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 9, Number 1 (2001)

Copyright © 2001 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


Teaching Statistics: Resources for Undergraduate Statistics

Thomas Moore, Editor (2000). Joint Publication of the American Statistical Association and the Mathematics Association of America (MAA Notes).

This book includes a collection of classic original articles that helped to shape the statistics education reform movement, as well as guidance to others who are involved in the process of improving their teaching. It includes descriptions and teacher notes regarding several of the most innovative and effective projects and products that have been developed in recent years. The book also includes ideas for using real data in teaching, how to choose a textbook, how to most effectively use technology, as well as guidance regarding assessment. It can be ordered through the ASA (see the ASA website at http://www.amstat.org).


"Challenges of Implementing Innovation"

Barbara S. Edwards (2000), The Mathematics Teacher (Online), 93(9).
http://www.nctm.org/mt/2000/12/innovation.html

In this informative paper, Edwards outlines the major steps involved in the process of undergoing educational reform, as well as some of the major obstacles that are likely to be encountered. She provides a thorough citation of the latest research in this area of "the process of change." Edwards makes an important point: "A strong desire to change does not by itself ensure a successful innovative effort. Indeed, research has shown that a commitment to change is only one ingredient needed for successful change." Some of the factors cited by Edwards as being important to the process of change include: a vision of what the change should be (goals), a well-defined context within which the change is to take place, an ability to compare what is practiced to what is envisioned, a means to provide teacher support, as well as consideration of teachers’ past experiences, beliefs about teaching learning, and a teacher’s knowledge of mathematics and pedagogy.


"Are our Teachers Prepared to Provide Instruction in Statistics at the K-12 Levels?"

Christine Franklin (2000), Mathematics Education Dialogues, 2000-10, National Council for Teachers of Mathematics.
http://www.nctm.org/dialogues/2000-10/areyour.htm

In this essay, Franklin addresses the critical need for better training and preparation of pre-service and in-service K-12 teachers in the area of statistics. She stresses the need for teachers to be able to handle the rapid growth in the number of students taking Advanced Placement statistics courses and examinations in high school, stating that the number of AP Statistics exams taken has increased from 7,500 in 1997 to 35,000 in 2000. Franklin points out that the reformed statistics curriculum requires teachers to move beyond the traditional formula and algorithm approach, which is a good idea, but presents a problem, since most K-12 teachers believe their backgrounds to be inadequate to teach under the reform guidelines.


"Deciding When to Use Calculators"

Anthony D. Thompson and Stephen L. Sproule (2000), Mathematics Teaching in the Middle School, 6(2).

Abbreviated Abstract: The influence of technology, particularly the calculator, in the middle school classroom has become a compelling issue for both practicing and prospective teachers. The National Council of Teachers of Mathematics (1989) encourages the use of calculators in the middle grades, but teachers face a number of difficulties when they introduce calculators in their classrooms. These teachers ask, "When should I use calculators?" and "What should students know before I allow them to use calculators?" The larger question that teachers often ask is "On what basis do I make the decision to use calculators with my students?” The purpose of this article is to share a framework that we provide to middle school mathematics teachers to help them decide when to use calculators with their students. This framework helps the teacher focus less on the calculator and more directly on his or her own educational goals and the students' needs and abilities.


Teaching Ideas and Applications


"Herman Hollerith: Punching Holes in the Process"

Art Johnson (2000), Mathematics Teaching in the Middle School, 5(9).

What was it like to work for the Census Bureau over one hundred years ago? An short but very interesting biography on Herman Hollerith (1860-1929), the man who designed and developed the first mechanical tabulating system. Hollerith was a census statistician whose first task was to analyze the data from the 1880 census. His new tabulating system involved the use of punch cards to activate electric counters.


"A Career that Counts"

Art Johnson (2000), Mathematics Teaching in the Middle School, 5(9).

