It is well known that meaningful knowledge of statistics involves more than simple factual
or procedural knowledge of statistics. For an intelligent use of statistics, conceptual
understanding of the underlying theory is essential. As conceptual understanding is usually
defined as the ability to perceive links and connections between important concepts that may
be hierarchically organized, researchers often speak of this type of knowledge as structural
knowledge. In order to gain insight into the actual structure of a studentŐs knowledge network,
specific methods of assessment are sometimes used. In this article we discuss a newly developed,
specific method for assessing structural knowledge and compare its merits with more traditional
methods like concept mapping and the use of simple open questions.
Key Words: Conceptual understanding; Concept mapping; MPM.
Both researchers and teachers of statistics have made considerable efforts during the last
decades to re-conceptualize statistics courses in accordance with the general reform
movement in mathematics education. However, students still hold misconceptions about
statistical inference even after following a reformed course. The study presented in
this paper addresses the need to further investigate misconceptions about hypothesis
tests by (1) documenting which misconceptions are the most common among university students
of introductory courses of statistics, and (2) concentrating on an aspect of research about
misconceptions that has not yet received much attention thus far, namely the confidence that
students have in their misconceptions. Data from 144 college students were collected by means
of a questionnaire addressing the most common misconceptions found in the literature about
the definitions of hypothesis test, p-value, and significance level. In this questionnaire,
students were asked to select a level of confidence in their responses (from 0 to 10) for
each item. A considerable number of participants seemed to hold misconceptions and lower
levels of concept-specific self-perceived efficacy were found to be related to misconceptions
more than to the correct answers. On average, students selected significantly lower levels of
confidence for the question addressing the definition of the significance level than for the
other two items. Suggestions for further research and practice that emerge from this study are
Key Words: Confidence; University Students; Misconceptions p-value;
Misconceptions Significance Level.
Previous research has demonstrated that studentsŐ cognitions about statistics are related to
their performance in statistics assessments. The purpose of this research is to examine the
nature of the relationships between undergraduate psychology studentsŐ previous experiences
of maths, statistics and computing; their attitudes toward statistics; and assessment on a
statistics course. Of the variables examined, the strongest predictor of assessment outcome
was studentsŐ attitude about their intellectual knowledge and skills in relation to
statistics at the end of the statistics curriculum. This attitude was related to studentsŐ
perceptions of their maths ability at the beginning of the statistics curriculum. Interventions
could be designed to change such attitudes with the aim of improving studentsŐ learning of
Key Words: Cognitive competence; Value of statistics; Difficulty of statistics;
Affect about statistics.
This paper describes a unique graduate-level course that prepares teachers of introductory
statistics at the college and high school levels. The course was developed as part of a
graduate degree program in statistics education. Although originally taught in a face-to-face
setting, the class has been converted to an online course to be accessible to more students.
The course serves students who are pursuing graduate degrees in a variety of disciplines but
who want to teach statistics as part of their careers. It also serves current teachers in high
school who are teaching the Advanced Placement Statistics course as well as teachers at two-year
and four-year colleges. The curriculum for the course is based on the theory that good teachers
of statistics need to be developed, as opposed to being trained. Building on recent teacher
preparation theory, we describe a course that models and builds specific knowledge about
teaching and learning statistics. In addition, this course is organized around the six
recommendations of the ASA-endorsed Guidelines for Assessment and Instruction in Statistics
Key Words: Teacher development; Statistics education; GAISE.
Group activities are an excellent way to enhance learning. When students are actively involved
in a relevant project, understanding and retention are improved. The proposed activity introduces
a timely and interesting project typical of the type encountered in statistical practice.
Using the computer to successfully developing an appropriate model is a valuable educational
experience that builds confidence
Key Words: Linear regression; Undergraduate learning.
In a statistics course for bachelor students in econometrics a new format was adopted in which
students were encouraged to study more actively and in which cooperative learning and peer
teaching was implemented. Students had to work in groups of two or three students where each
group had to perform certain tasks. One of these tasks was: explaining theory and/or solutions
of problems to the other groups. In order to prepare them for this task the groups had separate
regular meetings with the teacher. Students report higher involvement and greater satisfaction
in this format than in the traditional format. For the teacher the format may be more time
consuming, but also more rewarding.
Key Words: Cooperative learning; Peer teaching; Higher education; Bachelor
study; Econometrics; Small groups.
Hypothesis testing is one of the more difficult concepts for students to master in a basic,
undergraduate statistics course. Students often are puzzled as to why statisticians simply
donŐt calculate the probability that a hypothesis is true. This article presents an exercise
that forces students to lay out on their own a procedure for testing a hypothesis. The result
is that the students develop a better understanding for the rationale and process of hypothesis
testing. As a consequence, they improve their ability to grasp the meaning of a p-value and to
interpret the results of a significance test
Key Words: Problem-based learning; Chi-square; P-value.
Following the Guidelines for Assessment and Instruction in Statistics Education (GAISE)
recommendation to use real data, an example is presented in which simple linear regression
is used to evaluate the effect of the Montreal Protocol on atmospheric concentration of
chlorofluorocarbons. This simple set of data, obtained from a public archive, can be used
to tell a compelling story of success in international diplomacy solving a global environmental
problem. A description of the use of these data and analyses are presented for a number of
courses in applied statistics including introductory statistics.
