Literature Index

Displaying 371 - 380 of 3326
  • Author(s):
    Schupp, H.
    Editors:
    Davidson, R., & Swift, J.
    Year:
    1986
    Abstract:
    We will present and discuss the outlines of a curriculum for stochastics instruction in the middle grades. Four criteria for a sequence of study are analyzed, and six phases of learning are described.
  • Author(s):
    Richardson, M., & Gajewski, B.
    Year:
    2003
    Abstract:
    This paper describes an interactive project developed to use for teaching statistical sampling methods in an introductory undergraduate statistics course, an Advanced Placement (AP) statistics course, or, with adaptation, in a statistical sampling course or a statistical simulation course. The project allows students to compare the performance of simple random sampling, stratified random sampling, systematic random sampling, and cluster random sampling in an archaeological setting.
  • Author(s):
    Cosmiders, L. & Tooby, J.
    Year:
    1996
    Abstract:
    Professional probabilists have long argued over what probability means, with, for example, Bayesians arguing that probabilities refer to subjective degrees of confidence and frequentists arguing that probabilities refer to the frequencies of events in the world. Recently, Gigerenzer and his colleagues have argued that these same distinctions are made by untutored subjects, and that, for many domains, the human mind represents probabilistic information as frequencies. We analyze several reasons why, from an ecological and evolutionary perspective, certain classes of problem-solving mechanism in the human mind should be expected to represent probabilistic information as frequencies. Then, using a problem famous in the "heuristics and biases" literature for eliciting base rate neglect, we show that correct Bayesian reasoning can be elicited in 76% of subjects - indeed, 92% in the most ecologically valid condition - simply by expressing the problem in frequentist terms. This result adds to the growing body of literature showing that frequentist representations cause various cognitive biases to disappear, including overconfidence, the conjunction fallacy, and base-rate neglect. Taken together, these new findings indicate that the conclusion most common in the literature on judgment under uncertainty - that our inductive reasoning mechanisms do not embody a calculus of probability - will have to be re-examined. From an ecological and evolutionary perspective, humans may turn out to be good intuitive statisticians after all.
  • Author(s):
    Hawkins, A. & Hawkins, P.
    Year:
    1997
    Abstract:
    Recently there has been a trend towards admitting expert statistical evidence in UK court cases. There have been a number of cases, however, in which outcomes have been distorted by statistical or probabilistic misconceptions and by faulty inference. Typically, lawyers receive no training in these areas apart from their compulsory school mathematical education. In this study, data was taken from five groups of trainee lawyers. This demonstrated that they made errors in assessing likelihoods, irrespective of the level and type of mthematical education that they have received. The typical approaches and content of mathematical education at school or college need to be re-considered. Data from two other groups of subjects (one of statistical educators) with different types of mathematical backgrounds were available for comparison purposes.
  • Author(s):
    Meacock, S.
    Editors:
    Goodall, G.
    Year:
    2005
    Abstract:
    This article shows how consideration of seating arrangements in theatres can be used as a basis for constructing an interesting probability model.
  • Author(s):
    Juan D. Godino, Carmen Batanero, Rafael Roa and Miguel R. Wilhelmi
    Year:
    2008
    Abstract:
    In this paper we describe a model of pedagogical content knowledge with a formative cycle directed to simultaneously increase the teachers' statistical and pedagogical knowledge. In this cycle, teachers are first given a statistical project to work with and then carry out a didactical analysis of the project. An analysis guide, based on the notion of didactical suitability, helps increase the teachers' competence related to the different components of pedagogical content knowledge and their ability to carry out didactical analyses. At the same time it provides the teacher educator with information regarding the future teachers' previous knowledge and learning. Results of experimenting with this formative cycle for a particular project in a group of 55 prospective teachers indicated a need for better statistics preparation of these teachers and illustrated the usefulness of the formative cycle and analysis guide proposed.
  • Author(s):
    Pange, J.
    Editors:
    Rossman, A., & Chance, B.
    Year:
    2006
    Abstract:
    This study refers to an experiment on teaching probabilities, conducted in Greece at preschools in Athens and Ioannina. The aim of this study was to assess teachers on how they introduced common statistical concepts to children throughout the academic year of 2004-2005. Moreover, this study presents a new didactical model on the way we tried to educate preschool teachers on how to introduce to preschool children probabilistic concepts that are not contained in the official national curriculum. The majority of the teachers agreed that the study was interesting and that their intentions were positive, but they lacked the ability and specification to include those concepts in their everyday class curriculum.
