Newsletter of the Stat Ed Section - V2N1

Newsletter of the Section on Statistical Education Section of the American Statistical Association


Contents of Volume 2 Number 1:

  • From the Editors
  • "Readers' Survey Informs Section about Newsletter" by Tom Moore
  • "Statistical or Quantitative Thinking -- A Fundamental Intelligence" by Neil Ullman
  • "How to Get Involved in ASA Volunteer Activities" by Jim Landwehr
  • "Q & A -- The Perfect Statistics Gift?" by Michael R. Frey
  • "Stat Ed Program for Chicago JSM" by Allan Rossman
  • "Best Contributed Paper Award from 1995" by Ron Wasserstein
  • "New Handbook on Assessment in Statistical Education" by Joan Garfield
  • "NCTM and Statistics Education in 1996: A Status Report" by Gail Burrill
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    FROM THE EDITORS

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    At last summer's meetings in Orlando, the Section decided to continue publishing its newsletter for at least two more years at two issues per year. This was based upon the positive feedback of readers, both formally via a readers' survey (see article on page 2) and informally through personal communications between readers, editors, and section officers.

    Reader input also helped us decide upon a few changes. First, beginning with the next issue (i.e., volume 2, number 2 to appear in June of 1996) the newsletter will be available on e-mail. Since overseas postage is expensive, we wish to make the e-mail version the default version for our international readers. We strongly urge all international readers to send a request for e-mail subscription to Carol Blumberg. Others who prefer to get their newsletter via e-mail should also send such a request to Carol.

    To get the newsletter by e-mail just send a short request to Carol Blumberg at wncarolj@vax2.winona.msus.edu.

    The Section also decided on a subscription policy for non- section or non-ASA members. Non-section members who are ASA members should simply join the section to become subscribers to the newsletter. Non-ASA members who do not wish to join ASA may subscribe to the newsletter at an annual cost of $8. These people should mail in the form (or a copy of it) given at the end of this article.

    The content of the newsletter beginning with this issue also reflects some editorial changes suggested by readers. Besides articles that describe resources for teaching or announce or report on conferences, we will have more substantive articles about teaching or statistics. In this newsletter Neil Ullman gives us one such article, a philosophical piece on teaching statistics based upon some current thinking of his. Michael Frey's article initiates a "Q & A" column. Readers suggested both types of articles in the reader survey last summer.

    As always, we encourage your input about the newsletter. Is it useful; can you suggest improvements? Please let us know what you think.

    Carol Joyce Blumberg
    Department of Mathematics and Statistics
    Winona State University
    Winona, MN 55987-5838
    PHONE: (507) 457-5589 or 457-5370
    FAX: (507) 457-5376
    WNCAROLJ@VAX2.WINONA.MSUS.EDU

    Joan Garfield
    Department of Educational Psychology
    University of Minnesota
    332 Burton Hall
    128 Pillsbury Drive, SE
    Minneapolis, MN 55455
    PHONE: (612) 625-0337
    FAX: (612) 624-8241
    JBG@MAROON.TC.UMN.EDU

    Tom Moore
    Department of Mathematics and Computer Science
    Grinnell College
    Grinnell, IA 50112
    PHONE: (515) 269-4206
    FAX: (515) 269-4984
    MOORET@AC.GRIN.EDU

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    READERS' SURVEY INFORMS SECTION ABOUT NEWSLETTER

    Tom Moore
    Grinnell College

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    You may recall that with last June's Section Newsletter we included a short readers' survey. We wanted reader opinion to help the Section decide upon the future of the Newsletter. We also were looking for good ideas from you for improving the Newsletter.

    In preparation for the Joint Statistical Meetings I summarized the responses received by August 10. There were 100, representing slightly less than a 10% response rate. Subsequently I received an additional 13 responses. While not part of the summary considered by the Section, these 13 responses were in essential agreement with the 100 in the formal summary. The results are tabled below.

