Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



rossman plus
Posted:
Apr 26, 1996 2:10 PM


Colleagues,
**************************************************************** If you have already received this, please forgive, and discard.* ****************************************************************
There are three entries below in this very long file. The first is on the Statistics Teacher Network newsletter, history and how to subscribe (gratis publication). The next is a review by Joan Garfield on Rossman's Workshop Statistics book. And the third is a review by Bob Hayden on Siegel and Morgan's book. Both of these reviews are to appear in the spring issue of the STN newsletter.
Keep in touch.
Jerry Moreno John Carroll University ***************************************************************
THE STATISTICS TEACHER NETWORK A BRIEF HISTORY
In 1967, the ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability for grades K12 was created by the American Statistical Association and the National Council of Teachers of Mathematics.
It was given four responsibilities:
1) to support a newsletter, The Statistics Teacher Network, for communication with precollege teachers. 2) to assist in securing funding to support curriuclum efforts for precollege programs. 3) to develop strategies to promote statistics and probability in the precollege classroom. 4) to provide leadership for the inclusion of statistics and probability in assessment and curriculum efforts.
The committee consists of 7 members: 3 appointed by ASA, 3 by NCTM, and one ASA staff person (the Director of Education).
Fred Mosteller was the first chair. Under his leadership, two publications were created: a four volume series called Statistics by Example (no longer in print); and, the book ``Statistics: A Guide to the Unknown'' edited by Judith Tanur (Wadsworth 1989, 3rd ed.).
In the 1980's, the Joint Committee created the highly successful project called Quantitative Literacy. QL has grown into several different projects. The first resulted in the publication of five volumes of handson probability and statistics materials for middle and high school programs. The Joint Committee has been involved in other activities as well. For example, the committee served in an advisory capacity in various facets of the creation of the Advanced Placement Statistics program (first examination, May 1997).
One of the Joint Committee's responsibilities was to create a newsletter for precollege teachers. The first issue of the ``Statistics Teacher Network'' newsletter appeared in September 1982 with Ann Watkins as editor. Beth Bryan took over the reigns three years later with issue 10, followed by Jack Kinney in December 1988 with issue 19. Jerry Moreno became editor with issue 31, fall 1992.
STN is a free publication whose purpose is to keep K12 teachers informed of statistical workshops, programs, and reviews of books, software, and calculators. In addition, articles are included that describe statistical activities that have been successful in the classroom. There are several thousand school teachers on the mailing list, including college faculty and others who are interested in statistical education in grades K12. Contributors come from all levels of statistical expertise; the Editor is responsible for collecting all appropriate information to be printed.
Currently (April 1996), to subscribe to STN, send your name and address to veronica@amstat.org; STN, c/o American Statistical Association, 1429 Duke St., Alexandria VA 223143402; 7036841221; fax 7036842036.
Past issues are not available. However, it is hoped that, by fall 1996, selected past articles can be obtained electronically.
Contact Jerry Moreno for further information, including volunteering to write or review articles. moreno@jcvaxa.jcu.edu; Dept. of Mathematics and Computer Science, John Carroll University, University Hts., OH 44118; 2163974681; fax 2163973033.
**************************************************************************
Book Review...
Workshop Statistics: Discovery with Data Allan Rossman, Dickinson College, Pennsylvania $25, 1995, 452pp., 0387944974,Jones and Bartlett, 8008320034, custserve@jbpub.com
Over the past few years I have written articles and given conference presentations describing ways statistics courses should be redesigned to better facilitate student learning. I have encouraged the use of active learning strategies, problem solving using real data sets of interest to students, small group discussions, writing assignments, and appropriate technology. Allan Rossman's new introductory text, Statistics Workshop, appears to have incorporated all of these important components in a lowcost softcover textbook.
This book is distinguished from other introductory textbooks in several important ways. There is a focus on "big ideas" rather than a large collection skills, definitions, explanations, and techniques. Instead of presenting students with methods of analyzing data and descriptions of concepts, Workshop Statistics is designed to provoke students to discover concepts themselves. When skills are presented it is because there is a reason to use them: to carry out the next step in solving a problem by analyzing data. Rossman explains that pages of expository material or solved examples are omitted to emphasize "the idea that students construct their own knowledge of statistical ideas as they work through the activities." While most textbooks contain problem sets at the end of the chapter, each focusing on a different (and often contrived) set of data, the homework activities in this text extend the types of activities conducted in class, examining a few real data sets in more detail. An emphasis on "writing to learn" is also embedded in the activities by continually asking students to write about different aspects of data analysis and to summarize what they have learned about a particular topic.
