Theory

  • Research on teacher knowledge has typically examined teachers outside of the classroom in which they use their knowledge. Recognising that it is difficult to separate a teacher's knowledge from the context in which it is used, there has been a move towards studies being conducted in the classroom. Statistics presents its own challenges for teaching and learning compared with mathematics teaching and learning, especially with the growing recognition of and research around statistical thinking. Consequently there is need for an approach to examining teacher knowledge in relation to the actual work of teaching of statistics. This paper suggests a framework for examining the knowledge of primary (elementary) teachers as they engage in teaching statistics. The framework recognises that teacher knowledge is dynamic and dependent on the context of the classroom and students within it.

  • Amongst researchers of statistics education and statistics educators alike, statistical literacy, statistical reasoning and statistical thinking have gained prominence as important learning goals for the teaching of statistics. Careful examination of the three concepts shows that considerable disagreement on their definition still exists, creating problems in the attempts to develop valid and useful measurement instruments. It is argued that the fuzziness of the three constructs stems from the fact that their conception was not motivated by empirical regularities in need of explanation, but rather by the desire to create new perspectives on the future development of statistics education. The inherent ambiguity of the three concepts makes them unsuitable as learning goals for statistics education. By focussing on different aspects of statistical knowledge, however, the intended differentiation in meaningful learning goals can be met in a less disputable way.

  • This paper describes data from the Community Mapping Project (CMP), a set of activities within a summer seminar for high school students. CMP was designed based on the principles of culturally relevant pedagogy to create conditions where students themselves would recognize the relevance of statistics in identifying and describing inequities that face their communities. Using mixed methods we analyzed pre- and post assessments, final projects and process data from video case studies to begin to understand how this learning was organized for the 21 twelfth graders participating in this project. Our qualitative analysis revealed several tensions that emerged between the social justice goals and statistical goals and how those tensions mediated learning. The article may help inform both teachers who wish to rethink their statistics pedagogy, and the designers of culturally relevant curricula.

  • Designers of educational software tools inevitably struggle with the issue of complexity. In general, a simple tool will minimize the time needed to learn it at the expense of range of applications. On the other hand, designing a tool to handle a wide range of applications risks overwhelming students. I contrast the decisions we made regarding complexity when we developed DataScope 15 years ago with those we recently made in designing TinkerPlots, and describe how our more recent tack has served to increase student engagement at the same time it helps them see critical connections among display types. More generally, I suggest that in the attempt to not overwhelm students, too many educational environments managed instead to under whelm them and thus serve to stifle rather than foster learning.

  • Piaget's constructivism and its further developments are used as the conceptual framework to relate, in the learning process, students' age with specific topics in probability and statistics. Such a perspective consists of opposing the notion of chance to that of a reversible sequence and, therefore, to causality. Nevertheless, when the contributions to probability theory developed during the 17th to the 19th centuries are considered, it can be noticed that the concept of chance is a characterization of "our ignorance of the causal chain." This fact motivates two questions which are discussed in this manuscript. The first one consists of understanding what constitutes the breaking-off between Cournot's viewpoint of probability and the traditional one. The second question consists of exploring what kind of probability and statistics teaching would be developed if the traditional viewpoint on chance and probability is considered.

  • In this paper we sketch the history and the philosophy of statistics and probability theory and the connections to its political aspects. Knowledge of the cultural embeddedness of statistics and probability theory is an added value in the teaching thereof. The use of statistics and probability is a phenomenon with which everyone is confronted on a daily basis. Beside literacy, numeracy is an important challenge for education. In order to succeed in this task, the traditional curriculum (technique-oriented and individual, competition-oriented) will need to be sacrificed for a curriculum in which there is room for the cultural aspects of statistics and probability theory. For this purpose, cooperative learning is a didactic entry which is suitable for interaction and critical input of pupils.

  • Expresses concern over the current mathematics education of students and discusses mathematics as a language, including: reading critically, mathematical metaphors, mathematical literature, the nature of knowledge, and how one becomes mathematically literate.

  • We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how this dependence alters the probability of a successful match of dog to owner, and thus alters the expected number of successful matches and the variance of this expected quantity. Finally, we show that a false assumption of independence that results in incorrect probability calculations changes the probability of incorrectly rejecting the null hypothesis (i.e. the Type I error).

  • Reasoning with data is already pervasive in society, and its importance as a life skill is increasing. We argue that the current statistics curriculum in the United Kingdom at the secondary level does not prepare our young people adequately, and suggest ways in which it could be improved.

  • In this paper I propose some basic elements of a model of knowledge structures used in comprehending and generating graphs, with emphasis on the concept of covariation and on the analogical character of graphical representation. I then use this competence model to attempt to organize and interpret some of the existing literature on misconceptions in graphing. Two types of common misconceptions, treating the graph as a picture, and slope-height confusions, will be discussed, as will the earliest recorded use of graphs in the work of Oresme in 1361. One of the motives for studying concepts used in graphing is that it may help us understand the nature of the more general concepts of variable and function and the role that analogue spatial models play in representation.

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