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Volume 16 (2008)

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An International Journal on the Teaching and Learning of Statistics

JSE Volume 16, Number 2 Abstracts

Linda L. Cooper and Felice S. Shore
Students' Misconceptions in Interpreting Center and Variability of Data Represented via Histograms and Stem-and-leaf Plots

This paper identifies and discusses misconceptions that students have in making judgments of center and variability when data are presented graphically. An assessment addressing interpreting center and variability in histograms and stem-and-leaf plots was administered to, and follow-up interviews were conducted with, undergraduates enrolled in introductory statistics courses. Assessment items focused upon comparing the variability of two data sets of common range represented by bell-shaped histograms on a common scale, computing measures of center from data extracted from graphs, and in comparing the relative location of the mean and median on a histogram from skewed data. Students’ misconceptions often stemmed from their difficulty in maintaining understanding of the data that are being represented graphically.

Key Words: Descriptive statistics; Mean; Median; Variation; Undergraduate statistics.


Ivo D. Dinov, Nicolas Christou, and Juana Sanchez
Central Limit Theorem: New SOCR Applet and Demonstration Activity

Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multi-faceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem).

Key Words: Statistics education; Technology-based blended instruction; Applets; Central limit theorem; SOCR.


Amy G. Froelich, W. Robert Stephenson, and William M. Duckworth
Assessment of Materials for Engaging Students in Statistical Discovery

As part of an NSF funded project we developed new course materials for a general introductory statistics course designed to engage students in statistical discovery. The materials were designed to actively involve students in the design and implementation of data collection and the analysis and interpretation of the resulting data. Our overall goal was to have students begin to think like statisticians, to construct ways of thinking about data collection and analysis, to solve problems using data in context. During their development, the materials and related activities were field tested in a small special section of an introductory statistics course for two semesters. This field testing was a ``proof of concept,'' that is that the materials could work in the laboratory setting and that the materials showed promise for improving students' learning. As a first step in evaluating these materials, students who enrolled in regular sections of the introductory course were used as a comparison group. In this paper, the development and use of the course materials will be discussed briefly. The strategy for evaluating the materials while they were being developed and analysis of students' performance on common assessment questions and the course project will be presented. In addition, the relationship between student attitudes toward statistics and students' performance will be examined.

Key Words: Activities; Introductory statistics; Statistical concepts.


Megan R. Hall and Ginger Holmes Rowell
Introductory Statistics Education and the National Science Foundation

This paper describes 30 National Science Foundation supported grant projects that have innovations designed to improve teaching and learning in the introductory statistics course. The characteristics of these projects are compared with the six recommendations given in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report for teaching an introductory course in statistics. Through this analysis, we are able to see how NSF-supported introductory statistics education projects during the last decade achieve the GAISE ideals. Thus, materials developed from many of these projects provide resources for first steps in implementing GAISE recommendations.

Key Words: Introductory statistics; Curriculum guidelines; Teaching materials; Grant projects.


Megan R. Hall and Ginger Holmes Rowell
Undergraduate Statistics Education the National Science Foundation

This paper describes 25 National Science Foundation supported projects that have innovations designed to improve education for students majoring or minoring in statistics. The characteristics of these projects and the common themes which emerge are compared with the American Statistical Association’s (ASA) guidelines for developing statistics education curricula for majors and minors and for teaching the corresponding statistics courses. Through this analysis, we are able to see how the last decade of NSF supported projects in statistics education exemplify these ASA guidelines.

Key Words: American Statistical Association; Curriculum guidelines; Teaching materials; Grant projects.


Lehana Thabane, Stephen D Walter, Steven Hanna, Charles H Goldsmith, and Eleanor Pullenayegum
Developing a Biostatistical Collaboration Course in a Health Science Research Methodology Program

Effective statistical collaboration in a multidisciplinary health research environment requires skills not taught in the usual statistics courses. Graduates often learn such collaborative skills through trial and error. In this paper, we discuss the development of a biostatistical collaboration course aimed at graduate students in a Health Research Methodology PhD program with Specialization in Biostatistics. The objectives of the course are to promote enthusiasm and commitment to excellence in statistical collaboration in clinical research; to enhance communication of statistical issues to non-statistician collaborators; to build statistical self-sufficiency and develop skill in applied statistics; and to enhance a culture of collaboration among statisticians and non-statistician researchers. The course uses a combination of lectures and tutorials led by faculty members, videotaped consulting practice sessions, and internship with mentoring of each student by an experienced biostatistician.