Workshop Statistics is divided into six units, each consisting of three to five topics. Over 100 data sets are either generated by students or included in tables (soon to be available on a data disk). Students combine data explorations by hand with use of a computer or calculator to generate graphs and statistics.
The first unit, Topic 1: "Exploring Data: Distributions," illustrates the handson data exploration approach. This unit is divided into five topics, each appropriate for one class session. On the first day of class students make predictions and gather data about themselves (gender, political views, opinions of statistics). They are guided through activities where they learn how to generate and analyze data to describe the number of states and countries they have visited. By the end of this first activity students have learned to distinguish different types of variables and data and how to construct and describe dotplots and histograms. In the next section students are asked to compare and examine dotplots, allowing ideas to emerge of center, spread, shape, and outliers as distinguishing features of these plots. Topics 3 and 4 introduce more details on measures of center and spread, and the fifth topic challenges students to integrate and use these techniques in comparing distributions.
The next unit of the text explores relationship between two variables with topics on graphing bivariate data, correlation and regression, and tables of categorical data. Students are first shown scatterplots of data where they develop their own ideas of association between variables. Later they analyze data on space shuttle oring failures, peanut butter cost and quality, and cars' fuel efficiency. By examining and manipulating different scatterplots while viewing correlation coefficients, students construct ideas of how different factors influence the correlation between variables. In an activity comparing the average number of television sets per person and life expectancy for 22 countries, students discover that correlation does not imply causation.
The third unit, "Randomness", is quite a departure from the typical chapter on probability in most introductory textbooks. Instead, this unit introduces sampling distributions and then focuses on the normal distribution and the central limit theorem. As Rossman explains in the introduction, there is no formal treatment of probability. Instead, ideas of probability are introduced in the context of simulation and random variation and as they apply to methods of statistical inference.
Topic 4 introduces statistical inference first through confidence intervals for proportions and then through significance tests. Topic 5 includes important aspects of designing experiments and extends inference to comparisons of two proportions. In the last unit, Inference From Data: Measurements, student learn to make inferences involving one or two population means.
This textbook not only looks exciting, it also works well with students. I know because I used an earlier version of Workshop Statistics in a class and have also observed Allan Rossman teaching a class at Dickinson College. Students typically work in pairs or groups on the data exploration activities after a wholeclass orientation to the day's topic. While Allan teaches his class in a room equipped with Macintosh computers, allowing students to easily analyze data using Minitab, the format of the book allows students to use any type of computer or graphing calculator either during or outside of class. I have found students to enjoy the activities and appreciate the varied and interesting data sets. Although students initially resist writing long verbal descriptions, they eventually learn how to do this and appear to value the process.
I encourage all statistics educators to seriously consider using this innovative text. I believe that it provides an exemplary instructional approach that should enable more students to overcome their fears about learning statistics and to become statistically literate.
Reviewed by Joan Garfield University of Minnesota Minneapolis, Minnesota
*******************************************************************
Statistics and Data Analysis: An Introduction (2nd ed.) Andrew F. Siegel and Charles J. Morgan Wiley, 1995, $68, ISBN 0471574244
This book is the second edition of an underground classic first published in 1988. The first edition (by Siegel alone) was reviewed for Volume 26 of STN (December 1990) by Joan Garfield. She used it for many years at the University of Minnesota, and colleagues and I used it at Plymouth State College until last summer. It recently showed up as one of the seven textbooks the College Board is recommending for the new Advanced Placement Test in Statistics. Even so, it is no secret that the book was not a great success in the marketplace. The second edition attempts to broaden the book's appeal. I think it succeeds, but sometimes at the expense of muting a few of the virtues that made the first edition so outstanding.
