualising of literacy and numeracy to students’ community and culture (see Priest, 2005). Here, Community describes “a culture that is oriented primarily towards the needs of the group. Martin Nakata (2007) describes contextualising to culture as about that which already exists, that is, Torres Strait Islander community, cultural context and home languages (Nakata, 2007, p. 2). Continuing, Ezeife (2002) cites Hollins (1996) in stating that Indigenous people belong to “high-context culture groups” (p. 185). That is, “high-context cultures are characterized by a holistic (top-down) approach to information processing in which meaning is “extracted” from the environment and the situation. Low-context cultures use a linear, sequential building block (bottom-up) approach to information processing in which meaning is constructed” (p.185). In this regard, students who use holistic thought processing are more likely to be disadvantaged in mainstream mathematics classrooms. This is because Westernised mathematics is presented as broken into parts with limited connections made between concepts and with the students’ culture. It potentially conflicts with how they learn. If this is to change the curriculum needs to be made more culture-sensitive and community orientated so that students know and understand what they are learning and for what purposes.

Property Education : an evaluation of how well undergraduate property students are prepared for commencing their careers

The evolution of property education to adapt to the changing business environment requires changes to course content, method of delivery and assessment. Many universities have a special interest in understanding how the students transition in and transition out of the property programs. The impact of the first year student experience is often easier to assess through students’ progression in the course and performance in their intermediate and advanced units. However, the students’ success in transitioning from university student to property professional is often more difficult to determine. In an environment where many property students commence their professional careers while still completing their undergraduate property qualification, a survey of current final year students was undertaken to identify the students’ perception of their level of preparedness for entry into the professional world. This study has also been informed by feedback received from and informal discussions held with industry representative bodies, alumni and senior members of professional organisations. The QUT UD40 Bachelor of Urban Development, Property Economics course has been designed to achieve graduate capabilities in core technical skills and generic professional skills which are required by property professionals. The results of this study were that some units in the program were perceived to provide direct preparation for students commencing their professional careers whilst the impact of other units was less tangible. Valuable feedback received during the study included an assessment of the relevance of many multi-disciplinary units, the appropriateness of the programming of units within the course and the appropriateness of repetition of content during the course. The further research question arises as to how universities can better assist students in the transition to the professional environment when frequently this occurs prior to completion of the property course.

A holistic approach to the support and engagement of first year students : a retention strategy

Institutions should enact holistic approaches that address students’ personal, social and academic engagement in the early weeks of first year to facilitate retention (Nelson, Kift & Clarke, 2008). This holistic approach is central to the FYE program at Queensland University of Technology (QUT), which was established to maximise learning engagement and hence positively influence the retention of commencing students. The program aims to • engage students in their learning through an intentionally designed and enacted curriculum (Kift, 2008) • facilitate timely access to life and learning support • promote a sense of belonging to the discipline, cohort and profession. The FYE program’s aims are achieved by strategic alliances between academic and professional staff across the institution.

A holistic approach to the support and engagement of first year students : a retention strategy.

Institutions should enact holistic approaches that address students’ personal, social and academic engagement in the early weeks of first year to facilitate retention (Nelson, Kift & Clarke, 2008). This holistic approach is central to the FYE program at Queensland University of Technology (QUT), which was established to maximise learning engagement and hence positively influence the retention of commencing students.

Measuring cognitive and dispositional characteristics of creativity in elementary students

This article describes the theoretical underpinning and development of a measurement instrument that provides teachers with a tool to observe the personal creativity characteristics of individual students. The instrument was developed by compiling a list of characteristics derived from the literature to be indicative of the personal characteristics of creative people. The list was then reduced by grouping like characteristics to 9 cognitive and dispositional traits that were considered appropriate for elementary students. The 9-item instrument was then administered in 24 classrooms to 520 Year 6 and Year 7 students. Factor analysis using maximum likelihood extraction with an oblimin rotation revealed a single factor with an eigenvalue greater than 1 and accounting for 63% of the variance. All 9 items on this factor loaded at .72 or greater. The results indicated that the Creativity Checklist has very high internal consistency and is a reliable measurement instrument (a = .93).

Seeing is understanding : the effect of visualisation in understanding programming concepts

How and why visualisations support learning was the subject of this qualitative instrumental collective case study. Five computer programming languages (PHP, Visual Basic, Alice, GameMaker, and RoboLab) supporting differing degrees of visualisation were used as cases to explore the effectiveness of software visualisation to develop fundamental computer programming concepts (sequence, iteration, selection, and modularity). Cognitive theories of visual and auditory processing, cognitive load, and mental models provided a framework in which student cognitive development was tracked and measured by thirty-one 15-17 year old students drawn from a Queensland metropolitan secondary private girls’ school, as active participants in the research. Seventeen findings in three sections increase our understanding of the effects of visualisation on the learning process. The study extended the use of mental model theory to track the learning process, and demonstrated application of student research based metacognitive analysis on individual and peer cognitive development as a means to support research and as an approach to teaching. The findings also forward an explanation for failures in previous software visualisation studies, in particular the study has demonstrated that for the cases examined, where complex concepts are being developed, the mixing of auditory (or text) and visual elements can result in excessive cognitive load and impede learning. This finding provides a framework for selecting the most appropriate instructional programming language based on the cognitive complexity of the concepts under study.

Training young people as researchers to investigate engagement and disengagement in the middle years

This paper reports on the first stage of a study that used Young People as Researchers to investigate the phenomenon of middle-year student engagement and disengagement. The first stage of the study focused on a two-day workshop that provided training for students and teachers from four secondary schools in conducting research in their schools. An overview of the three stages is presented and the workshop procedures and example activities for Stage 1 of the Young People as Researchers model are described. Further to this, the paper reports on data collected in the workshop to address the research question: How do middleyear students describe engagement and disengagement?

Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

Visuacy, imagination, and engagement

Australia’s National Review of Visual Education (DEEWR, 2009) asserts the primacy of visual language ability, or ‘visuacy” in problem-solving. This paper reports on a recent university/schools research project with ‘at risk’ middle school students in which visuacy was promoted as a primary medium for obtaining data relating to issues of immediate concern to the students. Using a students-as-researchers approach, the project investigated middle school students’ perspectives on school engagement and disengagement. In this project, novice researchers used a variety of data gathering methods including photography, video interviews and drawn images as well as more traditional verbal methods, such as interviews, and quantitative methods, such as questionnaires. Engaging student imagination was a key focus of the approach taken by the project, acknowledging that student participants may be reluctant to enter dialogue with teachers and researchers on matters to which they have previously had little input. Students who have previously been marginalized and prevented from contributing their voices to educational forums often have difficulty in adjusting to the novelty of collaborative research with adults (Rudduck, 2003) and may be uncertain of their own place in the relationship that defines teacher/student interactions. It is argued that the project’s promotion of visuacy, alongside more traditional literacies and numeracy in education research, helped to overcome these concerns, engaged the imaginations of the student researchers, and provided a medium for the expression of the voices of marginalised young people.