    Conclusions:

    The Section's decision to publish two more years of the newsletter is certainly consistent with the survey. Notice that the results on hard vs. soft copy were more equivocal. Because of this we are going to continue to mail hard copy for these two years, giving readers the option of getting the newsletter electronically. Because of cost, we will strongly encourage our international readers to use the electronic option if feasible.

    We asked for "suggested improvements" and received several good ideas. Generally a fair number of people seemed to want some articles that went beyond the informational. This issue includes a status report on statistics in the schools, a Q and A column, and a "position paper," all suggestions from readers. We still include plenty of informational articles because, while redundant in some cases to other publications, there were many positive comments about these.

    The Section thanks those of you who responded to the survey.

    Summary of Newsletter Evaluation Survey

    Affiliation of respondents:  
       Academic, grad and undergrad       51
       Academic, primarily undergrad      29
       Industry/business                  10
       Other                              10
                                                     
    Should the newsletter be continued?  
       Yes                                90
       No                                  2
       Maybe                               8
    
    Do you prefer hard copy or electronic?
       Electronic                         53
       Hard copy                          36
       Undecided                           6
       Either                              5
    
    Rate on scale of 1 (not interested) to 5 (very interested) your
    interest level for articles in the future on:
     
        Topic                                      Mean rating
     Stat Ed program at JSM                            3.6             
     ASA education activities (e.g. QL)                4.1
     Stat Ed activities of other orgs                  3.7
     Conference/workshop announcements                 3.8
     Descriptions of journals, newsletters             3.9  
    
    Should newsletter be available on the internet?
       Available on internet to everyone                83
       Available on internet to section members only     9
       Should NOT be made available on internet          3
    

    Tom Moore
    Department of Mathematics and Computer Science
    Grinnell College
    Grinnell, IA 50112
    PHONE: (515) 269-4206
    FAX: (515) 269-4984
    MOORET@AC.GRIN.EDU

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    STATISTICAL OR QUANTITATIVE THINKING -- A FUNDAMENTAL INTELLIGENCE

    Neil Ullman
    County College of Morris

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    Neil Ullman's article initiates what we hope to be a fairly regular feature of the Newsletter -- an opinion or provocative piece about the teaching of statistics. The editors heard Professor Ullman's talk at JSM last August and thought it would inaugurate this column well. (Eds.)
    I suggest there is a basic Quantitative Intelligence which everyone utilizes all the time. Although this by itself is not necessarily a radical idea, I further propose that there exists an informal spoken language of statistics that acts as a foundation to the traditional written form we teach.

    We are constantly measuring, estimating, and experimenting -- all without FORMAL statistics. This informal, essentially subconscious, statistical thinking begins from the moment we wake up in the morning and consider how much longer we can lie in bed. It continues all day in a multitude of ways as we decide whether the water in the shower is "the right temperature," how much coffee to put in the coffee pot, or when to leave for work or school. Just as we have learned to speak words without instruction, we act and think quantitatively without realizing it.

    Yet what we teach is generally a formal system relying on an assumption that the student has an internalized familiarity with mathematics, especially of algebra, and hopefully calculus. We begin by presuming measurements have already been taken and concentrate on teaching the grammar and syntax of some subset of mathematical statistics. Rarely is there any connection to something that even we as individuals could say is important to our daily activities or an appeal to our instinctive understanding.

    I suggest beginning a process to redefine what we call statistics, and offer some ideas:
    1. Statistical thinking is not just mathematics.

      Statistics should not be a vehicle for teaching mathematics or satisfying a "mathematics" requirement. Statistics needs to be recognized as much as a subject of problem definition and measurement as computing of special quantities. Courses need to be expanded to examine the whys and hows we get to the data in the first place, allowing more time for studying the source of the information and devoting more emphasis to the ways we actually encounter "data." All too often the formal statistical aspect of a problem is the least important.