  • Author(s):
    Jones, G., Perry, B., Putt, I., & Nisbet, S.
    Editors:
    Starkings, S.
    Year:
    2000
    Abstract:
    In response to the critical role that information plays in our technological society, there have been international calls for reform in statistical education at all grade levels (e.g., National Council of Teachers of Mathematics, 1989; School Curriculum and Assessment Authority &amp; Curriculum and Assessment Authority for Wales, 1996). These calls for reform have advocated a more pervasive approach to the study of statistics, one that includes describing, organizing, representing, and interpreting data. This broadened perspective has created the need for further research on the learning and teaching of statistics, especially in the elementary grades, where instruction has tended to focus narrowly on graphing rather than on broader topics of data handing (Shaughnessy, Garfield, &amp; Greer, 1996).<br><br>Notwithstanding these calls for reform, there has been relatively little research on children's statistical thinking and even less research on the efficacy of instructional programs in data exploration. Although some elements of children's statistical thinking and learning have been investigated (Cobb, 1999; Curcio, 1987; Curcio &amp; Artz, 1997; De Lange et al., 1993; Gal &amp; Garfield, 1997; Mokros &amp; Russell, 1995), research on students' statistical thinking is emergent rather than well established. Existing research on children's statistical thinking has certainly not developed the kind of cognitive models of students' thinking that researchers like Fennema et al. (1996) deem necessary to guide the design and implementation of curriculum and instruction.<br><br>In this paper, we will discuss how our research has built and used a cognitive model to support instruction in data exploration. More specifically, the paper will: (a) examine the formulation and validation of a framework that describes students' statistical thinking on four processes; and (b) describe and analyze teaching experiments with grades 1 and 2 children that used the framework to inform instruction.
  • Author(s):
    Polaki, M. V.
    Editors:
    Phillips, B.
    Year:
    2002
    Abstract:
    This paper describes two versions of a teaching experiment that traced the development of Basotho elementary students' thinking with regard to sample space and probability of an event. The instructional design phase of the teaching experiment was informed by a cognitive framework that describes and predicts Basotho elementary students' growth in probabilistic thinking (Polaki, Lefoka, &amp; Jones, 2000). Twelve students (9-10 year olds) drawn from grades 4 and 5 of an elementary school took part in a six-week instructional program. Analysis of qualitative data revealed, amongst other things, a weak and often unstable part-part schema that was minimally effective in enabling the students to order probabilities in 1-dimensional situations, and a stronger and more stable part-part schema that made it possible for some students to experience greater success at listing complete sets of outcomes, and to order probabilities in 1- and 2-dimensional situations.
  • Author(s):
    Jones, G. A., Thornton, C. A., Langrall, C. W., Johnson, T. M., &amp; Tarr, J. E.
    Year:
    1997
    Abstract:
    Curriculum recommendations in mathematics at international and national levels have advocated increased attention to probability instruction K-8 (Australian Education Curriculum Corporation, 1994; Department of Education and Science and the Welsh Office, 1991; National Council of Teachers of Mathematics, 1989). In response to these recommendations, current curriculum materials have placed increased emphasis on the teaching and learning of probability (Berle-Carman, Economopoulos, Rubin, Russell, &amp; Corwin, 1995; Chandler &amp; Brosnon, 1994). With respect to teaching and learning, numerous studies (Fennema, Franke, Carptenter, &amp; Carey, 1993; Fuys, Geddes, &amp; Tischler, 1988; Lamon, 1996; Mack, 1995), advocate the use of research-based knowledge of students' thinking to inform instruction. Although there has been considerable research on students' probabilistic reasoning (e.g., Falk, 1983; Fischbein, Nello, &amp; Marino, 1991; Hawkins &amp; Kapadia, 1984; Piaget &amp; Inhelder, 1975; Shaughnessy, 1992), none of this research has generated a framework for systematically describing and predicting students thinking in probability. Moreover, research has not generated or evaluated instructional programs at the elementary and middle school levels that are guided by research-based knowledge of students probabilistic thinking (Shaughnessy, 1992). This paper reports on a program of four research studies on probability in the elementary and middle grades. In particular, it examines: a) a research-based framework for describing and predicting how elementary and middle grades' students think in probability; b) an instructional program in probability for the elementary level that was informed by the research-based framework on students probabilistic thinking; and c) two instructional programs in the middle grades, one emphasizing conditional probability and independence, the other focusing on probabilistic thinking and writing in the context of probability.

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The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education