Teaching Bits: A Resource for Teachers of Statistics

From the Literature on Teaching and Learning Statistics

Deborah J. Rumsey
The Ohio State University

Journal of Statistics Education Volume 10, Number 1 (2002)

Copyright © 2002 by the American Statistical Association, all rights reserved.
This text may be freely shared among individuals, but it may not be republished in any medium without express written consent.


Research and Resources on Teaching and Learning Statistics


"Adultsí Statistical Literacy: Meanings, Components, Responsibilities"

Iddo Gal (2002), International Statistical Review, 70(1), 1-52.

Gal presents a thorough and comprehensive discussion of adult statistical literacy; what it means, the processes that are involved in obtaining a level of adult statistical literacy, the cognitive aspects of it, and many excellent illustrations of statistical texts in the media where statistical literacy is needed to correctly interpret the information. Gal also discusses the elements of the statistical knowledge and skills base required for statistical literacy, as well as the dispositional aspects of statistical literacy (what it means to behave in a statistically literate way). He ends with research and assessment challenges, and implications for statistics teachers. Gal frames the article within an international context, giving us a more global perspective.

Discussion papers follow by J.M. Watson, M.G. Ottaviani, D.J. Rumsey, C. Batanero, A. Ahlgren, K.L. Weldon, and J.L. Snell. I. Gal provides a rejoinder response.


"Quantitative Literacy and Statistics"

Richard L. Scheaffer (2001), Amstat Online Press Release.
www.amstat.org/publications/amstat_news/2001/pres11.html

Scheaffer presents background definitions and the history of quantitative literacy and the case for it. He also shines a spotlight on the current state of quantitative literacy, particularly within the context of the field of mathematics, and discusses the implications for statisticians. He presents the latest events of particular importance to the QL movement, and discusses the role of statisticians in these efforts, now and in the future.


American Statistical Association (ASA) Endorsement of the Mathematical Association of America (MAA) "Guidelines for Programs and Departments in Undergraduate Mathematical Sciences"

Amstat Online (2001).
www.amstat.org/education/ASAendorsement.html

Selected Quotes: "The American Statistical Association (ASA) endorses the Mathematical Association of America (MAA) 'Guidelines for Programs and Departments in Undergraduate Mathematical Sciences,' approved in August of 2000, and offers a position paper as a complement to them.

"The ASA strongly supports the position that mathematics and statistics are separate disciplines and that statistics courses should be taught by those trained in the subject. To assist mathematical sciences departments implement these policies, the ASA in this paper makes ... recommendations concerning hiring, support, and evaluation of statistics faculty members."


"New Web Resource for Mathematics and Statistics Education"

Eric Hsu (2001), Newsletter for the Section on Statistical Education, 7(2).
www.stat.ncsu.edu/stated/newsletter/v7n2/v7n2.html#Web

Excerpt: "The Better File Cabinet (betterfilecabinet.com) is a free searchable database of references to research in math and statistics education (nearly two thousand as of May 2001). The MAA's Special Interest Group collected the references on Research on Undergraduate Math Education (SIGMAA on RUME) and Joan Garfield collected references on Statistics Education. Using the Web interface, the references are searchable by author, title, full text, and keywords and there is an ongoing effort to add commentary on the papers. The site is in a very usable state, but it is still a preliminary beta version. Consolidation and cleaning of the keywords is planned for the near future, as well as a number of other new features. There is also a sister database of calculus problems that will eventually be expanded to other topic areas and integrated into a database containing both research papers and other educational resources."


"New Graduate Programs in Statistics Education"

Joan Garfield (2001), Newsletter for the Section on Statistical Education, 7(2).
www.stat.ncsu.edu/stated/newsletter/v7n2/v7n2.html#Programs

Garfield discusses the need that has been recognized by the ASA Undergraduate Statistics Education Initiative (USEI) to provide programs to better prepare teachers of statistics. To help meet this need, a new graduate program in Statistics Education is being offered by the University of Minnesota. Joan discusses the degree programs in more detail in this article.


"Statistics Education at the ASA"

Richard Scheaffer (2001), Newsletter for the Section on Statistical Education, 7(2).
www.stat.ncsu.edu/stated/newsletter/v7n2/v7n2.html#ASA

In this article, Scheaffer discusses initiatives taken by ASA in the area of statistics education, including an outline of the initiatives planned by the ASAís Center for Statistics Education (CSE).


Teaching Ideas and Applications


"Statistics Going to the Dogs"

Stephen Clarke and Anthony Bedford (2002), Teaching Statistics, (24)1, 6-9.

This article discusses a real-life example of statistics in gambling.


"Probability with Less Pain"

Maxine Pfannkuch, George Seber, and Chris Wild (2002), Teaching Statistics, 24(1), 24-30.