    2. Incorporate informal quantitative thinking into the statistical psyche.

      Restructure our courses to infuse informal quantitative concepts (accepting them as a legitimate part of a college statistics course) along with the formal statistical practices. Before this can become a universal practice we must develop a common "spoken" language so we all understand the principles and can communicate these ideas amongst ourselves.

    3. Recognize that there is a threshold between informal and formal methods.

      Most of our everyday encounters with "data" do not involve or need formal methods. In spite of all of our admonitions about statistics as a survival skill, most people seem to be surviving without us! Frequently the important consequences are so obvious that we can observe them and react appropriately without special effort. However, when differences are small, problems complex, or our ability to measure not adequate -- then we need to begin to use formal systems.

    Let me provide a couple of quick examples of rethinking what we do. I teach at a school where about 99% of my students commute by car. I begin the course with a questionnaire which includes asking how far they travel and how long it takes them. No one has a problem providing values. I challenge them to measure the time and distance it takes for their next trip. The results are brought to the class and then we engage in questions of the cause of different results. This leads to an operational definition so we can compare day to day and student to student trips. Then a data collection can, and does, begin in earnest. Class discussion can bring out points like:

    1. The calculations of mean and standard deviation may be useless if the measurement process is not consistent. If one student chooses to begin timing on leaving the house and another begins when the car is in motion, the values are not comparable. This is just one of the many very common problems with real data collection.


    2. The initial approximation might be more than adequate for most concerns. Furthermore, after gaining some insight from today's trip they have a better idea of what to expect the next time. An informal confidence interval evolves as an intuitive estimation.


    3. A shift in how to act begins if we want to compare routes, times of day, directions, day of the week, and so on. It is in these cases that formal statistical methodologies may be called for, although simple graphical techniques may be all that are necessary.

    In a similar fashion I explore how students perceive the comfort level in our classroom. I begin by asking "how do you feel," shift to a 5 or 10 point numeric scale that ranges from too cold to too hot, and finally request an estimate of temperature of the room. Just recording this information, along with collecting their responses into a simple table gives an indication of the relative feelings. A display of their response by seating location can quickly signal differences around the room. Finally I pass around a thermometer which gives a "real" measure of the temperature.

    Much insight into the conditions and the state of the room can be learned without any highly formalized statistics. However, if we pose a question such as whether opening the door changes the condition of the room, a formal approach involving taking separate samples and computing estimates of the temperature difference may become necessary.

    Let us take heed of the Quantitative Literacy efforts at the elementary level. I recently observed a group of first graders do in-class surveys. They gathered the data and individually prepared bar charts. Most incredible, however, was how they were able to verbalize the results and draw conclusions from their data. They presented their findings in ways I struggle to have my adult students do.

    We have been teaching a foreign language. As an adult I have failed miserably trying to learn to read foreign languages, especially when taught by memorizing words and learning grammar. But those same children can readily learn to speak other languages, and accelerate their ability to read them.

    Let us move away from the concerns about rigor, and "college level" and recognize that we need to rethink what is basic quantitative reasoning and stress that in standard courses. I recall a trip when the most important, but least accessible, thing I needed to know in a particular foreign language was how to ask the question "where is the bathroom?". What is the most critical thing most people really need in becoming aware of the statistical language?

    The above is based on a paper presented in Orlando last summer. Copies of the presentation and a longer paper are available.

    Neil R. Ullman
    County College of Morris
    Randolph, NJ 07869
    Phone: (201) 328-5716
    FAX: (201) 328-1003
    nullman@ccm.edu

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    HOW TO GET INVOLVED IN ASA VOLUNTEER ACTIVITIES

    Jim Landwehr
    AT&T Bell Laboratories

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    Many ASA activities are organized and implemented by volunteer members working through chapters, sections, and committees. If you're a new member of the statistics profession, or if you're not such a new member but decide that now would be a good time to become more involved in professional activities through ASA, you can easily look at the organizational maze and not see a good way to get started. The newsletter editors asked me to write an article giving my suggestions.

