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 11, Number 2 (2003), www.amstat.org/publications/jse/v11n2/rumsey.html

Copyright © 2003 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


“Statistics: Challenges and Opportunities for the Twenty-First Century”

Jon Kettenring, Bruce Lindsay, and David Siegmund, Editors (2003), National Science Foundation Report.

This NSF report on the future of statistics is the result of a workshop that took place at NSF in May of 2002, including 50 statisticians from around the world. The goal of the workshop was to identify future challenges and opportunities for the profession, but it also covered important related topics, statistics education being one of them. Chapter 6 of this report is entirely devoted to statistics education, including K-12 statistics, undergraduate statistics training, graduate statistics training, post-graduate statistics training, special initiatives (such as the VIGRE program), continuing education, and educational research. All statisticians are encouraged to read the report and submit their comments to any of the three editors, Jon Kettenring, Bruce Lindsay, or David Siegmund. You can find the report at www.stat.psu.edu/%7Ebgl/nsf_report.pdf.


“Expanding Conceptions of Statistical Literacy: An Analysis of Products from Statistics Agencies”

Iddo Gal (2003), Statistics Education Research Journal, 2(1), 3-21. fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ2(1).pdf

Abbreviated Abstract: This paper reports the results of an exploratory study of the characteristics of key information products released by statistics agencies. Such products are central to debates and decisions in the public arena, but have received little attention in the literature on statistical literacy, statistics education, or adult numeracy. Based on a qualitative analysis of Internet-based products of six national and international statistics agencies, the paper sketches the characteristics of five product types (and) of the environments in which they are found. The paper discusses implications for the specification of the skills needed for accessing, filtering, comprehending, and critically evaluating information in these products. Directions for future research and educational practice are outlined.


“Assessing Statistical Reasoning”

Joan Garfield (2003), Statistics Education Research Journal, 2(1), 22-38. fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ2(1).pdf

Abbreviated Abstract: This paper begins with a discussion of the nature of statistical reasoning, and then describes the development and validation of the Statistical Reasoning Assessment (SRA), an instrument consisting of 20 multiple-choice items involving probability and statistics concepts. The SRA provides 16 scores which indicate the level of students’ correct reasoning in eight different areas and the extent of their incorrect reasoning in eight related areas. Results are presented of a cross-cultural study using the SRA to compare the reasoning of males and females in two countries.


“Relationships between Students’ Experience of Learning Statistics and Teaching Statistics”

Peter Petocz and Anna Reid (2003), Statistics Education Research Journal, 2(1), 39-53. fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ2(1).pdf

Abbreviated Abstract: Students in the same statistics course learn different things, and view the role of the lecturer in different ways. We report on empirical research on students’ conceptions of learning statistics, their expectations of teaching, and the relationship between them. The research is based on interviews, analyzed using a qualitative methodology, with statistics students studying for a mathematics degree. Students expressed a range of conceptions of learning in statistics, and a range of conceptions of their lecturers’ teaching. These conceptions of learning and teaching were related, but not as closely or as exclusively as previous researchers have indicated.


“The Future Direction of Statistical Training for the Promotion of Cooperation between Government and Academy”

Yunkee Ahn, Buhn Nam, and Chul Eung Kim (2003), International Statistical Review, 70(2), 461-467.

Abstract: A survey was carried out showing that the knowledge of academic statisticians about governmental data needs to be improved. We also state the current cooperative activities between government and academy, university education program, and statistical training program by the Korean National Statistical Office. We present some suggestions to promote cooperation between academia and government.


“The American Statistics Poster Competition”

Linda Quinn (2003), The Statistics Teacher Network, 62, 1-7.

This article discusses the results of the 13th Annual American Statistics Poster Competition, 2002, and gives advice on poster construction from the judges (both last year and in the past), including a very informative rubric for the judging of statistical posters.


Teaching Ideas and Applications


“Exploring the Probabilities of ‘Who Wants to be a Millionaire?’ ”

Robert Quinn (2003), Teaching Statistics, 25(3), 81-85.

Abstract: This article discusses three probabilistic scenarios based on the television game show ‘Who Wants to be a millionaire?’. These situations provide motivational opportunities for (students) to explore the concepts of expected value, permutations and independent events.


“Do Football Teams have Clusters of Wins, Draws, and Defeats?”

Nigel Smeeton (2003), Teaching Statistics, 25(3), 90-92.

Abstract: The issue of whether football teams have good or bad patches during the course of a season is of concern to many supporters. This interest can be harnessed to make classroom teaching of probability more relevant. In this article, the unfamiliar runs test for multiple outcomes is used to test for possible clustering in wins, draws and defeats in a short series of consecutive matches.