Key Words: Regression analysis; Introductory statistics; Ozone; GAISE
In response to the worldwide shortage of biostatisticians, Australia has established a national
consortium of eight universities to develop and deliver a Masters program in biostatistics.
This article describes our successful innovative multi-institutional training model, which may
be of value to other countries. We first present the issues confronting the future of biostatistics
in Australia, then relate our experience in establishing a new national consortium-based Masters
program, and finally explore the extent to which our initiatives have addressed the current
challenges of biostatistics workforce shortages.
Key Words: TBiostatistics; Teaching program; Collaboration; Statistics education.
Students increasingly need to learn to communicate statistical results clearly and effectively,
as well as to become competent consumers of statistical information. These two learning goals
are particularly important for business students. In line with reform movements in Statistics
Education and the GAISE guidelines, we are working to implement teaching strategies and
assessment methods that align instruction and assessment with our learning goals. One of the
main instructional tools we use is group projects with elements of data collection and analysis,
written and oral presentation, and self, peer and professor assessment. This paper addresses
specific challenges encountered while teaching and directing group work in a highly multicultural
context of 10 to 20 different nationalities in the same classroom. It also focuses on the learning
benefits of having students work collaboratively to discuss, write, present, and assess statistics
projects in English.
Key Words: Business statistics; Cooperative learning; Assessment.
This paper describes an interactive activity that revolves around the dice-based golf game GOLO.
The GOLO game can be purchased at various retail locations or online at igolo.com. In addition,
the game may be played online free of charge at igolo.com. The activity is completed in four
parts. The four parts can be used in a sequence or they can be used individually. Part 1
illustrates the binomial distribution. Part 2 illustrates the sampling distribution of the
sample proportion. Part 3 illustrates confidence intervals for a population proportion.
Part 4 illustrates hypothesis tests for a population proportion.
Extensions of the activity can be used to illustrate discrete probability distributions
(including the geometric, hypergeometric, and negative binomial) and the distribution of the
first order statistic. The activity can be used in an AP statistics course or an introductory
undergraduate statistics course. The extensions of the activity can be used in an intermediate
undergraduate statistics course or a mathematical statistics course. Each extension is
self-contained and can be carried out without having worked through other extensions or any
of the four parts of the main activity.
Key Words: Active learning; Statistics in sports; Binomial distribution;
Sampling distribution of a sample proportion; Confidence interval for a proportion;
Hypothesis test on a proportion; Geometric distribution; Hypergeometric distribution;
Negative binomial distribution; Distribution of the first order statistic; Theoretical
and empirical probabilities.
This study used a mixed-methods approach to evaluate a hybrid teaching format that incorporated
an online tutoring system, ALEKS, to address studentsŐ learning needs in a graduate-level
introductory statistics course. Student performance in the hybrid course with ALEKS was found
to be no different from that in a course taught in a traditional face-to-face format. Survey
and focus group interviews revealed that studentsŐ experience with ALEKS and learning of
statistics varied systematically across performance levels. Both quantitative and qualitative
data suggest that 1) class format may not be as important as studentsŐ mathematical ability and
skills for their success in introductory statistical courses, and 2) a teaching approach that
addresses the underlying determinants of learning behaviors would be more effective than simply
delivering the material in a different format.
Key Words: Hybrid course; Statistics education; Teaching software packages.
From Research to Practice
Humor has been promoted as a teaching tool that enhances student engagement and learning.
The present report traces the pathway from research to practice by reflecting upon various
ways to incorporate humor into the face-to-face teaching of statistics. The use of humor in
an introductory university statistics course was evaluated via interviews conducted with a
random sample of 38 students. Responses indicated that humor aided teaching by providing
amusement, breaking up content, bringing back attention, lightening the mood, increasing
motivation, reducing monotony, and providing a mental break. Students that were already
motivated and interested in statistics derived less benefit from humor, finding it at times
irrelevant and distracting. The selective use of humor is recommended in teaching statistics,
particularly for students that hold negative attitudes towards the subject.
Key Words: Mathematics teaching; Curriculum design; Higher education;
We located 27 articles that have been published in the first half of 2009 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.
Most of us are finished with the academic year; we can sit back and relax a bit during this
short summer and reflect on our past year of teaching before madly preparing for the next one.
One question I always ask myself at the end of each year is, ŇWhat did I learn from my students
this year?Ó Here are some of the thoughts that came to mind.
Datasets and Stories
Calibration is a technique that is commonly used in science and engineering research that requires
calibrating measurement tools for obtaining more accurate measurements. It is an important
technique in various industries. In many situations, calibration is an application of linear
regression, and is a good topic to be included when explaining and learning the concepts of
linear regression. However, calibration is not often mentioned in the introductory statistics
textbooks or in the introductory statistics classrooms. The goal of this paper is to share with
instructors an example with real data for simple linear regression and its application in
calibration. It can be used as a lecture example, a class project, or a lab activity.
Key Words: Calibration; Linear regression; Inverse regression.