Research

  • In this paper we present an onto-semiotic macroscopic analysis of the measures of dispersion: range, interquartile range, average deviation, variance, standard deviation and coefficient of variation by following the theoretical framework of the Theory of Semiotic Functions. This research has been carried out with a sample of textbooks from the most representative publishers used by Spanish second-cycle Secondary students of 15 and 16 years of age. The paper finishes by presenting several useful conclusions for the planning of the teaching process and for the research on the issue.

  • A prospective exam was performed to quantify the statistical knowledge of students before they start attending classes in college. A four question test (two of probability and two of descriptive statistics) was given to 95 students of Federal University of Lavras and 87 students of three secondary schools (two private and a public one). The mean scores were not statistically different and were considered poor. It was suggested that this poor student knowledge might be due to poor knowledge of their teachers or a lack of motivation and interest. To attempt to correct for this, secondary teachers attended a one-day class given by the authors of this paper. By examining student scores from before and after that information transference, it was found that teachers that attended the class could transmit more information and enhance their students' scores.

  • This paper focuses on developing students' informal ideas of inference and argumentation. This topic is of current interest to many researchers as well as teachers of statistics. We study fifth graders' learning processes in an exploratory interdisciplinary learning environment that uses the software TinkerPlots to scaffold students' statistical reasoning. The careful design of the learning trajectory based on increasing samples heuristics coupled with the unique features of TinkerPlots were found instrumental in supporting multiple dimensions of students reasoning about informal inference: multiplicative reasoning, aggregate reasoning, acknowledging the value of large samples, and accounting for variability. These were accompanied by greater ability to verbalize, explain and argue about data-based claims. In the light of the analysis, a description of what it may mean to begin reasoning about inference by young students is proposed, and implications to teaching, curriculum and research are drawn.

  • Pairs of students use the computer software Fathom for working on problems from Exploratory Data Analysis. The exploratory study was interested in identifying how the software as a tool supports or hinders students' thinking. Working styles of students related to distributional thinking in the context of group comparison tasks were studied.

  • Most statistics educators would agree that statistical inference is both the central objective of statistical reasoning and one of the most difficult ideas for students to understand. In traditional approaches, statistical inference is introduced as a quantitative problem, usually of figuring out the probability of obtaining an observed result on the assumption that the null hypothesis is true. In this article, we lay out an alternative approach towards teaching statistical inference that we are calling "informal inference." We begin by describing informal inference and then illustrate ways we have been trying to develop the component ideas of informal inference in a recent data analysis seminar with teachers; our particular emphasis in this article is on the ways in which teachers used TinkerPlots, a statistical visualization tool. After describing teachers' approaches to an inferential task, we offer some preliminary hypotheses about the conceptual issues that arose for them.

  • We conducted two design experiments aimed at engaging sixth graders (11 years old) in statistical reasoning about center and variation. We examine in particular students' informal notion of a "modal clump." Using Peirce's concept of diagrammatic reasoning, we analyze the interplay of 1) making plots with TinkerPlots - a computer data analysis tool, 2) experimenting with those plots, and 3) developing a language to talk about features of the data sets as represented in the plots by reflecting on judgments. More generally, we draw on Brandom's recent work in philosophy to argue that an "inferential" view should be privileged over a "referential" view of teaching and learning statistics.

  • This chapter outlines the challenges in teaching and learning probability and states the mission of this book. This book aims to review and analyze the research literature on the teaching and learning of probability in the K-12 curriculum.

  • In this chapter we will examine different interpretations of the nature of chance, randomness, and probability and will highlight how these multiple conceptions are complementary and can influence curriculum goals. Finally we include some implications for the teaching and learning of probability in schools.

  • This chapter focuses on "probability literacy", the knowledge and dispositions that students may need to develop to be considered literate regarding real-world probability matters. Models of adult literacy, numeracy, and statistical literacy that define the terrain in which knowledge of probability is situated are reviewed. Then, the five basic elements of probability-related knowledge and points to some dispositions that are needed for adults to be able to effectively interpret and engage real-world probabilistic situations are discussed. Implications for instructional practice and research are examined.

  • This is an historical overview of research on the learning and teaching of probability. Research will be classified chronologically as Phase 1, the Piagetian Period; Phase 2, the Post-Piagetian Period; and Phase 3, the Contemporary Period. The research of each of these phases will be analyzed and we will identify the theoretical developments and implications for teaching and learning that have been associated with each phase.

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