What is it like to work for the Census Bureau today? Johnson interviews Amy Smith, who works at the Administrative Records and Methodology Research Branch of the Population Division of the Census Bureau, and provides insightful information for students in practical, interesting terms. Johnson also includes some group activities that focus on collection and summarization of data relating to the U.S. Census.


"Using Beam and Fulcrum Displays to Explore Data"

David P. Doane and Ronald L. Tracy (2000), The American Statistician, 54(4), 289-290.

Abstract: The beam-and-fulcrum display is a useful complement to the boxplot. It displays the range, mean, standard deviation, and studentized range. It reveals the existence of outliers and permits some assessment of shape. Embellishments to the beam-and-fulcrum diagram can show the item frequency, and/or a confidence interval for the mean. Its intuitive simplicity makes the beam-and-fulcrum an attractive tool for exploratory data analysis (EDA) and classroom instruction.


"Well-Rounded Figures"

by Yves Nievergelt (2001), The College Mathematics Journal, January, 2001.

We always tell students to be careful when rounding during the process of a complex calculation, but a student might ask if rounding really makes a big difference. This article discusses the consequences of improper rounding procedures in the context of calculating a variance. An example is provided where a variance is calculated using three different rounding methods, obtaining incredibly different answers of: 2.88, 0.51, and even -21.00.


"Sumgo Here and Sumgo There"

David E. Meel (2000), Mathematics Teaching in the Middle School, 6(4).

Abstract: The idea of "sumgo" was suggested by the game of bingo and the need to illustrate the utility of educational games, help students practice skills, and introduce new concepts. This game was designed to investigate an interesting distribution while practicing a computational skill. As a result, the activity described in this article focuses on the concepts of sample spaces and exact probabilities while providing practice in addition. In designing "sumgo," I envisioned a mathematics class actively engaged with the game while practicing addition and learning about data interpretation, experimental and theoretical probability, and the consequences of randomness.


"Teaching Probability to Young Children - Part 2"

Cyrilla Bolster (2000), The Statistics Teacher Network, 55, 5-7.

Part 1 of this article (discussed in the previous issue) helps young children develop the idea of fairness in terms of probability through the use of games. In Part 2, the following issues are examined by looking at games: How do I know if a game is fair or unfair? What am I up against and what can I do about it? How can I be sure a game is random? Can I really predict what is going to happen in a game of chance? How do I decide whether to play a game or not?


"Enriching Students’ Mathematical Intuitions with Probability Games and Tree Diagrams"

Leslie Aspinwall and Kenneth L. Shaw (2000), Mathematics Teaching in the Middle School, 6(4).

This article provides some probability games and tasks designed to help students overcome misconceptions and misleading intuitions connected with the concept of "fairness" in outcomes.


"Runs With No Winner in a Lottery"

Richard Iltis (2000), The College Mathematics Journal, November, 2000.

This article puts a new spin on lottery discussions. The proposal is that people are more motivated to play the lottery when the likelihood of having to split the winnings is decreased. This occurs when there are more possible numbers to choose from. The article examines the issue of determining how many fewer winners one can expect in that case, using the case of the Oregon "Big Bucks" lottery.


"The Case of the Missing Lottery Number"

W.D. Kaigh (2001). The College Mathematics Journal, January, 2001.

In 1998, the Arizona state lottery experienced 32 games in a row where the digit “9” was never selected as one of the three digits in the winning sequence. Was this just a situation of random chance, or was there more to it? In this article, the author explains why he believes there was more to it.


"The Probability of Winning a Lotto Jackpot Twice"

Emeric T. Noone, Jr. (2000). The Mathematics Teacher (Online), v.93, n. 6.

A question that oftentimes comes up in student discussions about probability is the following: How likely is it that someone can win a lottery twice? This article provides some ideas for helping students answer this question by figuring out what the probability is, and thinking about it.


