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Volume 17 (2009)

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An International Journal on the Teaching and Learning of Statistics

JSE Volume 17, Number 2 Abstracts

Nick J. Broers
Using Propositions for the Assessment of Structural Knowledge of Statistics

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.

Ana Elisa Castro Sotos, Stijn Vanhoof, Wim Van den Noortgate, and Patrick Onghena
How Confident are Students in their Misconceptions about Hypothesis Tests?

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 proposed.

Key Words: Confidence; University Students; Misconceptions p-value; Misconceptions Significance Level.

Martin Dempster and Noleen K. McCorry
The Role of Previous Experience and Attitudes toward Statistics in Statistics Assessment Outcomes among Undergraduate Psychology Students

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 statistics.

Key Words: Cognitive competence; Value of statistics; Difficulty of statistics; Affect about statistics.

Joan Garfield and Michelle Everson
Preparing Teachers of Statistics: A Graduate Course for Future Teachers

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 Education (GAISE).

Key Words: Teacher development; Statistics education; GAISE.

Teresa Jacobson, Josh James, and Neil C. Schwertman
An Example of Using Linear Regression of Seasonal Weather Patterns to Enhance Undergraduate Learning

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.

Sytse Knypstra
Teaching Statistics in an Activity Encouraging Format

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.

Leigh Lawton
An Exercise for Illustrating the Logic of Hypothesis Testing

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.

Dean Nelson
Using Simple Linear Regression to Assess the Success of the Montreal Protocol in Reducing Atmospheric Chlorofluorocarbons

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 recommendations

Judy M Simpson, Philip Ryan, John B Carlin, Lyle Gurrin, and Ian Marschner
Training a New Generation of Biostatisticians: A Successful Consortium Model

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.

Michelle Sisto
Can you Explain that in Plain English? Making Statistics Group Projects Work in a Multicultural Setting

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.

Paul Stephenson, Mary Richardson, John Gabrosek, and Diann Reischman
How LO Can You GO? Using the Dice-based Golf Game GOLO to Illustrate Inferences on Proportions and Discrete Probability Distributions

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 In addition, the game may be played online free of charge at 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.

Yonghong Jade Xu, Katrina A. Meyer, Dianne D. Morgan
A Mixed-methods Assessment of Using an Online Commercial Tutoring System to Teach Introductory Statistics

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

David L. Neumann, Michelle Hood, and Michelle M. Neumann
Statistics? You Must Be Joking: The Application and Evaluation of Humor when Teaching Statistics

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; Statistics anxiety.

Teaching Bits

Audbjorg Bjornsdottir and Joan Garfield
Teaching Bits: Statistics Education Articles from 2009

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.

Deborah J. Rumsey
Random Thoughts on Teaching: It's Amazing What You Don't Have to Tell Them

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

G. Andy Chang, G. Jay Kerns, D. J. Lee, and Gary L. Stanek
Calibration Experiments for a Computer Vision Oyster Volume Estimation System

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.

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