“Regression through the Origin”

Joseph G Eisenhauer  (2003), Teaching Statistics, 25(3), 76-80.

Abstract: This article describes situations in which regression through the origin is appropriate, derives the normal equation for such a regression and explains the controversy regarding its evaluative statistics. Differences between three popular software packages that allow regression through the origin are illustrated using examples from previous issues of Teaching Statistics.


“Intuition in Using Nominal Variables in Prediction”

Ron Suich and Richard Turek (2003), Teaching Statistics, 25(3), 86-89.

Abstract: The notion of independence between two nominal variables is typically introduced through the use of chi-square analysis of contingency tables, while the topic of prediction of one nominal variable from a second nominal variable using optimal prediction to the mode is often omitted. Through the use of a questionnaire, this article indicates that there is considerable confusion among students on the difference between concepts of independence and prediction, and remedies are suggested.  


“Handling Continuous Data in Excel”

Neville Hunt (2003), Teaching Statistics, 25(2), 42-45.

Abstract: This article demonstrates how Microsoft Excel 2000 can best be used to tabulate and chart continuous data. 


“Collecting Data on Train Performance”

Roger Porkess (2003), Teaching Statistics, 25(2), 49-53.

Abstract: This article illustrates many of the problems of defining and obtaining a 'representative' sample in the context of a real-life survey of train performance.   


“The Weakest Link”

Mike Fletcher and Claire Mooney (2003), Teaching Statistics, 25(2), 54-55.

Abstract: This article discusses optimal strategies for contestants in (this) well-known television game show.  


“A Theoretical Framework for Teaching Statistics”

Jamie d Mills (2003), Teaching Statistics, 25(2), 56-58.

Abstract: This article explores a theoretical framework to consider when teaching statistics. It is discussed and illustrated using one innovative approach to teaching using computer simulation methods. This framework can be considered across many different disciplines and age levels.


“By Comparison: A Procession of Incomes. What Do You Really Mean?”

Sidney Tyrrell (2003), Teaching Statistics, 25(2), 59-61.

Abstract: The Family Expenditure Survey provides details of household incomes. This article looks at income distribution afresh and what is meant by the mean.


“A Lottery Misfortune”

Danny Helman (2003), Teaching Statistics, 25(2), 40-41.

Abstract: This article looks at a national lottery in which the fifth prize is more probable than the sixth.


“Fairness of Dice: A Longitudinal Study of Students' Beliefs and Strategies for Making Judgments”

Jane M. Watson and Jonathan B. Moritz (2003), Journal for Research in Mathematics Education, 34(4), pp. 270–304.

Abstract: One hundred eight students in Grades 3, 5, 6, 7, and 9 were asked about their beliefs concerning fairness of dice before being presented with a few dice (at least one of which was "loaded") and asked to determine whether each die was fair. Four levels of beliefs about fairness and four levels of strategies for determining fairness were identified. Although there were structural similarities in the levels of response, the association between beliefs and strategies was not strong. Three or four years later, we interviewed 44 of these students again using the same protocol. Changes and consistencies in levels of response were noted for beliefs and strategies. The association of beliefs and strategies was similar after three or four years. We discuss future research and educational implications in terms of assumptions that are often made about students' understanding of fairness of dice, both prior to and after experimentation.


“Greek Letters in Measurement and Statistics:  Is it All Greek to You?”

Elena C. Papanastasiou (2003), STATS Magazine, 36.

Excerpt from Editors’ Column: Students of statistics quickly learn that our field involves so many symbols that we have to make heavy use of the Greek alphabet to make room for them all! Elena Papanastasiou, a native of Greece and a faculty member at the University of Kansas, offers suggestions for dealing with this potential confusion by learning how to pronounce Greek letters correctly.


“Birthday Lies”

Dale K. Hathaway (2003), Mathematics Teacher, 96 (4), 244-248.

Abstract: This article investigates how potentially dishonest students can affect the classic birthday problem.


“The Play-off Probability Problem”

Murray L. Lauber (2003), Mathematics Teacher, 96 (4), 258-269.

Abstract: This article builds on a classroom-generated solution to explore, to compare, and to generalize, a number of approaches to the problem of determining the probability of a team winning a playoff series.