Abstract: The teaching of probability theory has been steadily declining in introductory statistics courses as students have difficulty with handling the rules of probability. In this article we give a data-driven approach, based on two-way tables, which helps students to become familiar with using the usual rules, but without the formal structure.


"Making Observations Interactive"

Lillie Albert, Gail Mayotte, and Sheila Cutler Sohn (2002), Mathematics Teaching in the Middle School, 7(7), 396-403.

Abstract: This article focuses on observational assessment in student learning of mathematical concepts in two sixth grade classrooms. Many of the class activities involved algorithms and open-ended problems in which students worked in collaborative groups, pairs, or individually.


"Hockey Stats: Data Collection on Ice"

Joanne Harris (2002), Mathematics Teaching in the Middle School, 7(7), 386-389.

Software developers and statisticians record and present data collected on hockey players and hockey games and summarize them with statistics accessible to middle school students.


"Stand Up and Be Counted: The Mathematics of Congressional Apportionment"

Peggy House (2001), Mathematics Teacher, 94(8), 692-697.

A discussion of the implications of congressional apportionment using a number of different methods: fixed ratio, fixed total, and on the basis of equal proportions. Census data from 1990 is used as a reference.


"Connecting Data and Geometry"

Tim Erickson (2001), Mathematics Teacher, 94(8), 710-714.

Abstract: This article connects data and geometry by finding relationships between the areas and perimeters of randomly generated rectangles.


"Generating Random Sequences"

Mike Shor (2001), Journal of Online Mathematics and its Applications [Online], 1(3).
www.joma.org/more/shormore.html

Abstract: This Mathlet allows the user to input a sequence of 0's and 1's of length 20 and then tests the sequence for randomness using three tests: Kolmogorov-Smirnov, Wald-Wolfowitz, and Mann-Whitney. An overall assessment of how likely the sequence was generated randomly is given, as well as basic information on how the tests work.


"Is Presidential Greatness Related to Height?"

Paul M. Sommers (2002), The College Mathematics Journal, 33(1), 14-16.

Excerpt: "Well, yes, actually it is. The taller you are, the more likely you are to be a great president, or so statistics shows."


"Symmetric or Skewed?"

Joseph G. Eisenhauer (2002), The College Mathematics Journal, 33(1), 48-51.

Abstract: Mean, median, and mode: they can, of course, occur in any order. But what if our distribution is skewed? Then we must know something about the order in which the measures of central tendency must appear, mustnít we? No, we mustnít.


"Statistics for Homeland Defense"

David Banks (2002), Chance, 15(1), 8-10.

Excerpt: "The flying bombs of September 11, the subsequent anthrax letters, and credible threats of future attacks have prompted a comprehensive reevaluation of U.S. security systems. Statisticians are not major players in this effort, but there are contributions we can make. One forum in which such efforts are being organized is the Committee on Applied and Theoretical Statistics, which is part of the National Academy of Sciences. That committee (met) on November 5 to identify ways in which statistical research can support counterterrorism. This paper elaborates on several topics that they discussed, as well as other statistical issues raised by the current conflict."

Issues such as risk analysis strategies under situations involving imperfect information, profiling, the rapid identification of disease clusters, in the case of bioterrorism, and finding a reliable defense for our computer systems comprising the information network are all discussed in this paper.


"Does Having Boys or Girls Run in the Family?"

Joseph Lee Rodgers and Debby Doughty (2001), Chance, 14(4), 8-13.

Is there a genetic factor that produces a bias in favor of one sex for some families? The authors discuss this issue, touching upon items such as factors that have been identified in the past literature as potentially affecting the human sex ratio at birth, and a background of various theories on this subject. They also present empirical analyses and mathematical models to evaluate whether sex bias "runs in the family." The data come from the National Longitudinal Survey of youth. The authors find no compelling evidence that sex bias runs in the family.


"Community-Based Projects in Applied Statistics: Using Service-Learning to Enhance Student Understanding"

Rob Root and Trisha Thorme (2001), The American Statistician, 55(4), 326-331.

Abstract: Community-based projects can enhance student understanding of descriptive statistics and the use of and value of inferential statistics. This article relates the authorsí experiences with and reflections on three semesters of elementary college-level statistics courses that included an optional service-learning component. Reasons to try community-based projects in mathematics, and suggestions for identifying and implementing them, are offered.


"Statistics in Preschool"

Sterling Hilton, Scott Grimshaw, and Genan Anderson (2001), The American Statistician, 55(4), 332-336.

Abbreviated Abstract: Statistics education has become established in the elementary school curriculum. Because the principles of statistics underlie many basic learning concepts, it is not surprising to discover statistics principles in the preschool curriculum as well. This article describes how statistical tools and concepts are included in the Brigham Young University Child and Family Studies Laboratory preschool curriculum.


"Counting Eights: A First Activity in the Study and Interpretation of Probability"

Bradley Hartlaub and Brian Jones (2001), STAR Library.
www.starlibrary.net/activities/hartlaub_jones2001.htm

Abbreviated Abstract: Students explore the definition and interpretations of the probably of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency."


