The purpose of the study was to identify the important aspects of statistical knowledge needed for teaching at the middle school level and to assess prospective teachers ’ conceptions and misconceptions of statistics related to teaching data analysis. An analytic study of the current literature, including state and national standards, was conducted to identify the important aspects of statistical knowledge for teaching. A written assessment instrument was developed and administered to a sample of 42 prospective middle school teachers. The purpose of the instrument was to gather data in order to describe teachers ’ conceptions for teaching data analysis and statistics. A subset of the sample (n = 7) was interviewed to provide deeper insight into their conceptions and to assure reliability of the instrument. Results show that state and national standards differ greatly on their expectations of what students and teachers should know about data analysis and statistics. The variation is also large for the emphasis or importance given to the content. The average emphasis of all the documents reviewed is given to the selection and proper use of graphical representations of data, and measures of center and spread. Important aspects of knowledge applied to teaching are proper selection and use of teaching strategies and inferring students ’ understanding from their work and discourse. Prospective teachers that participated in this study performed better at the level of pure statistical knowledge than at the level of application of this knowledge to teaching. In particular, they showed abilities on reading, interpreting, and constructing graphical representations, and computing measures of center and spread. Difficulties were shown in judging students ’ comments and identifying students ’ mistakes. ©Copyright by

We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use selfgenerated external visual representations while solving probability problems. The types of visual representations used include: reorganization of the given information, pictures, novel schematic representations, trees, outcome listings, contingency tables, and Venn diagrams. The frequency of use of each of these different external visual representations depended on the type of probability problem being solved. We interpret these findings as showing that problem solvers attempt to select representations appropriate to the problem structure, and that the appropriateness of the representation is determined by the problem’s underlying schema.

histogram; bar graph; variation

Most institutions of higher learning in the United States offer introductory statistics courses in a variety of flavors. Integration of the subject-specific concepts with the basic applied statistical techniques should be the primary goal of these flavored courses. Solely lecture-based traditional instruction method is not suitable to satisfying this objective. We argue for the incorporation of business-style cases into the introductory statistics curriculum using Constructivist learning theory and the notion of the “liberal arts ” education. A typical business case setup is presented and its compatibility with an introductory statistics course is assessed. Finally, a sample business-style case for the application of the simple linear regression is provided.

Les résultats sont tirés d’une étude plus large sur les stratégies de résolution que des élèves de 2 e, 3 e et 4 e secondaires (14 à 16 ans) utilisent pour résoudre des problèmes de moyenne. Dans ce texte, les résolutions de trois problèmes seront analysées. Ces problèmes ont été composés de telle sorte que nous puissions distinguer entre la capacité des élèves de calculer une moyenne et celle de saisir les liens qu’il y a entre la modification de l’effectif et d’une donnée et celle de la moyenne. Les problèmes visaient aussi à tester l’influence d’une donnée égale à zéro, influence signalée dans les études précédentes. Les résultats de la présente étude font voir que, dans le contexte choisi, le type et le sens des modifications effectuées influencent les comportements des élèves et que des conceptions inadéquates ou des glissements de sens apparaissent dans certaines situations et pas dans d’autres. Note: Un long resume en anglais precede l’article qui est ecrit en francais. Mots-clés: Recherche en enseignement de la statistique; Moyenne arithmétique; Enseignement secondaire The results are taken from a much larger study on the strategies that pupils in the 2nd, 3rd and 4th stages at secondary school (ages 14-16) use for solving problems concerning the mean. In this paper the solutions of three problems are analysed. These problems have been formulated to be of such a kind that we can distinguish between the ability of pupils to calculate a mean, and that of realising the effect of a change in the number of observations or in the value of an observation, on the mean. The problems were also seen to test the influence of a value equal to zero on the

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith, Henningsen, & Silver, 2000). Standards-era textbook series devoted significantly more attention to probability than other series; more than half of all tasks analyzed were located in Standards-era textbooks. More than 85 % of tasks for six series required low levels of cognitive demand, whereas the majority of tasks in the alternative series from the Standards era required high levels of cognitive demand. Recommendations for future research are offered.

This is a phenomenological study that examines how teachers perceive students ’ thinking about chance situations when students have used heuristics-based reasoning, and how teachers help students to overcome that heuristic-based reasoning. The particular heuristic examined in this study is the representativeness, a heuristic widely explored in the literature. In-depth interviews were used to elicit the perceptions of five statistics teachers from different schools in a southeastern U.S. state. Each teacher participated in two onehour interviews where they were confronted with tasks related to the heuristic of representativeness. Teachers were asked to predict students ’ responses, students ’ difficulties and teachers ’ interventions. Interviews were recorded and transcribed for hermeneutic analysis. Results suggest that expert teachers are more accurate in predicting students ’ difficulties and in providing pedagogical strategies than novice teachers. KEYWORDS. Expert-Novice, Teacher Knowledge, Probabilistic Thinking, Representativeness.

The general acceptance afforded the national image of Australians as gamblers has given gambling a legitimacy rare in other countries. Concerns with the social effects of this have led many State governments to implement programs to counteract negative social effects. The Queensland Treasury has allocated funds for the development of teaching resources for this purpose including the development of the Unit presented here. In 2006 the author constructed a Unit of work for Queensland Senior Secondary (Years 11 and 12) Mathematics classes entitled “The mathematics of responsible gambling ” as a consultancy to the Queensland State Government. Towards the end of 2007 the “Secondary Mathematics Teaching Resources Kit ” was distributed to all secondary government schools. This paper describes the activities of the Unit, their relationship to the Queensland Syllabus objectives, the research upon which the Unit is based, and the current research into the effectiveness of its implementation which began in November 2008 and will continue in February of 2009.

Abstract Based on deployment throughout a term, this paper suggests the potential of a computer-based approach to promote learner awareness of their knowledge states. We consider in particular the extent to which students are interested in finding out about their misconceptions in the context of independent study. It was found that many first year students held misconceptions in introductory electrical circuits and mathematics courses at some stage of their learning, and most viewed information about their misconceptions to assist them in identifying their problems. We suggest, therefore, that an approach of highlighting an individual's misconceptions can be found useful by students to help them recognise their knowledge, difficulties and misconceptions to support self-assessment and facilitate their identification of an appropriate focus of their efforts, to meet their learning needs. Keywords misconceptions; electrical circuits; mathematics; engineering undergraduates; open learner model The existence of learner problems and misconceptions is well-recognised at both pre-university and university level in electrical circuits 1,2,3,4,5 and mathematics 6,7,8,9. As an example of difficulties students may have, consider the misconception that potential difference is caused by current flow (whereas in fact, the converse is true 3). This refers to the relationship between potential difference and potential energy, and can be illustrated by making an analogy to gravitational potential energy: when water flows downhill it is because it is flowing from a region of higher gravitational potential energy to one

This exploratory study investigated teachers ’ perception of students ’ thinking about chance. In particular, the study explored how teachers anticipated and explained students’ difficulties with the idea of chance, and the strategies teachers claimed to use to help students reorganize their thinking. Two teachers, one expert and one novice, members of an AP Statistics learning community, participated in this study. They were observed in the learning community meetings, and interviewed in depth. The interviews explored four core ideas in statistics that have been associated with the source of students ’ difficulties about chance: sample space, randomness, independence, and the law of large numbers. The results of this study highlighted that the expert and novice teachers exhibited differences in the way they perceived students ’ difficulties and in the way they dealt with them.