Computer simulations and animations for developing statistical concepts are often not understood by beginners.
Hands-on physical simulations that morph into computer simulations are teaching approaches that can build students'
concepts. In this paper we review the literature on visual and verbal cognitive processing and on the efficacy of
animations in promoting learning. We describe an instructional sequence, from hands-on to animations, developed for
14 year-old students. The instruction focused on developing students' understanding of sampling variability and using
samples to make inferences about populations. The learning trajectory from hands-on to animations is analyzed from the
perspective of multimedia learning theories while the learning outcomes of about 100 students are explored, including
images and reasoning processes used when comparing two box plots. The findings suggest that carefully designed learning
trajectories can stimulate students to gain access to inferential concepts and reasoning processes. The role of verbal,
visual, and sensory cues in developing students' reasoning is discussed and important questions for further research on
these elements are identified.
Key Words: Animations; Cognitive theories; Comparing groups; Informal inferential reasoning;
It is common to consider Tukey's schematic ("full") boxplot as an informal test for the existence of outliers.
While the procedure is useful, it should be used with caution, as at least 30% of samples from a normally-distributed
population of any size will be flagged as containing an outlier, while for small samples (N<10) even extreme outliers
indicate little. This fact is most easily seen using a simulation, which ideally students should perform for themselves.
The majority of students who learn about boxplots are not familiar with the tools (such as R) that upper-level students
might use for such a simulation. This article shows how, with appropriate guidance, a class can use a spreadsheet such as
Excel to explore this issue.
Key Words: Boxplot; Outlier; Significance; Spreadsheet; Simulation.
This paper discusses common approaches to presenting the topic of skewness in the classroom,
and explains why students need to know how to measure it. Two skewness statistics are examined:
the Fisher-Pearson standardized third moment coefficient, and the Pearson 2 coefficient that compares
the mean and median. The former is reported in statistical software packages, while the latter is all
but forgotten in textbooks. Given its intuitive appeal, why did Pearson 2 disappear? Is it ever useful?
Using Monte Carlo simulation, tables of percentiles are created for Pearson 2. It is shown that while
Pearson 2 has lower power, it matches classroom explanations of skewness and can be calculated when
summarized data are available. This paper suggests reviving the Pearson 2 skewness statistic for the
introductory statistics course because it compares the mean to the median in a precise way that students
can understand. The paper reiterates warnings about what any skewness statistic can actually tell us.
Key Words: Moment Coefficient; Pearson 2; Monte Carlo; Type I Error; Power;
A well-designed experiment is the best method for establishing efficacy of any intervention, be it medical,
behavioral, or educational in nature. This paper reviews the steps necessary in conducting a comparative experiment
in an educational setting, and illustrates how these steps might be fulfilled within the context of a large-scale
randomized experiment conducted in an introductory statistics course. The primary goal of this paper is to help
researchers identify salient issues to consider and potential pitfalls to avoid when designing a comparative experiment
in an educational setting.
Key Words:Quantitative research; Efficacy; Evaluation; Statistics education; Clickers.
A statistics course can be a very challenging subject to teach. To enhance learning, today's modern course in statistics
might incorporate many different aspects of technology. Due to advances in technology, teaching statistics online has also
become a popular course option. Although researchers are studying how to deliver statistics courses in this new technological
environment, there is still much to learn about how to effectively implement these online courses. The purpose of this paper
is to report the results of an extensive review of the literature conducted across several disciplines from the last decade in
an effort to summarize, identify, and understand overall trends and themes in online instruction. A summary of effective
practices that might be useful to teachers teaching statistics online concludes this paper.
Key Words: Statistics learning online; Statistics Education; Best Practices.
Technology is increasingly used to aid the teaching of statistics. Personal Response Systems (PRS) involve
equipping students with a handset allowing them to send responses to questions put to them by a lecturer. PRS
allows lectures to be more interactive and can help reinforce material. It can also allow the lecturer to monitor
students' understanding of course content. PRS is most commonly used in large lectures where interaction from the
students is particularly difficult. However, we consider its use in a small group (around 15 students) of MSc in
Statistics students. Recommendations based on this experience are discussed, in particular the importance of good
question design. We consider possible diagnostics for the appropriateness of questions based on response data.
Key Words: Technology; Interactivity; Personal Response System; Active learning.
Nicholas N. Watier, Claude Lamontagne, and Sylvain Chartier
What does the mean mean?
The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students
rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it.
According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a
particular concept are better equipped to teach that concept in a meaningful way. With this in mind, this
article outlines five conceptualizations of the arithmetic mean and discusses how each conceptualization
can be presented in the classroom. Educators can use these conceptualizations in order to foster insight
into the mean.
Key Words: Arithmetic Mean; Constructivism; Least Squares; Analytic Geometry.
Interviews with Statistics Educators
E. Jacquelin Dietz is Professor and Department Head, Meredith College Department of Mathematics and
Computer Science. She was a faculty member for 26 years in the Department of Statistics at North Carolina
State University. She is a Fellow of the American Statistical Association and a recipient of ASA's Founders Award.
The founding editor of the Journal of Statistics Education, she served as Editor from 1992 - 2000. The following
interview took place via email on May 16 - June 6, 2011.
We located 28 articles that have been published from January 2011 through June 2011 that pertained to
statistics education. In this column, we highlight a few of these articles that represent a variety of
different journals that include statistics education in their focus. We also provide information about the
journal and a link to their website so that abstracts of additional articles may be accessed and viewed.
In this column, we share news from two recent
conferences the United States Conference on Teaching Statistics (USCOTS)
and the Emerging Technologies for Online Learning conference. In addition,
as always, we highlight the recent teaching and learning and activity
webinars presented through CAUSEweb and share information on how to become
involved in reviewing resources for CAUSEweb and MERLOT.