“The Consumer Price Index and Inflation”

Elizabeth B. Appelbaum (2003), Journal of Online Mathematics and its Applications, 3(1) www.joma.org/vol3/modules/appelbaum/appelbaum.html

Abstract: The Consumer Price Index affects the wages of 2 million workers covered by collective bargaining, the payments to 48.4 million people on Social Security, food stamps for 19.8 million people, and the cost of lunches at school for 26.5 million children. It is used to measure inflation. TheU.S. Department of Labor's Bureau of Labor Statistics makes the index, using the average change in prices paid by urban consumers for a fixed set of goods and services. Categories include food and beverages, housing, and clothing. In this module we explore how to find the Index on the Internet, convert its history to a table in Microsoft Excel, graph the data, fit an exponential curve to the data, adjust prices for inflation, and calculate the rate of inflation. The methods can be adapted for other spreadsheets -- the figures and tables will show what functions are needed.


“An Unusual Episode”

Mary Richardson (2003), Statistics Teaching and Resource (STAR) Library. www.starlibrary.net/activities/richardson_2003.htm

Abstract: Dawson (1995) presented a data set giving a population at risk and fatalities for an “unusual episode” (the sinking of the ocean liner Titanic) and discussed the use of the data set in a first statistics course as an elementary exercise in statistical thinking, the goal being to deduce the origin of the data. Simonoff (1997) discussed the use of this data set in a second statistics course to illustrate logistic regression. Moore (2000) used an abbreviated form of the data set in a chapter exercise on the chi-square test. This article describes an activity that illustrates contingency table (two-way table) analysis. Students use contingency tables to analyze the “unusual episode” data (from Dawson 1995) and attempt to use their analysis to deduce the origin of the data. The activity is appropriate for use in an introductory college statistics course or in a high school AP statistics course.


“Sampling Distributions of the Sample Mean and Sample Proportion”

Douglas M. Andrews (2003) Statistics Teaching and Resource (STAR) Library. www.starlibrary.net/activities/andrews_2003.htm

Abstract: In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples. Outside of class, students generate samples of dice rolls and coin spins and draw random samples from small populations for which data is given on each individual. Students report their sample means and proportions to the instructor who then compiles the results into a single data file for in-class exploration of sampling distributions and the Central Limit Theorem.


“Monotone Regrouping, Regression, and Simpson’s Paradox”

Yosef Rinott and Michael Tam (2003), The American Statistician, 57(2), 139-141.

Abstract: This article shows in a general setup that if data Y are grouped by a covariate X in a certain way, then under a condition of monotone regression of Y on X, a Simpson’s type paradox is natural rather than surprising. This model was motivated by an observation on recent SAT data which are presented.


Reviews


Book Review: The Practice of Statistics: Putting the Pieces Together, by John Spurrier (2000), Duxbury.

Carolyn Pillers Dobler (2003), The American Statistician, 57(2), 142-143.

Excerpt: (This book) is one of the initial attempts to provide a resource for a capstone experience to undergraduate students of statistics. It succeeds in attaining the goals and objectives for a capstone experience, despite several weaknesses....The biggest deficiency in these 11 capstone experiences is that they are too artificial.


Book Review: A Handbook of Statistical Analyses using S-Plus, 2nd ed., by Brian Everitt (2001), Chapman & Hall/CRC.

Judith Manola (2003), The American Statistician, 57(2), 146.

Excerpt: This volume is a worthwhile investment for students or statisticians who want to improve their facility with S-Plus and who learn well from examples.


Book Review: Weighing the Odds: A Course in Probability and Statistics, by David Williams (2001), Cambridge University Press.

Paul Roback (2003), The American Statistician, 57(2), 144-145.

Excerpt: (This is) a textbook that on one hand defies convention and contains intriguing topics not often accentuated in traditional books in this area, but which one the other hand, may have difficulty finding its niche in the statistics curriculum....This book falls at a level slightly more advanced than many MS-level probability and mathematical statistics sequences, but not approaching the rigor of a PhD-level probability or mathematical statistics course. For instructors of undergraduate or MS-level probability and mathematical statistics courses, this book is worth a peek to explore how modern statistical methods can be incorporated into both (areas), how Bayesian and frequentist approaches compare, and what supplemental topics might be interesting to consider.


Book Review: The Statistical Sleuth (2nd ed.), by Fred Ramsey and Daniel Schafer (2002), Duxbury.

Johannes Ledolter (2003), The American Statistician, 57(2), 145-146.

Excerpt: I expect that this book will please instructors who wish to teach students and researchers the right way (i.e. the process) of doing statistics. The question-driven approach is what sets this book apart from the rest. Students, on the other hand, may find this approach demanding, as they have to learn two things art the same time: the methods/procedures, and the modeling process.


Deborah J. Rumsey
Department of Mathematics
The Ohio State University
Columbus, OH 43210
USA
rumsey@math.ohio-state.edu


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