"Using Deming’s Funnel Experiment to Demonstrate Effects of Violating Assumptions Underlying Shewhart’s Control Charts"

Ross S. Sparks and John B. F. Field (2000), The American Statistician, 54(4), 291-302.

Abbreviated Abstract: Deming’s funnel experiment is used to demonstrate the effect of blind use of Shewhart’s (sample mean) and R charts for process data that violate at least one of the assumptions underlying their correct application. Simple graphical methods of checking the assumptions are given. How to correctly apply Shewhart charts to the funnel experiment data is discussed and an application is used to illustrate a solution. This article also outlines how the funnel experiment could be used for training in the correct use of statistical process control charts.


"Spinning for Confidence"

Marie A. Revak (2000), The Statistics Teacher Network, 55, 4.

Students create and spin a spinner that contain wedges of different proportion and color, collecting data on the proportion of spins for each wedge (each student’s spinner looks exactly the same.) Confidence intervals are created by each student, and are presented on the board using the same scale. After collecting the results, the students try to estimate the true proportions; then the actual answers are revealed. The data collection for this project is very swift, and the project fosters a sound interpretation of confidence interval and feelings of data ownership.


"Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures"

Alan Agresti and Brian Caffo (2000), The American Statistician, 54(4), 280-288.

Abbreviated Abstract: The standard confidence intervals for proportions and their differences used in introductory statistics courses have poor performance, the actual coverage probability often being much lower than intended. However, simple adjustments of these intervals based on adding four pseudo observations, half of each type, perform surprisingly well even for small samples. In teaching with these adjusted intervals, one can bypass awkward sample size guidelines and use the same formulas with small and large samples.


"Estimation in Discrete Choice Models with Choice-Based Samples"

Donald M. Waldman (2000), The American Statistician, 54(4), 303-306.

Abbreviated Abstract: Students of applied statistics and econometrics need exposure to problems in the theory of estimation under ideal conditions. Such problems include heteroscedsticity, variable measurement error, and endogeneous covariates. One problem that is sometimes overlooked is whether the sample has been independently drawn. This article explores the importance of random sampling in behavioral models of choice. A popular method of data collection in those models is to sample individuals who have made the same choice, and then pool several such subsamples. This selection on the dependent variable presents problems in estimation. A weighted maximum likelihood estimator which overcomes the problem with the nonrandom nature of the sample is investigated with both a hypothetical and a real example.


Reviews


Book Review: Minitab Handbook, 4th ed. (Ryan and Joiner)

Robert W. Hayden (2000), The Statistics Teacher Network, 55, 3-4.

Hayden provides a very favorable review of the latest edition of this handbook: "Many feel that it is just the book they have been looking for...it can be very useful to you even if you do not use Minitab in teaching statistics. It is in a class by itself, somewhere between a software manual and a statistics textbook." Hayden points out that this handbook promotes an understanding of data, and the learning of statistics within the setting of using Minitab to analyze real data sets and answer real questions. A minor distraction is that solutions are not provided for the exercises.


Program Review: The Data Detectives: A Student Simulation in Data Collection and Analysis (The Exchange Network)

Susan J. Bates (2000), The Statistics Teacher Network, 55, 1-3.

A middle school teacher discusses her positive classroom experience with this research exchange program, which pairs classrooms of students from different geographic locations together (grades 1-3, 4-6, and 7-9) to design, collaborate, and exchange field and descriptive data research. Teaching materials and readiness activities are also included. Bates notes the strong sense of ownership, interest, and discovery-based learning that took place when her class participated in this project: "We worked only two class periods a week on Data Detectives and the students could hardly wait to get back to their partner students to continue each time ... I encourage you to consider becoming an exchange partner!"


Software Review: ActivStats (Paul Velleman)

Norman Preston (2001), The College Mathematics Journal, March, 2001.

This reviewer gives a positive review of ActivStats, saying that it does just what its name implies: teaches statistics in a way that actively involves students.


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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