"Random Rendezvous"

Allan Rossman and Beth Chance (2001), STAR Library.
www.starlibrary.net/activities/rossman_chance2001.htm

Abbreviated Abstract: This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. The scenario of the activity is easy to state and to understand: Tom and Mary agree to meet for lunch at a certain restaurant, but their arrival times are random variables. Furthermore, they agree to wait only for a certain length of time for the other to arrive. The goal is to calculate the probability that they meet.


"What is the Shelf Life?"

Christopher Bilder (2001), STAR Library.
www.starlibrary.net/activities/bilder2001.htm

Abstract: The Food and Drug Administration requires pharmaceutical companies to establish a shelf life for all new drug products through a stability analysis. This is done to ensure the quality of the drug taken by an individual is within established levels. The purpose of this out-of-class project or in-class example is to determine the shelf life of a new drug. This is done through using simple linear regression models and correctly interpreting confidence and prediction intervals. An Excel® spreadsheet and SAS® program are given to help perform the analysis.


Reviews


Book Review: AP Statistics: Preparing for the Advanced Placement Examination, by James Bohan with Beth Chance (2001), Amsco.

Dan Shuster, The Statistics Teacher Network, 57.

Excerpt: "On the whole, this is a quality reference that should be helpful to both the student and teacher of AP Statistics. I feel that it is the best AP Statistics review book available. The exposition is well written, thorough and attractively designed. It can be used as both a supplement and as preparation for the exam in the spring. The price is attractive as well (around $14.00)."


Book Review: Introduction to Statistics and Data Analysis, by Peck, Olsen, and Devore (2001), Duxbury Press.

Susan Mead, The Statistics Teacher Network, 57.

Excerpt: "As the authors state, Introduction to Statistics and Data Analysis is designed with a particular eye toward the syllabus of the Advanced Placement Statistics course and the needs of high school teachers and students. They have succeeded magnificently. This textbook is a wonderful primary text, needling little or no supplementation, or at least a must-have reference text."


Book Review: A First Course in the Design of Experiments: A Linear Models Approach, by Donald Weber and John Skillings (2000), Chapman and Hall/CRC Press.

Russell Lenth (2001), The American Statistician, 55(4), 370.

Excerpt: "If we want to do a good job of teaching experimental design to people other than graduate students in statistics, we should skip the mathematical rigor and emphasize the practical rigor that is exemplified in Cobbís book. If we want to do a good job of teaching statistics to graduate students, we should not skip the mathematical rigor, but neither should we short-change (students) on practical rigor. We need to do more for our graduate students in challenging them to ask "where do data come from?" and to explain just how important that question is. Weber and Skillingsís text appears to be a promising resource for the mathematical part. However it does not say nearly enough about design, and I do not recommend it if you can spend only one semester on experimental design."


Book Review: Statistics for Management and Economics, Fifth Edition, by Gerald Keller and Brian Warrack (2000), Brooks/Cole.

Norean Radke Sharpe (2001), The American Statistician, 55(4), 370-371.

Excerpt: "This is a comprehensive text with interesting examples, clear explanations, and a good array of exercises. The emphasis on data analysis using two different software packages with explicit descriptions of commands used to generate the output makes this text attractive to instructors who use either Minitab®® or Excel®. Augmented with supplements, this text may be an appropriate choice for a two-course sequence in business statistics."


Book Review: Basic Engineering Data Collection and Analysis, by Stephen B. Vardeman and J. Marcus Jobe (2001), Brooks/Cole Thompson Learning.

Bradley Warner (2001), The American Statistician, 56(1), 76-77.

Excerpt: "... this is the best textbook that I have ever seen for an introductory statistics course for engineering students and as it is only the first edition it should improve in subsequent editions. I am recommending it to my colleagues." Some of the positives Warner mentions include the focus on engineering problems, and how to use statistics to solve them, and the emphasis on the scientific method.


Book Review: Workshop Statistics: Discovery with Data, A Bayesian Approach, by Allan Rossman and James Albert (2001), Springer-Verlag.

Kevin Rees, (2001), The American Statistician, 56(1), 77-78.

Excerpt: "Overall this is a very excellent addition to the Workshop Statistics series, and one that will make people who have wished to introduced Bayesian methods to all undergraduate students very happy. It is highly readable, has excellent problems, and (the authors) Web sites include solutions to the problems, sample syllabi, sample exams, datasets, Minitab® programs and macros, Java applets, and a guide for instructors. Even if you do not feel that this textbook is suitable as the main text for your introductory course I would recommend a copy as a reference, or as a lab manual, as many of the examples and problems re suitable activities for any introductory class."


Deborah J. Rumsey
Director, Mathematics and Statistics Learning Center
Department of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210
USA
rumsey@math.ohio-state.edu


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