    My suggested overall principle is to volunteer for something SPECIFIC that you're interested in doing; then when your offer is accepted, follow through and do a conscientious job. This will likely create an expanding series of future opportunities.

    The ASA Chapters offer an ideal way to get started since they are geographically organized and you shouldn't have to travel much. First join the chapter for your region. Most have several talks or programs throughout the year; attend a few, introduce yourself, and see what goes on. Every meeting needs someone to take care of the arrangements, handle reservations or registrations, etc., and from my experience there is never an oversupply of people to do these. It's not too exciting but it needs to be done. Your offer to volunteer for this is almost sure to be accepted. By doing this work and showing you're a responsible person, you're likely to get the opportunity to serve on the chapter's program committee. This lets you help decide on the topics and speakers and have a real influence on what goes on in the chapter. Serving on the program committee also gives you a good excuse to call people you'd like to know but don't and ask them for their ideas and input. Most people are flattered to receive a call asking for advice, whether they know the caller or not, and by doing this you expand your personal network of contacts in the profession.

    After you've done a good job on some arrangements and program for a year or two, there's a good chance you will be nominated to be a chapter officer. This gives you further leadership opportunities, you can continue to expand your personal network, and you may also have the opportunity to attend special workshops for chapter officers that are held at the national ASA meetings.

    Another important area of chapter activities involves outreach such as Adopt-A-School and Quantitative Literacy programs. If such activities are going on in your chapter, talk to the people already involved and consider expanding them to schools or school districts where you have your own contacts. If there isn't such activity in your chapter, talk to staff in the ASA office in Alexandria and they can help you get started. What you need to have is some point of contact in a school district so you're not just calling someone out of the blue, an interest in trying to find out how the school perceives its needs, and a willingness to follow through.

    The Chapters are easy to get involved in. They offer great opportunities for networking in your geographic region and can help you get to know other nearby statisticians who work in different fields from yours. Personally, I have found this rewarding and it has broadened my knowledge of the statistics profession.

    The ASA Sections are organized on a national basis. Their main activities take place at national and regional meetings and through publications. They offer great opportunities to become part of a national network within a statistical discipline of interest to you. To get involved, you need to have the interest and opportunity to attend professional meetings outside your region.

    A good way to get started in a section is to offer to chair, and possibly find a discussant for, a contributed paper session at a meeting you will be attending. This gives you a good opportunity to meet and talk with people in the field and to present yourself briefly at the meeting. Section program chairs are always looking for people to chair sessions, so your offer to do so is quite likely to be accepted as long as you are aware of the deadlines and volunteer in time (often far in advance of the meeting).

    Organizing an invited paper session for a section allows you to have important influence by shaping a part of the program. Each section has a very limited number of invited sessions, however, so your offer to organize one is more likely to be accepted if you have already been involved in some way in the section's activities. Volunteering for a specific section office such as secretary, treasurer, publication officer, or "webmaster" for the section's homepage on the internet is also a good way to get started. The nominees for senior offices in a section -- such as program committee and chair, newsletter editor, representative to the council of sections, and section chair -- are usually drawn from people who have already fulfilled some of the other roles listed above.

    ASA's many committees offer a third type of involvement in professional activities. Members to most committees are appointed by the ASA president-elect in consultation with the executive director. I believe they try to come up with a mix of experienced people and new faces. While they don't want the appointments to be limited only to people they know personally, they also have a huge membership to choose from and don't make appointments at random. Thus, if there is a specific ASA committee you are interested in serving on, it is quite reasonable to nominate yourself by writing a letter to the executive director in which you specify the committee and describe why you are interested in serving on it and your qualifications. It won't hurt to mention successful chapter or section experience, and there's nothing wrong with asking someone else to send a note attesting to your qualifications for the committee. In fact, section and chapter chairs are regularly asked to suggest names of people for committee appointments.

