Abstract not found

This paper considers the development of school students ’ understanding of three terms that are fundamental to statistical literacy: sample, random, and variation. A total of 738 students in grades 3, 5, 7, and 9 were asked in a survey to define and give an example for the word sample. Of these, 379 students in grades 7 and 9 were also asked about the words random and variation. Responses were used to describe developmental levels overall and to document differences across grades on the understanding of these terms. Changes in performance were also monitored after lessons on chance and data emphasising variation for 335 students. After two-years, 199 of these students and a further 209 students who were surveyed originally but did not take part in specialised lessons, were surveyed again. The difference after two-years between the performance of students who experienced the specialised lessons and those who did not was considered, revealing no differences in longitudinal performance. For students in grades 7 and 9 the association of performance on the three terms was explored. Implications for mathematics and literacy educators are discussed.

Many of the designations used by the manufactures and sellers to distinguish their products are claimed as trademarks. Every attempt has been made to supply trademark information about manufactures and their products mentioned in this dissertation. A list of the trademark designations and their owners appears below. Trademark notice Access, Netmeeting, Sharepoint Team Services, Windows, and Windows 2000 Server are trademarks of Microsoft Corporation Post-it is a trademark of 3M Linux is a trademark of Linus Torvalds Professional Quest is a trademark of Dipolar Pty Limited Yahoo! Groups is a trademark of Yahoo! Domino is a trademark of IBM/Lotus Authorware is a trademark of Macromedia Toolbook is a trademark of Click2Learn

This paper describes the first year of a three-year collaborative curriculum development project in a secondary school that is underpinned by a theoretical statistical thinking framework. The teachers developed and implemented the statistics unit for their Year 11 (15 year-olds) classes based on their understanding of the framework and within the constraints of the national curriculum and assessment. Data gathered on the development of the statistics unit and its subsequent implementation are presented and discussed. An initial finding was that teachers were able to begin changing their practice to foster students ’ statistical thinking that was consonant with the framework. The influences of the framework, identifying problematic situations, collaboration, and assessment, which are impinging on the curriculum development, are elaborated upon and questions are raised about the nature of the development.

Group decision making methods such as Multi-Criteria Decision Making (MCDM) have been developed extensively, but their organizational use for group decision making has been difficult. According to Arrow's Impossibility Theorem, one possible reason is that a group decision outcome could never satisfy every decision maker's individual preference. This paper proposes a fuzzy GSS (Group Support System) approach to improve the quality of the group decision outcome. The fuzzy GSS approach integrates a fuzzy MCDM model and a structured group decision making process with a GSS. The fuzzy MCDM model includes fuzzy individual preference generation and group aggregation. Supported by the GSS, the structured decision making process makes group participation effective. The proposed approach aims at providing more decision information, and enhancing group consensus, satisfaction and understanding of the decision outcome. This paper also postulates that the fuzzy GSS approach enhances group consensus, satisfaction and understanding of the group decision outcome. An empirical study was conducted to test the research predictions.

This study documented efforts to facilitate ideas of beginning inference in novice grade 7 students. A design experiment allowed modified teaching opportunities in light of observation of components of a framework adapted from that developed by Pfannkuch for teaching informal inference with box plots. Box plots were replaced by hat plots, a feature available with the software TinkerPlots TM. Data in TinkerPlots files were analyzed on four occasions and observed responses to tasks were categorized using a hierarchical model. The observed outcomes provided evidence of change in students’ appreciation of beginning inference over the four sessions. Suggestions for change are made for the use of the framework in association with the intervention and the software to enhance understanding of beginning inference.

Traditional curricula in the social sciences result in students having statistical knowledge that is inert and consequently of low transferability. This is in part because these curricula separate mathematical and probabilistic content (present in statistics service courses) from the context in which the collection of observational and experimental data is designed (present in courses about research methods). This paper proposes a curriculum that removes this separation by merging the two domains into the research competency, in line with emergent pedagogical insights. This study describes the new curriculum and compares some preliminary learning outcomes of students following the proposed integrated competency-based curriculum with that of students following the traditional curriculum. The results suggest a higher level of understanding is achieved through the integrated approach.

Several factors contribute to the importance of students developing statistical literacy skills at the school level. First is the expectation for participation as citizens in an information and data driven age where decision-making is likely to be based on critical skills from the realms of statistical literacy. Wallman (1993) foresaw this as both a public and private issue and Gal (2002) suggested two components required of adults. One component is the ability to interpret and evaluate critically statistical information in a variety of contexts and the other is the ability to communicate this understanding in a fashion that can have an impact on decision-making. With respect to these components of adult statistical literacy, Gal also noted the need for dispositions associated with attitudes and beliefs that would motivate citizens to be critical thinkers in this arena. To have adults meeting the goals set by Wallman (1993) and Gal (2002) it is necessary to begin at the school level. Reform to the mathematics curriculum in many countries from around 1990 (e.g., National Council of Teachers of Mathematics [NCTM], 1989; Australian Education Council [AEC], 1991), which brought topics related to statistics and probability into the school curriculum, provided a starting point for consideration of statistical literacy. Although curriculum documents focus mainly on the traditional stages in statistical investigations, they at least

This paper will report on the use of a three-tiered model to assess the statistical understanding of school students in the context of a media report. Data from 229 Australian students will be presented to show levels of performance in relation to the model reflecting increasing complexity of response. Four groups of students were tested at two-year intervals with one of these groups also tested after four years. The media item used in this report contained a misleading claim about a population based on an unrepresentative sample. The assessment was designed to determine if students could question the claim. Results indicate that educators have a long way to go in creating a statistically literate citizenry.

This paper discusses the long-term cognitive development of the meaning of symbols in algebra, starting with symbols in arithmetic as procedure, process and concept, on to generalised arithmetic, evaluation algebra (treating expressions as evaluation processes), manipulation algebra and then axiomatic algebra. We discuss cognitive changes required to move from one form of algebra to another, changes in meaning that occur and epistemological obstacles that arise in the development. Cognitive development of arithmetic leading to algebra Early whole number arithmetic has been widely researched (Fuson, 1992). It is well known that processes of addition and subtraction become seen as concepts of sum and difference, a viewpoint that continues to be valuable in algebra. These phenomena are part of a more general ‘process-object ’ theory of cognitive development (Piaget, 1985; Dienes, 1960; Davis, 1983), expressed succinctly by Dubinsky (1986, 1991) and Sfard (1991, 1995) in terms of ‘encapsulation ’ or ‘reification ’ of a process as an object. (See Tall, Thomas, Davis, Gray, & Simpson, 2000 for a critical summary.) This theory grows from Piaget’s idea (1985, p. 45, but originated much earlier) in which “actions and operations become thematized objects of thought or assimilation”. Gray & Tall (1994) took a more pragmatic view of this theory, noting that symbols