This study aimed to examine the role knowledge of context plays in supporting or interfering with middle school students' statistical thinking. A model of context knowledge use was developed based on a model of context support developed by Beck, McKeown and McCaslin (1983) to describe students' use of context knowledge. The results of the study showed that students' use of context knowledge fell into three categories.
This study investigated the factors that 12th grade students in United Arab Emirates take into consideration when judging the validity of a given statistical generalization, in particular, in terms of the sample size and sample selection bias. The sample consisted of 360 students who had not studied sampling yet. Results show that a small percentage of the students take the sample size and selection bias into consideration properly. Many students based their judgment on their personal beliefs regardless of the properties of the selected sample. This study identified some pre- teaching misconceptions that students have with regard to 'sampling'. Such misconceptions are 'any sample represents the population', and, 'any sample does not represent the population'.
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.
This paper reports on an American Statistical Association project which developed ASA-endorsed guidelines for teaching and learning statistics at the Pre K-12 level. A group of leading statistics and mathematics educators developed the report, "A Curriculum Framework for Pre K-12 Statistics Education." These guidelines complement the NCTM Principals and Standards of School Mathematics - providing additional guidance and clarity on the data analysis strand. A major goal of the document is to describe a statistically literate high school graduate and, through a connected curriculum, provide steps to achieve this goal. Topics for discussion include: developing statistical literacy within the Pre K-12 mathematics curriculum; links to the NCTM Standards; impact of high stakes testing; differences between mathematics and statistics; key components and concepts associated with the data analysis process; examples illustrating connections in key statistical concepts across all grade levels.
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 is a culmination of the study carried out after using project work as an intervention to enhance the learning of statistics as a service subject. It discusses how a project encompassing real-world problems directly relevant to the learners chosen career-path helps in motivating and sustaining the students' quest for learning statistics. The sample group comprised of learners studying towards the Diploma in Extraction Metallurgy and the project work was centred on the main-stream course Mineral Processing. This project was based on actual experiments conducted by learners in their Mineral Processing course so that learners could see the relevance of applied statistics to main-stream courses. The learners' performance was tracked throughout this study.
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.