    One final point. It's not something the editors asked me to address, but I think it's a reasonable question to ask yourself: WHY should I become involved in ASA volunteer activities? My answer includes several reasons. These activities can give you broader contact with the statistics profession and a broader knowledge about statistics than any of us is likely to get through our normal day-to-day job activities alone. Meeting different statisticians and finding out about different kinds of statistical problems are valuable activities, and they are hard to achieve otherwise. Professional volunteer work can also lead to nice feelings of personal accomplishment, to expanded career opportunities through networking, and to professional recognition. Finally, and by no means least importantly, it can be a lot of fun and you can meet interesting people and make good friendships. Good luck, and I hope it is fun for you, too!

    James M. Landwehr
    AT&T Bell Laboratories
    Room 2C-257
    600 Mountain Ave.
    Murray Hill, NJ 07974-0636;
    Phone: (908) 582-7405
    FAX: (908) 582-3340
    jml@research.att.com

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    Q & A--THE PERFECT STATISTICS GIFT?

    Michael R. Frey
    Bucknell University

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    We invite contributions to future Q & A articles. If you have a question about teaching statistics, send it to us and we can solicit answers. If you have both a question and answers, write a short article and send it to us. Send correspondence to Tom Moore. (Eds.)
    In September of this year a man asked me to suggest a gift suitable for his son who was enthusiastically studying statistics at college. I made a few suggestions but was satisfied with none of them. I teach statistics at Bucknell University, a small school in central Pennsylvania, and have few colleagues with whom to share these sorts of questions. So I turned to the internet and sent a message to a distribution list of about fifty statisticians, each like myself, professionally isolated. This list, maintained by Jeff Witmer at Oberlin College, can be reached at "isostat@oberlin.edu." Here is the message I sent to the group:

    Hello fellow isolated statisticians! I was asked this morning by a student's father to recommend a statistics/ probability book to be given as a gift to his son. The son is a third-year student at William and Mary, loves statistics (who doesn't?!), and plans to go on to graduate study in statistics. The father asked me to suggest a book that I find indispensable and that his son would appreciate. OK everyone, help me out. I thought to suggest The Handbook of Small Data Sets by Hand et al. or maybe Counterexamples in Probability. Of course, a gift ASA membership might also work. Does anybody have other suggestions? Thanks, Mike Frey.

    This question evidently sparked some interest because of the number and rapidity of the responses. Included were several requests that I assemble the results and share them back with the group. After brief editing this is what I sent back to the group:

    Hello isolated statisticians! I recently asked for suggestions for a book gift that might be appreciated by an undergraduate student of statistics. Here's an edited, cut-and-paste summary of your recommendations. Thanks to everyone - Mike Frey, Bucknell University.

    1. Statistics for Experimenters by Box, Hunter & Hunter or The History of Statistics by Stigler. These books were the most often recommended.


    2. Edward Tufte's two books on graphics make nice gifts, since they are so artistically put together--one is The Visual Display of Quantitative Information and the other is Envisioning Information. These books are truly works of art and contain information that beginning statisticians should be required to learn. Moreover, they are not books that a student is likely to buy for a course. These two books received several recommendations.


    3. A useful reference set is the Johnson and Kotz series on distributions--four volumes. A couple of them are available in new editions; these would be the ones to purchase if one doesn't want to lay out for all four. Two recommendations for this set.


    4. ASA gift membership including subscriptions to The American Statistician , Stats, and Chance.


    5. Statistics: A Guide to the Unknown, by Tanur et. al. --a largely nontechnical collection of applications of prob & stats to a wide variety of areas (predicting the chance of an earthquake in the next few years, estimating whale population sizes, forecasting elections, looking at the bunt strategy in baseball). Put out by Wadsworth Brooks/Cole.


