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