# From the Literature on Teaching and Learning Statistics

Deborah J. Rumsey
The Ohio State University

Journal of Statistics Education Volume 11, Number 1 (2003), ww2.amstat.org/publications/jse/v11n1/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

### “A Modeling Perspective on Students’ Mathematical Reasoning about Data”

Helen Doerr and Lyn English (2003), Journal for Research in Mathematics Education, 34(2), 110-136.

Abstract: A modeling approach to the teaching and learning of mathematics shifts the focus of the learning activity from finding a solution to a particular problem to creating a system of relationships that is generalizable and reusable. In this article, we discuss the nature of a sequence of tasks that can be used to elicit the development of such systems by middle school students. Student reasoning about the relationships between and among quantities and their application in related situations is discussed. The results suggest that students were able to create generalizable and reusable systems or models for selecting, ranking, and weighting data. Furthermore, the extent of variations in the approaches that students took suggests that there are multiple paths for the development of ideas about ranking data for decision making.

### “An Exploration of Students’ Statistical Thinking with Given Data”

Maxine Pfannkuch and Amanda Rubick (2002), Statistics Education Research Journal [Online], 1(2), 4-21. (fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ1(2).pdf)

Excerpts from Summary: This paper examines how two twelve-year old students built up their recognition and understanding of relationships in a set of data. Using a small multivariate data set, the students conducted an investigation of their choice in a pencil-and-paper environment. From the analysis we identified five issues that should be considered for determining how students construct meanings from data. They are: prior contextual and statistical knowledge; thinking at a higher level than constructed representations; actively representing and construing; the intertwinement of local and global thinking; and the changing statistical thinking dialogue across the representations (cards, tables and graphs).

### “Teaching Students the Stochastic Nature of Statistical Concepts in an Introductory Statistics Course”

Maria Meletiou-Mavrotheris and Carl Lee (2002), Statistics Education Research Journal [Online], 1(2), 22-37. (fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ1(2).pdf)

Excerpts from Summary: This article argues that the persistence of student difficulties in reasoning about the stochastic, despite significant reform efforts, might be the result of the continuing impact of the formalist mathematical tradition, affecting instructional approaches and curricula and acting as a barrier to instruction that provides students with the skills necessary to recognize uncertainty and variability in the real world. It describes a study driven by the conjecture that the reform movement would have been more successful in achieving its objectives if it were to put more emphasis on helping students building sound intuitions about variation.

### “New Approaches to Gathering Data on Student Learning for Research in Statistics Education”

Beth Chance and Joan Garfield (2002), Statistics Education Research Journal [Online], 1(2), 38-44. (fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ1(2).pdf)

Excerpts from Summary: Over the last fifteen years there has been a strong emphasis on active learning, use of real data in the classroom, and innovative uses of technology for helping students learn statistics. Now more than ever, more research is needed on the effects of these instructional methods and materials on student learning, retention and motivation. This article will present and critique methods for obtaining research data on how students develop an understanding of statistics, including classroom-based research and videotaped student interviews/observations.

### “Some Basic References for the Teaching of Undergraduate Statistics”

Peter Holmes (2002), Statistics Education Research Journal [Online], 1(2), 49-53. (fehps.une.edu.au/F/s/curric/cReading/serj/current_issue/SERJ1(2).pdf)

An international collection of basic references that, according to Holmes, “attempts to pull together the various strands of research about undergraduate teaching so that new lecturers will be able to get a quick overview of current thinking and where it has come from. Older references are to give an historical context and reflect the influences on today’s practice.”

### “Getting the Best from Teaching Statistics”

Teaching Statistics regularly publishes articles to help those teaching any type of statistics to pupils aged 9 to 19. Getting the Best from Teaching Statistics brings together about 50 of the best articles from volumes 15 to 21 of Teaching Statistics . The articles are classified under the headings: students’ understanding; statistical topics; primary school focus; practical activities; using computers and information technology; statistics at work; probability topics; lessons from history; and miscellany. This anthology is available freely online (see science.ntu.ac.uk/rsscse/ts/gtb/contents.html).

### “Interview with Bob Hogg”

Jackie Dietz (2002), STATS Magazine, 35.

Excerpt from Editor’s Column: In this article Jackie Dietz presents an interview with Bob in which he recounts how he became interested in statistics, describes some of the professors and students with whom he has worked, and offers advice to current students of statistics. During the course of the interview Jackie and Bob even discovered that they are academic relatives of each other!

## Teaching Ideas and Applications

### “Finding the Findings Behind the News”

Christopher Paul (2002), STATS Magazine, 35.

Excerpt from Editor’s Column: Statistics often make headlines. Presidential popularity polls, unemployment rates, stock market returns, and heart attack rates for people who do and do not take aspirin regularly are but a few examples of statistics that find prominent display in the popular press. But do the headlines and popular articles do a credible job of representing the findings from research studies? In the lead article of this issue, Christopher Paul offers “how to” advice for digging behind the headlines to find the original reports on which to judge the accuracy of the media representation. He also presents a helpful list of questions that all students of statistics and all educated consumers of statistical information should ask. He illustrates his advice with a case study involving teenage consumption of alcohol that generated some media controversy.

### “Statistical Sampling and Data Collection Activities”

Andrew Gelman and Deborah Nolan (2002), Mathematics Teacher, 95(9), 688-701.

Abstract: This article presents several student participation activities combining (i) the basics of random sampling, (ii) practical complications (e.g., how do survey takers deal with biases from selection, nonresponse, and question wording), and (iii) theoretical ideas (e.g., sampling with unequal probabilities).

### “A New Look at Probabilities in Bingo”

David B. Agard and Michael Schakleford (2002), The College Mathematics Journal, 33(4), 301-305.