    6. Fisher's Statistical Methods, Experimental Design and Scientific Inference or Student (a biography of Gossett), both published by Oxford University Press. R.A. Fisher: The Life of a Scientist would be good too. Historical/biographical materials regarding statisticians are hard to come by and make valued gifts.


    7. Thisted, The Elements of Statistical Computing; Kendall et. al., The Advanced Theory of Statistics; De Finetti, Theory of Probability; Kotz and Johnson, Breakthroughs in Statistics; Mosteller and Wallace, Applied Bayesian and Classical Inference: The Case of the Federalist Papers; Tanner, Tools for Statistical Inference; and Feller, An Introduction to Probability Theory and Its Applications.


    8. Problem Solving: A Statistician's Guide by C. Chatfield or Counting for Something: Statistical Principles and Personalities, by W.S. Peters (Springer-Verlag).


    9. Don't underestimate C.R. Rao's Linear Statistical Inference and Its Applications or a matrix-theory- useful-for-statistics book like Graybill's or Searle's. Everybody takes a linear models course but nobody has had all the linear algebra that graduate school assumes they've had.


    10. Two recent books offer numerous datasets to supplement an introductory statistics course. The books differ in level and the extent to which sample analyses for the data are supplied. One is A Casebook for a First Course in Statistics and Data Analysis by Chatterjee, Handcock and Simonoff (Wiley, 1995). The other is A Handbook of Small Data Sets by Hand et. al. (Routledge, 1994). Robert W. Hayden of Plymouth State College has written a joint review of these books which will soon appear in The American Statistician.


    11. Of course, a dream gift suitable for the newly-minted stats Ph.D. is the multi-volume Statistical Encyclopedia. But it is oh-so-expensive!

    The father, when I gave him this list, was amazed and delighted. He's decided to give his son a student ASA membership. Oh, and now he wants me to suggest a gift for his wife ...

    Michael Frey
    Department of Mathematics
    Bucknell University
    Lewisburg, PA 17837
    Phone: (717)524-1598
    FAX: (717)524-3760
    mfrey@bucknell.edu

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    STAT ED PROGRAM FOR CHICAGO JSM

    Allan Rossman
    Dickinson College

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    The Section on Statistical Education will be well represented on the program for the 1996 Joint Statistical Meetings in Chicago. We are sponsoring four invited paper sessions and will co-sponsor several others that should be of interest to our members. Topics range from questioning whether or not to teach Bayesian statistics at the introductory level to discussing how to evaluate reforms in the teaching of statistics to demonstrating the newest multimedia and software programs for helping students learn statistics. (This last topic produced so many intriguing suggestions as to warrant two sessions.) The titles of these invited sessions are:
    Updating Opinions: Bayesian Possibilities for Introductory Statistics,
    Evaluating Reforms in Teaching Statistics: A Panel Discussion,
    Technology for Helping Students Learn Statistics, and
    Software for Learning Probability and Statistics.

    More details on these sessions will appear in the next newsletter, but suffice it to say that leading statistics educators will be presenting their viewpoints.

    We are also hoping to arrange several sessions of special and regular contributed papers. Special contributed paper sessions are arranged around a common theme, while individuals are welcome to speak on any topic related to statistics education in the regular contributed paper sessions. Details and instructions for submissions of abstracts can be found in the October and November issues of Amstat News. Please consider making a presentation at one of these sessions, but be advised that the submission deadline is February 1, 1996. (We realize that this deadline may have passed when you get this newsletter.) Also, we invite you to volunteer to be a discussant or a chair for one of these contributed paper sessions. To volunteer, contact Allan Rossman.

    Our section will also be hosting several roundtable luncheons arranged according to various themes related to statistical education. Roxy Peck has been organizing these sessions.