One of those virtues is the writing. The first edition was by far the most readable introductory statistics text I have ever used. It was also written in a warm and friendly tone that remains unusual in statistics textbooks. The second edition maintains a high level of readability. The warmth is somewhat diluted.
Another thing that set the book apart was its content. Although the NCTM Standards suggest big changes in how mathematics is taught, and smaller changes in what mathematics is taught, the underlying mathematics has not changed much. One and one still is two, and has been for quite some time. Statistics, on the other hand, underwent a great revolution in the 1960's, a revolution often linked with the name of John Tukey. One of the first things I look for in a statistics textbook is whether there is any sign that the author has heard about this revolution yet. Because so many statistics textbooks are written by nonstatisticians, the news has spread very slowly. Andrew Siegel was part of the Tukey revolution, and I think that is one reason why the first edition was ahead of its time. All the good K12 statistics materials from NCTM and QLP are definitely postTukey, but many college textbooks still are not. Caveat emptor.
One sign of Tukey's influence is the use of stem (and leaf) plots and box (and whisker) plots. These are a necessary condition for textbook adoption these days, but alas not a sufficient one. A few of you may remember the "new math" era, when set ideas were supposed to unify all of mathematics. We then saw textbooks that sprouted an obligatory "Chapter 0" where set notation (not ideas) was introduced, and then forgotten, and certainly never used to unify the rest of the content. Similarly, we have reached the point where most textbooks now mention the stem and leaf or boxplot, but many really don't know what they are for, and so never use them for anything.
Another way people characterize the Tukey revolution is in terms of the "three R's" of postTukey statistics
residuals reexpression robustness
Residuals are usually first encountered in the context of fitting lines to data. There they are the (signed) distances between the points and the fitted line. Analyzing them helps us to evaluate how well our straight line model fits the data. Siegel and Morgan introduce residuals very early  the deviations from the mean that figure in the computation of variance and standard deviation are presented as residuals. Toward the end of the book there is a masterful example of the use of residuals in regression analysis. Data is presented on the average heights of girls for ages 211. Height versus age looks like a nearly perfect straight line, and the correlation is 0.997. Yet a graph of the residuals shows pronounced curvature in the relationship, something you would never see without examining the residuals! (Although the book does not mention it, fitting a quadratic to the data gives a residual plot that clearly indicates a cubic component!) This is an example of one of the great strengths of this book  it not only shows you the latest techniques, it shows them to you in examples that indicate what the technique does for you and why it is important, rather than with examples that merely show you the mechanics of carrying out the technique. Without the "why", the "how" is useless.
Reexpression is more often called "transformation". Perhaps the most traditional example of that is the fact that some relationships are better plotted on logarithmic or semilogarithmic graph paper. The TI82 calculator uses such transformations (taking logs of x or y or both) to fit a variety of models to twovariable data. The first edition of Siegel contains the best elementary introduction to the use of transformations in statistics. They are introduced early in the book and used in both the analysis of variance and regression chapters. The second edition contains the secondbest elementary introduction to the use of transformations in statistics. The initial coverage is cut about in half, and the applications to regression have disappeared. This is especially unfortunate for use in the high schools, where the logarithmic and exponential curve fitting features have found many uses in mathematics and science classes, and raised a lot of questions and confusion among teachers about what is going on there. In this instance, I think Wiley has stepped backward too far. While the first edition may have been (too far?) ahead of its time, much has changed since 1988, and in this area the second edition is behind the times  though still ahead of most other textbooks!
The third R, robustness, refers to the the ability of a statistical measure or technique to resist the effects of errors and outliers in the data, or violations of the assumptions underlying the technique. The traditional mean and standard deviation are not very robust to outliers, and so the more robust median and interquartile range are preferred in many situations. (Note that the boxplot is based on them.) Siegel and Morgan introduce these robust measures first, and present them as the standard tools. The mean and standard deviation are then introduced as specialized tools particularly appropriate to normally distributed data. This makes it clear that the Tukey revolution really was a revolution  it not only introduced additional techniques, but changed the way statisticians regard the older techniques. Siegel and Morgan understand this, but many other textbook authors do not.
The new edition extends the coverage of nonparametric techniques. These are techniques that make fewer assumptions than the traditional techniques, and generally handle outliers better. They may be less efficient if your data really are drawn from a normal distribution, but safer if they are not, or if you cannot tell, as with small samples.
