Journal Article

  • Various terms are used to describe mathematical concepts, in general, and statistical concepts, in particular. Regarding statistical concepts in the Hebrew language, some of these terms have the same meaning both in their everyday use and in mathematics, such as Mode; some of them have a different meaning, such as Expected value and Life expectancy; and some have the opposite meaning, such as Significance level. Spoken language plays an important role in shaping how the informal statistical definitions taught in schools are remembered. In the present study we examine the impact of the everyday use of terms on the students' informal definitions of various statistical concepts. Though all the study participants were familiar with the concepts they were asked to define, a high percentage of them failed to provide correct definitions of the given statistical concepts. Analysis of the incorrect definitions revealed that the everyday use of the terms used to label the concepts, influenced the informal definitions provided by the students.

  • In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and learning of statistics through real contexts. We also report the development of a corresponding assessment regime and how this works in the classroom.<br><br>Controversially, in September 2006 the UK government announced that coursework was to be dropped for mathematics exams sat by 16-year-olds. A consequence of this decision is that areas of the curriculum previously only assessed via this method will no longer be assessed. These include the stages of design, collection of data, analysis and reporting which are essential components of a statistical investigation. The mechanism outlined here could provide some new and useful ways of coupling new teaching methods with learning and doing assessment - in short, they could go some way towards making up for the educational loss of not doing coursework. Also, our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages.

  • A standard topic in many Introductory Statistics courses is the analysis of dependent samples. A simple graphical approach that is particularly relevant to dependent sample comparisons is presented, illustrated and discussed in the context of analyzing five real data sets. Each data set to be presented has been published in a textbook, usually introductory. Illustrations show that comprehensive graphical analyses often yield more nuanced, and sometimes quite different interpretations of data than are derived from standard numerical summaries. Indeed, several of our findings would not readily have been revealed without the aid of graphic or visual assessment. Several arguments made by John Tukey about data analysis are seen to have special force and relevance.

  • While split-plot designs have received considerable attention in the literature over the past decade, there seems to be a general lack of intuitive understanding of the error structure of these designs and the resulting statistical analysis. Typically, students learn the proper error terms for testing factors of a split-plot design via expected mean squares. This does not provide any true insight as far as why a particular error term is appropriate for a given factor effect. We provide a way to intuitively understand the error structure and resulting statistical analysis in split-plot designs through building on concepts found in simple designs, such as completely randomized and randomized complete block designs, and then provide a way for students to "see" the error structure graphically. The discussion is couched around an example from paper manufacturing.

  • Internationalisation is an important but contentious issue in higher education. For some it means the facilitation of student mobility and an important source of funding for universities, while for others it forms a philosophy of teaching and student engagement, highlighting issues of global inequality. In this study, the papers from a recent statistics education conference, the 7th International Conference on Teaching Statistics, are subjected to a critical discourse analysis against a theoretical frame derived from research describing different ways of understanding and working with internationalisation. The analysis demonstrates how a specific discipline-based community - the statistics education community - involves itself with issues of internationalisation.

  • This article presents statistical power analysis (SPA) based on the normal distribution using Excel, adopting textbook and SPA approaches. The objective is to present the latter in a comparative way within a framework that is familiar to textbook level readers, as a first step to understand SPA with other distributions. The analysis focuses on the case of the equality of the means of two populations with equal variances for independent samples with the same size.<br><br>This is the situation adopted as case 0 by Cohen (1988), a pioneer in the subject, to develop his set of tables and so, the present article can be seen as an introduction to Cohen's methodology applied to tests based on samples from normal populations. We also discuss how to extend the calculation to cases with other characteristics (cases 1 to 4), similarly to what Cohen proposes, as well as a brief discussion about the advantages and shortcomings of Excel. We teach mainly in the area of business and economics, which determines the scope of our analysis.

  • Since educational statistics is a core or general requirement of all students enrolled in graduate education programs, the need for high quality student engagement and appropriate authentic learning experiences is critical for promoting student interest and student success in the course. Based in authentic learning theory and engagement theory graduate educational statistics CAPSULES (Community Action Projects for Students Utilizing Leadership and E-based Statistics) engage graduate students in service-learning projects involving managing, conducting, and delivering authentic data-driven research. The community action projects utilizing leadership and e-based statistics skills are spearheaded by a university-based Community Outreach Research and Authentic Learning (CORAL) Center. The graduate educational statistics CAPSULES program includes: (1) restructuring educational statistics courses to include real-world active learning and authentic assessment; (2) providing opportunities for graduate students to engage in team-driven quantitative research prior to the thesis or dissertation experience with projects generated from community agencies/educational institutions; and (3) connecting graduate students with community action projects as research managers, leaders, and presenters. Highlights of initial formative and summative student outcomes are presented relative to specific examples of student-directed CAPSULES. Student outcomes from the CAPSULES program indicate positive increases in graduate students' attitudes toward statistics and research, and students' leadership and project management skills.

  • The aim was to revise a statistics course in order to get the students motivated to learn statistics and to integrate statistics more throughout a psychology course. Further, we wish to make students become more interested in statistics and to help them see the importance of using statistics in psychology research. To achieve this goal, several changes were made in the course. The theoretical framework to motivate teaching method changes was taken from the statistics education literature together with the ideas of student-centered learning and Kolb's learning circle. One of the changes was to give the students research problems in the beginning of the course that were used throughout the course and which they should be able to solve at the end of the course. Other changes were to create a course webpage and to use more computer-based assignments instead of assignments with calculators. The students' test results and their answers on the Survey of Attitudes Toward Statistics, SATS, (Schau, Stevens, Dauphinee, &amp; Del Vecchio, 1995) together with course evaluations showed that by changing the course structure and the teaching, students performed better, and were more positive towards statistics even though statistics was not their major.

  • The case study examined two groups of grade 7 students as they engaged in four inquiry phases: posing a question and collecting, analyzing, and representing data. Previous studies reported analyses of statistical reasoning on a single inquiry phase. Our goal was to identify the modes of statistical reasoning displayed during group discussions in all phases as children designed and conducted their own inquiry. A content analysis of audio and video recorded discussions yielded 10 statistical reasoning modes: six relate to Garfield and Gal's [Garfield, J., Gal, I. (1999). Teaching and assessing statistical reasoning. In L. V. Stiff, &amp; F. R. Curcio (Eds.), Developing mathematical reasoning in grades K-12. 1999 Yearbook (pp. 207-219). Reston, VA: National Council of Teachers of Mathematics] statistical reasoning types involved in the collection, analysis, and representation of data and four modes deal with an aspect of inquiry not exclusively focused upon in the literature on statistical reasoning - i.e., the problem-posing phase. Although students' reasoning reflected an incomplete understanding of statistics they serve as building blocks for instruction.

  • Many aspects of statistical design, modelling, and inference have close and important connections with causal thinking. These are analyzed in the paper against a philosophical background that regards formal mathematical models as having dual interpretations, reflecting both objectivist reality and subjectivist rationality. The latter aspect weakens the need for an objective theory of probabilistic causation, and suggests that a traditional image of causes as deterministic mechanisms should remain primary. It is argued that such causes should guide much preformal thinking about what to include in formal statistical models, especially of dynamic phenomena. The statistical measurement of causal effects is facilitated by good statistical design, including randomization where feasible, and requires other methodologies for controlling and assessing uncertainties, for example in model construction and inference. Illustrative examples include case studies where the problem is to assess retrospectively the causes of observed events and where the task is to assess future risks from controllable factors.

Pages