Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

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.

Preventing consumer credit over-commitment and irresponsible lending in Australia

Mirroring the trends in other developed countries, levels of household debt in Australia have risen markedly in recent years. As one example, the total amount lent by banks to individuals has risen from $175.5 billion in August 1995 to $590.5 billion in August 2005.1 Consumer groups an~ media commentators here have long raised concerns about the risks of increasing levels of household debt and over-commitment, linking these issues at least in part to irresponsible lending practices. And more recently, the Reserve Bank Governor has also expressed concerns about the ability 'of some households to manage if personal or economic circumstances change.2

Comprehension as social and intellectual practice : rebuilding curriculum in low socioeconomic and cultural minority schools

This article reframes the concept of comprehension as a social and intellectual practice. It reviews current approaches to reading instruction for linguistically and culturally diverse and low socioeconomic students, noting an emphasis on comprehension as autonomous skills. The Four Resources model (Freebody & Luke, 1990) is used to make the case for the integration of comprehension instruction with an emphasis on student cultural and community knowledge, and substantive intellectual and sociocultural content in elementary school curricula. Illustrations are drawn from research underway on the teaching of literacy in primary schools in low SES communities.

Using concept mapping to scaffold learning for students who experience learning difficulties in science classes

In order to develop scientific literacy students need the cognitive tools that enable them to read and evaluate science texts. One cognitive tool that has been widely used in science education to aid the development of conceptual understanding is concept mapping. However, it has been found some students experience difficulty with concept map construction. This study reports on the development and evaluation of an instructional sequence that was used to scaffold the concept-mapping process when middle school students who were experiencing difficulty with science learning used concept mapping to summarise a chapter of a science text. In this study individual differences in working memory functioning are suggested as one reason that students experience difficulty with concept map construction. The study was conducted using a design-based research methodology in the school’s learning support centre. The analysis of student work samples collected during the two-year study identified some of the difficulties and benefits associated with the use of scaffolded concept mapping with these students. The observations made during this study highlight the difficulty that some students experience with the use of concept mapping as a means of developing an understanding of science concepts and the amount of instructional support that is required for such understanding to develop. Specifically, the findings of the study support the use of multi-component, multi-modal instructional techniques to facilitate the development of conceptual understanding with students who experience difficulty with science learning. In addition, the important roles of interactive dialogue and metacognition in the development of conceptual understanding are identified.

Analysing Seasonal Health Data

Seasonal patterns have been found in a remarkable range of health conditions, including birth defects, respiratory infections and cardiovascular disease. Accurately estimating the size and timing of seasonal peaks in disease incidence is an aid to understanding the causes and possibly to developing interventions. With global warming increasing the intensity of seasonal weather patterns around the world, a review of the methods for estimating seasonal effects on health is timely. This is the first book on statistical methods for seasonal data written for a health audience. It describes methods for a range of outcomes (including continuous, count and binomial data) and demonstrates appropriate techniques for summarising and modelling these data. It has a practical focus and uses interesting examples to motivate and illustrate the methods. The statistical procedures and example data sets are available in an R package called ‘season’. Adrian Barnett is a senior research fellow at Queensland University of Technology, Australia. Annette Dobson is a Professor of Biostatistics at The University of Queensland, Australia. Both are experienced medical statisticians with a commitment to statistical education and have previously collaborated in research in the methodological developments and applications of biostatistics, especially to time series data. Among other projects, they worked together on revising the well-known textbook "An Introduction to Generalized Linear Models," third edition, Chapman Hall/CRC, 2008. In their new book they share their knowledge of statistical methods for examining seasonal patterns in health.

Critical literacies in schools : a primer

A review of theoretical principals and practice of school-based approaches to critical literacy, with a specific focus on the middle years of schooling.

Comprehension and content : planning literacy curriculum in low socioeconomic and culturally diverse schools

This article reframes comprehension as a social and intellectual practice. It reviews literature on current approaches to reading instruction for linguistically and culturally diverse and low socioeconomic students, noting the current policy emphasis on the teaching of comprehension as autonomous skills and ‘strategies’. The Four Resources model (Freebody & Luke, 1990) is used to situate comprehension instruction with an emphasis on student cultural and community knowledge, and substantive intellectual and sociocultural content in elementary and middle school curricula. Illustrations are drawn from research underway on the teaching of literacy in low socioeconomic schools.