One serious flaw in the first edition was the very small number of problems for students. I would estimate that the new edition has three to five times as many. There are answers to about half of these, and the answers contain more words than numbers. The words deal with interpretation of the data, which, after all, is what statistics is all about. There is also an Instructor's Solution Manual in the works with more detailed solutions. (I put it on reserve in the library for student use.)
Another criticism of the first edition was that it contained hardly any formulas. Calculations were explained in a manner resembling instructions for filling out your income tax forms. Personally, I saw this as an asset. I teach a general education statistics course to first and second year students at a small former state teachers' college. For most of these students, formulas would be a barrier to understanding rather than a path to understanding. However, if you are a high school teacher trying to show students the use of algebra in statistics, you will want to see formulas. If you are a high school teacher doing an AP Statistics course, you will want to keep your students' algebra skills reasonably fresh for when they take the SAT and go on to college. Indeed, the sample questions distributed for AP Statistics require much more algebraic facility than most of my college students have. For those who like a little algebra in their statistics, the second edition of this book is now bilingual.
Indeed, the second edition is trilingual. The steps of carrying out a procedure are given in words, in formulas, and in commands for the Minitab statistical software. The computer examples do not replace a manual for the software; often you see just the final steps of an analysis, without any explanation of how they set up the database or how they got to the last step. At least the examples get you started and provide some experience in interpreting computer printout in situations where no computer is available. I think the choice of the Minitab software package is a good one. There are versions of Minitab for DOS, Windows, and the Macintosh. The software was originally designed for educational purposes, and is probably the most widely used software in college statistics courses, yet it is also used by a majority of the Fortune Top 50 companies in the US. It was also one of the first packages to reflect the Tukey revolution. A disk containing most of the data sets from the book is promised. The draft disk I examined had some bugs in it but there were about 100 data sets, some of them definitely too large to ask students to type in.
There is no mention of calculators in either edition of the book. That does not bother me, since a computer is a much more appropriate tool for statistics, but it may bother some high school teachers for whom graphing calculators are more familiar and accessible to both themselves and their students. While we all have to do the best we can with what we have, I hope prior comfort levels with calculators will not divert teachers from pressing for more appropriate technology.
One of the limitations of calculators in statistics is their limited data storage capacity. This book "recycles" many of its data sets over and over, using them to illustrate a number of different points. Sometimes a question raised in one chapter is not fully answered until a later chapter when the same data is examined again. I think this is a good technique, but I would hate to have to constantly be retyping or reloading the data into a calculator.
My biggest disappointment with this text is that it does not do a very good job of convincing the student that statistics is important. There are many real data sets, and they are often extremely well chosen to illustrate the techniques, but the techniques are not often used to answer any real question of interest. For example, the areas of important islands in the Atlantic Ocean are used as an example of transforming data. It is a wonderful example for that purpose. If you plot the data on a linear scale you get Greenland at one end of the graph and a big smudge including all the other islands at the other end. You can not even get a legible graph without transforming this data. However, no reason is ever given as to why we might want to study the areas of these islands. We come away from the example knowing more about statistics, but we do not know any more about islands. This is sad, because statistics is primarily a tool to answer real questions in areas outside of statistics. I should make it clear that the present book is not outstandingly bad in this regard. It is actually somewhat above average. However, it is a failing of most textbooks that has come to bother me more and more each year. You will need to supplement this one (and most others) with some more motivating and realistic examples.
One potential supplement would be _Statistics by Example_ by Sincich (Dellen). This book contains a huge number of problems based on real studies. Often the background is too sketchy or too technical, and sometimes we get only summary statistics rather than raw data, but there are so many problems that it is still a worthwhile resource. (The book is pretty ordinary otherwise, with only slight signs of Tukeyawareness.)
My colleague Bill Roberts and I are currently half way through an introductory statistics course using the Siegel and Morgan text, and we are quite happy with it. I urge anyone looking for a textbook to adopt to look at it. Those wanting to learn more about statistics themselves might want to try to dig up a copy of the first edition.
Reviewed by Robert Hayden Plymouth State College Plymouth, New Hampshire
*********************************************************



