Conference Paper

  • This paper focuses on developing students' informal ideas of inference and argumentative skills. This topic is of current interest to many researchers and teachers of statistics. We study fifth graders' learning processes in an exploratory interdisciplinary learning environment that usesTinkerPlots to scaffold and extend students' statistical reasoning. The careful design of the learning trajectory based on growing samples heuristics coupled with the unique features ofTinkerPlots were found instrumental in supporting students' multiplicative reasoning, aggregate reasoning, acknowledging the value of large samples, and accounting for variability. These processes were accompanied by greater ability to verbalize, explain and argue about data-based inferences. In the light of the analysis, a description of what it may mean to begin reasoning and arguing about inference by young students is proposed.

  • This paper will focus on another aspect of the teaching experiment that has heretofore been alluded to in the literature, but never fully addressed; namely, the epistemological considerations one must make when contemplating the teaching experiment as a research methodology. While the following remarks may well apply to any subject matter area, they will be couched in terms of mathematics education, since this is the area of our own interest and specialty.

  • In 1997 a skills inventory was developed to define the statistical literacy attribute for a University of Wollongong graduate. Identification of the inventory elements, however,represented only the first step in the process: Once the definition was accepted, there wasa need to translate it into a program that provided students with opportunities to developand demonstrate the required skills.Developing the statistical literacy program has raised a number of questions. In this paperwe reflect upon our efforts to resolve these and to translate the skills inventory into aneffective program that can be applied across the University. Our choice of an onlineenvironment has implications for others who are contemplating developing similarprograms. A particular challenge is being faced in pushing the boundaries of the relevanttechnologies as we strive to achieve a level of interactivity that we think is necessary toengage students in learning.

  • In 2000 the UK Government published a paper on Higher Education (HE) outlining, amongst other things, its desire that all new staff should receive proper training in lecturing/teaching at the induction stage of their careers and existing lecturing/teaching staff should undertake Continuing Professional Development (CPD). The general expectation was that in most universities the CPD material would be generic (non-subject-specific) and would be delievered by educational or staff development groups. As a similar time a Learning and Teaching Support Network (LTSN) comprising 24 Subject Centres was established for HE to promote good practice, and its dissemination, in teaching and learning. One of these Centres was in Mathematics, Statistics and OR (MSOR), with responsibility for Statstics and OR resting jointly with the Univeristy of Nottingham Trent University. Also at the same time the Institute for Learning and Teaching in HE (ILTHE) was set up to establish a UK professional body of teachers in HE.

  • Attempts to identify the development of students' knowledge in science, mathematics, and other disciplines have included proposals concerning the development of naive theories or framework theories (Carey, 1999; Ioannides & Vosniadou, 2002), abstractions or abstract structures (Fuchs et al., 2003; Hershkowitz, Schwarz, & Dreyfus, 2001), and abstract rules or schemata (Gentner & Medina, 1998; Reed, 1993). While all these ideas represent different research methods and traditions as well as attempts to explain different aspects of learning and performance, I argue that all of them suggest assumptions about the abstract nature of students' naive and developing knowledge that deserve scrutiny. This notion of abstraction, while sometimes explicit, is often hidden in researchers' broad assertions that students make use of some single idea, meaning, theory, or knowledge structure across a wide span of situations with marked contextual differences. This paper calls on researchers across theses research agendas to make more careful distinctions between claims purporting to identify apparent consistency in students' performance and claims concerning that nature or structure of the knowledge that supports that performance.

  • In response to the critical role that information and data play in our technological society, there have been national calls for reform in statistical education al all grade levels (Lajoie Romberg, 1998; National Council of Teachers of Mathematics, 1998; School Curriculum and Assessment Authority & Curriculum and Assessment Authority for Wales, 1996; Australian Education Council, 1994). These calls for reform have advocated a more pervasive approach to the study of statistics, one that includes describing, organizing and reducing, representing, and interpreting data. This broadened perspective has created the need for further research on the learning and teaching of statistics, especially at the elementary grades, where there has been a tendency to focus narrowly on some aspects of graphing rather than the broader topics of data handling and data analysis (Shaughness, Garfield, & Greer, 1996).

  • In this article we describe two types of informal, formative assessment items that we are developing: "What Went Wrong?" exercises and "Practice Problems."<br>In this paper, we further describe our goals for these assessments and briefly suggest the principles on which they are based. Then we present several illustrative examples of the assessment items. We conclude with some preliminary evaluation results.

  • Learning to make good choices in a probabilistic environmentrequires that the Decision Maker resolves the tension betweenexploration (learning about all available options) andexploitation (consistently choosing the best option in order tomaximize rewards). We present a mathematical learningmodel that makes selections in a repeated-choice probabilistictask based on the expected payoff associated with each optionand the information gain that will result from choosing thatoption. This model can be used to analyze the relative impactof exploration and exploitation over time and under differentconditions. It predicts the aggregated and individual learningtrajectories of participants in various versions of the tasksufficiently well to support our basic argument: Informationgain is a valid and rational criterion underlying humandecision making. Future modeling work will be addressingthe exact nature of the interaction between exploration andexploitation.

  • In this paper first we present results from an initial assessment to a sample of 132 trainee teachers at the Faculty of Education, University of Granada that show they frequently hold three probabilistic misconceptions. We secondly analyse two experiments where simulation served to confront trainee primary school teachers with their probability misconceptions. At the same time these experiments served to present these teachers with some activities based on a constructivist and social approach to teaching. The activities seemed to influence a change of conceptions for a sizeable part of students with a previous misconception; however, a large proportion of the students were still unable to give a correct response after simulation. We conclude that a better prior training for teachers as well as permanent support for these teachers from University departments and research groups is an urgent necessity.

  • This students examined students' development of reasoning about quantitative bivariate data during a one-semester university-level introductory statistics course. There were three research questions of interest: (1) What is the nature, or pattern of change in students' development in reasoning about bivariate data?; (2) Is the sequencing of bivariate data within a course associated with changes in the pattern of change in students' reasoning about bivariate data?; and (3) Are changes in students' reasoning about the foundational concepts of distribution associated with changes in the pattern of development of students' reasoning about bivariate data?<br>Students' covariational and distributional reasoning were measured four times during four sections of an introductory statistics course using instruments developed by the NSF-funded ARTIST project. Two instructors were used as blocks to randomly assign each of four sections of the course to one of two different instructional sequences.<br>Data were analyzed using linear mixed-effects model (LMM) methodology. The results of the analyses suggest that students tend to exibit both linear and quadratic rates of change in their development of covariational reasoning. The results also suggest that the instructional sequence did not have a statistically significant effect of development of reasoning. There was some evidence that students' development of reasoning about univariate distribution was significantly positively related to the quadratic rate of development of their reasoning about bivariate data.