Individual differences in learning from worked examples by senior secondary mathematics students

The primary purpose of this research was to examine individual differences in learning from worked examples. By integrating cognitive style theory and cognitive load theory, it was hypothesised that an interaction existed between individual cognitive style and the structure and presentation of worked examples in their effect upon subsequent student problem solving. In particular, it was hypothesised that Analytic-Verbalisers, Analytic-Imagers, and Wholist-lmagers would perform better on a posttest after learning from structured-pictorial worked examples than after learning from unstructured worked examples. For Analytic-Verbalisers it was reasoned that the cognitive effort required to impose structure on unstructured worked examples would hinder learning. Alternatively, it was expected that Wholist-Verbalisers would display superior performances after learning from unstructured worked examples than after learning from structured-pictorial worked examples. The images of the structured-pictorial format, incongruent with the Wholist-Verbaliser style, would be expected to split attention between the text and the diagrams. The information contained in the images would also be a source of redundancy and not easily ignored in the integrated structured-pictorial format. Despite a number of authors having emphasised the need to include individual differences as a fundamental component of problem solving within domainspecific subjects such as mathematics, few studies have attempted to investigate a relationship between mathematical or science instructional method, cognitive style, and problem solving. Cognitive style theory proposes that the structure and presentation of learning material is likely to affect each of the four cognitive styles differently. No study could be found which has used Riding's (1997) model of cognitive style as a framework for examining the interaction between the structural presentation of worked examples and an individual's cognitive style. 269 Year 12 Mathematics B students from five urban and rural secondary schools in Queensland, Australia participated in the main study. A factorial (three treatments by four cognitive styles) between-subjects multivariate analysis of variance indicated a statistically significant interaction. As the difficulty of the posttest components increased, the empirical evidence supporting the research hypotheses became more pronounced. The rigour of the study's theoretical framework was further tested by the construction of a measure of instructional efficiency, based on an index of cognitive load, and the construction of a measure of problem-solving efficiency, based on problem-solving time. The consistent empirical evidence within this study that learning from worked examples is affected by an interaction of cognitive style and the structure and presentation of the worked examples emphasises the need to consider individual differences among senior secondary mathematics students to enhance educational opportunities. Implications for teaching and learning are discussed and recommendations for further research are outlined.

Eucharistic rituals in Catholic primary schools in the Archdiocese of Brisbane : a study of administrators' conceptions

The focus of this study is the celebration of Eucharist in Catholic primary schools within the Archdiocese of Brisbane. The context of the contemporary Australian Catholic primary school embodies certain 'problematical realities' in relation to the time-honoured way in which school Eucharistic rituals have been celebrated. These contemporary realities raise a number of issues that impact on school celebrations of Eucharist. The purpose of this study is to explore administrators' differing conceptions of school Eucharistic rituals in an attempt to investigate some of these issues and assist members of individual school communities as they strive to make celebrations of Eucharist appropriate and meaningful for the group gathered. The phenomenographic research approach was adopted, as it is well suited to the purpose of this study and the nature of the research question. Phenomenography is essentially a study of variation. It attempts to map the 'whole' phenomenon under investigation by describing on equal terms all conceptions of the phenomenon and establishing an ordered relationship among them. The purpose of this study and the nature of the research question necessitate an approach that allows the identification and description of the different ways in which administrators' experience school Eucharistic rituals. Accordingly, phenomenography was selected. Members of the Administration Team, namely the principal, the APRE (Assistant to the Principal Religious Education) and, in larger primary schools, the AP A (Assistant to the Principal Administration) share responsibility for leading change in Catholic primary schools in the Archdiocese of Brisbane. In practice, however, principals delegate the role of leading the development of the school's religion program and providing leadership in the religious life of the school community to the APRE (Brisbane Catholic Education, 1997). Informants in this study are nineteen APREs from a variety of Catholic primary schools in the Archdiocese of Brisbane. These APREs come from schools across the archdiocese, rather than from within one particular region. Several significant findings resulted from this study. Firstly, the data show that there are significant differences in how APREs' experience school Eucharistic rituals, although the number of these qualitatively different conceptions is quite limited. The study identifies and describes six distinct yet related conceptions of school Eucharistic rituals. The logical relationship among these conceptions (the outcome space) is presented in the form of a diagram with accompanying explication. The variation among the conceptions is best understood and described in terms of three dimensions of the role of Eucharist in the Catholic primary school and is represented on the model of the outcome space. Individual transcripts suggest that individual APREs tend to emphasise some conceptions more than others. It is the contention of the present study that change in the practice of school Eucharistic rituals is unlikely to occur until all of a school community's conceptions are brought out into the open and articulated. As leaders of change, APREs need to be alerted to their own biases and become aware of alternative ways of conceiving school Eucharistic ritual. It is proposed that the different categories of description and dimensions, represented by the model of the outcome space, can be used to help in the process of articulating a school community's conceptions of Eucharist, with the APRE as facilitator of this process. As a result, the school community develops a better understanding of why their particular school does what it does in relation to school Eucharistic rituals.

Validation of FHWA crash models for rural intersections - Lessons learned

A national-level safety analysis tool is needed to complement existing analytical tools for assessment of the safety impacts of roadway design alternatives. FHWA has sponsored the development of the Interactive Highway Safety Design Model (IHSDM), which is roadway design and redesign software that estimates the safety effects of alternative designs. Considering the importance of IHSDM in shaping the future of safety-related transportation investment decisions, FHWA justifiably sponsored research with the sole intent of independently validating some of the statistical models and algorithms in IHSDM. Statistical model validation aims to accomplish many important tasks, including (a) assessment of the logical defensibility of proposed models, (b) assessment of the transferability of models over future time periods and across different geographic locations, and (c) identification of areas in which future model improvements should be made. These three activities are reported for five proposed types of rural intersection crash prediction models. The internal validation of the model revealed that the crash models potentially suffer from omitted variables that affect safety, site selection and countermeasure selection bias, poorly measured and surrogate variables, and misspecification of model functional forms. The external validation indicated the inability of models to perform on par with model estimation performance. Recommendations for improving the state of the practice from this research include the systematic conduct of carefully designed before-and-after studies, improvements in data standardization and collection practices, and the development of analytical methods to combine the results of before-and-after studies with cross-sectional studies in a meaningful and useful way.

Empirical investigation of interactive highway safety design model accident prediction algorithm : Rural intersections

One major gap in transportation system safety management is the ability to assess the safety ramifications of design changes for both new road projects and modifications to existing roads. To fulfill this need, FHWA and its many partners are developing a safety forecasting tool, the Interactive Highway Safety Design Model (IHSDM). The tool will be used by roadway design engineers, safety analysts, and planners throughout the United States. As such, the statistical models embedded in IHSDM will need to be able to forecast safety impacts under a wide range of roadway configurations and environmental conditions for a wide range of driver populations and will need to be able to capture elements of driving risk across states. One of the IHSDM algorithms developed by FHWA and its contractors is for forecasting accidents on rural road segments and rural intersections. The methodological approach is to use predictive models for specific base conditions, with traffic volume information as the sole explanatory variable for crashes, and then to apply regional or state calibration factors and accident modification factors (AMFs) to estimate the impact on accidents of geometric characteristics that differ from the base model conditions. In the majority of past approaches, AMFs are derived from parameter estimates associated with the explanatory variables. A recent study for FHWA used a multistate database to examine in detail the use of the algorithm with the base model-AMF approach and explored alternative base model forms as well as the use of full models that included nontraffic-related variables and other approaches to estimate AMFs. That research effort is reported. The results support the IHSDM methodology.

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.