Abstract: In a bingo game with 100 cards in play, how many numbers must be called before there is a better than even chance that someone will yell, “Bingo!”? After you guess and get the wrong answer, you may use this as a test of bingo-intuition to annoy your friends and loved ones. The answer is 16. Several other bingo questions are answered too.

### “Runs in Coin Tossing: Randomness Revealed”

Geoffrey C. Berresford (2002), The College Mathematics Journal, 33(5), 391-394.

Abstract: If you ask people to make up random sequences of Hs and Ts, they will fail; our brains have so much structure that they cannot produce chaos. Here is how to tell real randomness from the fake, human-created, kind.

### “Baseball’s All-Stars: Birthplace and Distribution”

Paul M. Sommers (2003), The College Mathematics Journal, 34(1), 24-30.

Abstract: Baseball can provide any number of data sets on which to practice your statistics. Here is one more sample.

### Tossing a Fair Coin

Leonard Lipkin (2003), The College Mathematics Journal, 34(2), 128-133.

Abstract: As long as probability endures we will be tossing coins, and as long as students endure some will fail to grasp what happens when we toss them for a long time. We know that the difference between the number of heads and the number of tails gets large, and it is good to remind students of this.

### “Teaching Matrices from a Data Point of View”

Jerry Moreno (2002), The Statistics Teacher Network, 61, 6-7.

Excerpt: As statistics continues to increase its presence in the school curriculum, particularly the mathematics one, teachers complain that if statistics must be included, then something must go. One suggestion to solve the problems is to combine the topics of statistics and mathematics so that both are presented together. The NSF-funded project, Data-Driven Mathematics has done precisely that. This article will introduce one idea in the module “Modeling with Matrices” by G. Burrill, J. Burrill, J. Landwehr, and J. Witmer (Dale Seymour Publishing).

### “College Students’ Conceptions of Probability”

James Albert (2003), The American Statistician, 57(1), 37-45.

Abstract: Students in an introductory statistics class were surveyed regarding their views about probability. The students were asked to assign some probabilities and give explanations for their assignments. Results from the surveys indicate that students were generally confused about the classical, frequency, and subjective notions of probabilities. Although the students were able to solve stylized classical probability problems, they were apt to assume that experimental outcomes were equally likely even when this assumption was inappropriate. In addition, the students were not comfortable specifying probabilities using the frequency and subjective views. This article discusses how this confusion about the interpretation of probability affects the teaching of an introductory statistics class and provides some activities helpful for teaching the various probability viewpoints.

### “Teaching Experiences with a Course on “Web-Based Statistics”

Jurgen Symanzik and Natascha Vukasinovic (2003), The American Statistician, 57(1), 46-50.

Abstract: Many statistics courses have been taught that make use of Web-based statistical tools such as teachware tools, electronic textbooks, and statistical software on the Web. However, to our best knowledge, there has been no course before where statistical issues and the Web have been discussed systematically. This article provides an overview on our “Web-Based Statistics” course aimed at advanced undergraduate and beginning graduate students, including detailed discussions of lecture topics, homework assignments, and student projects. We discuss references (papers and URLs) useful for such a course and summarize students’ feedback. We finish this article with recommendations for future similar courses.

### “Illustrating the Law of Large Numbers (and Confidence Intervals)”

Jeffrey Blume and Richard Royall (2003), The American Statistician, 57(1), 51-57.

Abbreviated Abstract: Instructors of introductory statistics classes tend to separate out abstract probability concepts because of the level of mathematics required to present them. The Law of Large Numbers, which explains why making repeated observations on a population is informative, seems especially vulnerable to this tendency. This is unfortunate because the Law validates students’ intuitive understanding about why statistics works and reinforces the notion that abstract probability concepts have important, real-life consequences. Instead of presenting the Law in a mathematical fashion, we propose a graphical presentation designed to communicate and emphasize the Law’s importance.

### “The Gourmet Guide to Statistics: For an Instructional Strategy that makes Teaching and Learning a Piece of Cake”

Gunapala Edirisooriya (2003), Teaching Statistics, 25(1), 2-5.

Summary: This article draws analogies between the activities of statisticians and of chefs. It suggests how these analogies can be used in teaching, both to help understanding of what statistics is about and to increase motivation to learn the subject.

### “Confident in a Kiss?”

Mary Richardson and Susan Haller (2003), Teaching Statistics, 25(1), 6-11.

Summary: This article describes an interactive activity for illustrating general properties of confidence intervals and the construction of confidence intervals for proportions. In completing this activity, students generate, collect, and analyze data.

### “The Same but Different - How to Introduce Variation within Computing Assessment Tasks”

Flavia Jolliffe (2003), Teaching Statistics, 25(1), 12-16.

Summary: In this article, suggestions are made for introducing an individual element into formative assessment of the ability to use computer software for statistics.

### “Fifteen to One”

Susan Meacock (2003), Teaching Statistics, 25(1), 17-21.

Summary: This article shows how data from a television game show can be used as a basis for illustrating many statistical procedures.

## Reviews

### Book Review: A First Course in Design and Analysis of Experiments, by Gary Oehlert (2000), Kluwer Academic Publishers.

Shaun Wulff (2003), The American Statistician, 57(1), 66-67.

Excerpt: As the title suggests, this text provides an introduction to design and analysis of experiments. It is intended for undergraduate and graduate students who have had an introductory statistical methods course. This text is written for statisticians and nonstatisticians alike. As a result, the focus is on application and not mathematical theory. Unlike other comparable texts, considerable attention is given to randomization, how to choose a design, and how to identify a design. Given the readability, the use of relevant examples, and the practical approach to design and analysis, this text is a valuable reverence for a first course in experimentation. (Wulff also recommends this text for advanced graduate students in statistics.)

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