Personal epistemology in pre-service teachers : belief changes throughout a teacher education course

Classrooms of the 21st century are complex systems. They support diverse learners from varied contexts and function in a “messy” bricolage of policy contexts. This complexity is also evident in the nature of teaching and learning deployed in these classrooms. There is also, in current contexts, a general expectation that teachers will support students to construct, rather than simply receive knowledge. This process of constructing knowledge requires a focus on critical thinking in complex social and real world contexts (see also Elen & Clarebout, 2001; Yang, Chang & Hsu 2008). Critical thinking, which involves the identification and evaluation of multiple perspectives when making decisions, is a process of knowing – a tool of wisdom (Kuhn & Udell, 2001). Schommer-Aikens, Bird and Bakken (2010) refer to classrooms that encourage critical thinking as “epistemologically based” in which “the teacher encourages his/her students to look for connections among concepts within the text, with their prior knowledge, and with concepts found in the world beyond themselves” (p. 48).

NAPLAN, a high priority or . . . ? Statements about its purpose in Queensland schools

This paper reports on statements from Professional Development participants who were asked to comment on NAPLAN. The participants were involved in a project designed by the YuMi Deadly Centre (YDC) for implementation into 25 Queensland School to enhance the teaching and learning of mathematics to Aboriginal and Torres Strait Islander students and low SES students. Using an action research framework and a survey questionnaire, the preliminary data obtained from participating principals is mixed, with statements indicating that NAPLAN is a high priority for some schools while others indicated that it does not “tell” the whole story of student learning.

Contextualising the teaching and learning of measurement within Torres Strait Islander schools

A one year mathematics project that focused on measurement was conducted with six Torres Strait Islander schools and communities. Its key focus was to contextualise the teaching and learning of measurement within the students’ culture, communities and home languages. There were six teachers and two teacher aides who participated in the project. This paper reports on the findings from the teachers’ and teacher aides’ survey questionnaire used in the first Professional Development session to identify: a) teachers’ experience of teaching in Torres Strait Islands, b) teachers’ beliefs about effective ways to teach Torres Strait Islander students, and c) contexualising measurement within Torres Strait Islander culture, Communities and home languages. A wide range of differing levels of knowledge and understanding about how to contextualise measurement to support student learning were identified and analysed. For example, an Indigenous teacher claimed that mathematics and the environment are relational, that is, they are not discrete and in isolation from one another, rather they interconnect with mathematical ideas emerging from the environment of the Torres Strait Communities.

Tissue engineered prefabricated vascularized flaps

BACKGROUND.: Microvascular free tissue transfer has become increasingly popular in the reconstruction of head and neck defects, but it also has its disadvantages. Tissue engineering allows the generation of neo-tissue for implantation, but these tissues are often avascular. We propose to combine tissue-engineering techniques together with flap prefabrication techniques to generate a prefabricated vascularized soft tissue flap. METHODS: Human dermal fibroblasts (HDFs) labeled with fluorescein diacetate were static seeded onto polylactic-co-glycolic acid-collagen (PLGA-c) mesh. Controls were plain PLGA-c mesh. The femoral artery and vein of the nude rat was ligated and used as a vascular carrier for the constructs. After 4 weeks of implantation, the constructs were assessed by gross morphology, routine histology, Masson trichrome, and cell viability determined by green fluorescence. RESULTS: All the constructs maintained their initial shape and dimensions. Angiogenesis was evident in all the constructs with neo-capillary formation within the PLGA-c mesh seen. HDFs proliferated and filled the interyarn spaces of the PLGA-c mesh, while unseeded PLGA-c mesh remained relatively acellular. Cell tracer study indicated that the seeded HDFs remained viable and closely associated to remaining PLGA-c fibers. Collagen formation was more abundant in the constructs seeded with HDFs. CONCLUSIONS: PLGA-c, enveloped by a cell sheet composed of fibroblasts, can serve as a suitable scaffold for generation of a soft tissue flap. A ligated arteriovenous pedicle can serve as a vascular carrier for the generation of a tissue engineered vascularized flap.