Key Words: : Biostatistical collaboration course; Mentorship; Mentoring, Internship; Health research; Biostatistics training; Collaborative research.


Paul F. Velleman
Truth, Damn Truth, and Statistics

Statisticians and Statistics teachers often have to push back against the popular impression that Statistics teaches how to lie with data. Those who believe incorrectly that Statistics is solely a branch of Mathematics (and thus algorithmic), often see the use of judgment in Statistics as evidence that we do indeed manipulate our results.

In the push to teach formulas and definitions, we may fail to emphasize the important role played by judgment. We should teach our students that they are personally responsible for the judgments they make. But we must also offer guidance for their statistical judgments. Such guidance requires that we acknowledge the role of ethics in Statistics. The principle guiding these judgments should be the honest search for truth about the world, and the principle of seeking such truth should have a central place in Statistics courses.

Key Words: Damn lies; Twain; Ethics; Statistics education.


Andrew Zieffler, Joan Garfield, Shirley Alt, Danielle Dupuis, Kristine Holleque, and Beng Chang
What Does Research Suggest About the Teaching and Learning of Introductory Statistics at the College Level? A Review of the Literature

Since the first studies on the teaching and learning of statistics appeared in the research literature, the scholarship in this area has grown dramatically. Given the diversity of disciplines, methodology, and orientation of the studies that may be classified as “statistics education research,” summarizing and critiquing this body of work for teachers of statistics is a challenging and important endeavor. In this paper, a representative subset of studies related to the teaching and learning of statistics in introductory, non-calculus based college courses is reviewed. As a result of this review, and in an effort to improve the teaching and learning of statistics at the introductory college level, some guidelines to help advance future research in statistics education are offered.

Key Words: Statistics Education Research; Teaching and learning; College students.


From Research to Practice

Alexander White and M. Alejandra Sorto
The Gumball Machine: Linking Research and Practice about the Concept of Variability

Inspired by the research of Reading and Shaughnessy (2004), we modified an existing lesson from the National Council of Teachers of Mathematics. This lesson, a variation on the “Gumball Task”, gives students the opportunity to explore and discuss the variation which occurs in sampling. This paper describes our experience using this lesson as an enrichment activity in a fifth grade classroom.

Key Words: Variability; Sampling; Lollie Task.


Datasets and Stories

R. Adam Molnar
Bus Arrivals and Bunching

Finding suitable projects for introductory courses that blend real-world data with relevant questions and feasible instructor effort is often difficult. This paper describes one such project – tabulating the intervals between bus arrivals. By including data gathering, descriptive statistics, hypothesis tests, and regression, it covers most of the topics in a first course. This paper describes the genesis of the project, classroom implementation, analysis results for the student-generated dataset, and adaptations available for other classes and course sizes

Key Words: : Course project; Data vollection; Exploratory analysis; Hypothesis testing; Evaluating assumptions.

Iain Pardoe
Modeling Home Prices Using Realtor Data

It can be challenging when teaching regression concepts to find interesting real-life datasets that allow analyses that put all the concepts together in one large example. For example, concepts like interaction and predictor transformations are often illustrated through small-scale, unrealistic examples with just one or two predictor variables that make it difficult for students to appreciate how these concepts might be applied in more realistic multi-variable problems. This article addresses this challenge by describing a complete multiple linear regression analysis of home price data that covers many of the usual regression topics, including interaction and predictor transformations. The analysis also contains useful practical advice on model building---another topic that can be hard to illustrate realistically---and novel statistical graphics for interpreting regression model results. The analysis was motivated by the sale of a home by the author. The statistical ideas discussed range from those suitable for a second college statistics course to those typically found in more advanced linear regression courses.

Key Words: : Graphics; Indicator variables; Interaction; Linear regression; Model building; Quadratic; Transformations.



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