    Please plan to attend the Chicago meetings and to support the many Stat Ed sessions on the program. For further information on our Section's program for the Chicago meetings, please contact:

    Allan Rossman
    Department of Mathematics and Computer Science
    Dickinson College
    Carlisle PA 17013-2896
    Phone: (717) 245-1668
    FAX:(717) 245-1690
    rossman@dickinson.edu

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    BEST CONTRIBUTED PAPER AWARD FROM 1995

    Ron Wasserstein
    Washburn University

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    W. Robert "Bob" Stephenson of the Department of Statistics at Iowa State University will be the recipient of the 1995 Statistical Education Section Best Contributed Paper Award. Dr. Stephenson will receive a plaque at the Section Business Meeting in Chicago next August.

    Thirty-five contributed papers were presented in the Section at the Orlando meetings. Audience members were given a form to evaluate the speakers (on a scale of 4=excellent to 1=poor) on several aspects of their presentations. To be eligible for an award, a speaker must be evaluated by at least 15 people. Among those eligible, Stephenson received the highest overall rating with an average score of 3.68 for his talk, entitled "Statistics at a Distance."

    The Best Contributed Paper Award was established by the Section over 10 years ago to encourage better contributed paper presentations. The Statistics Education Section is grateful to all those who presented, as well as to those who took the time to evaluate the talks. Questions or comments about the award may be addressed to

    Ron Wasserstein
    Assistant Vice-President for Academic Affairs
    Washburn Universit
    Topeka, KS 66621
    Phone: (913) 231-1010 x 1108
    FAX: (913) 231-1089
    ZZWASS@AC.WUACC.EDU

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    NEW HANDBOOK ON ASSESSMENT IN STATISTICAL EDUCATION

    Joan Garfield
    University of Minnesota

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    Iddo Gal (University of Haifa) and Joan Garfield (University of Minnesota) are pleased to announce that the International Statistical Institute and IOS press (both in the Netherlands) will jointly publish their book: The Assessment Challenge in Statistics. The book will consist of approximately 20 chapters written by authors from the USA, Canada, Spain, United Kingdom, Australia, and New Zealand. Chapters discuss conceptual and pragmatic issues in assessing statistical knowledge and reasoning skills of students at all educational levels. The book is organized in four sections: Assessment goals and frameworks, Assessing conceptual understanding, Innovative models for classroom assessment, and Assessing the learning of probability. The book is scheduled for publication in early 1997.

    Joan Garfield
    Department of Educational Psychology
    University of Minnesota
    332 Burton Hall
    128 Pillsbury Drive, SE
    Minneapolis, MN 55455
    PHONE: (612) 625-0337
    FAX: (612) 624-8241
    JBG@MAROON.TC.UMN.EDU

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    NCTM AND STATISTICS EDUCATION IN 1996: A STATUS REPORT

    Gail Burrill
    University of Wisconsin, Madison

    Newsletter for the Section on Statistical Education
    Volume 2, Number 1 (Winter 1996)


    In 1986 when the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards were being crafted, a draft version of the probability and statistics standards was sent to the NCTM/American Statistical Association Joint Committee on Probability and Statistics for review. The standards, enriched by input from the committee, proposed that statistics become a main strand in the K-12 mathematics curriculum. The standards were published in 1989. Now, seven years later, where are we?

    As educators struggle to implement the standards, statistics, under the guise of quantitative literacy, has become an accepted component of elementary, middle, and secondary mathematics programs. Exploratory data analysis modeled on Exploring Data by James Landwehr and Ann Watkins from the Quantitative Literacy Series can be found in nearly every middle and high school text series; box plots, stem-and- leaf plots, exercises on the mean, median, range and interquartile range. The February 1990 issue of the Mathematics Teacher was a special focus issue on statistics. NCTM published an addenda series to help teachers implement the Standards. The sales of the three addenda books on statistics, Making Sense of Data (grades K-6), Dealing with Data and Chance (grades 5-8), and Data Analysis and Statistics Across the Curriculum (grades 9-12), indicate they have been purchased by a very large number of teachers and schools around the country and in Canada. Many sessions at NCTM annual and regional meetings have been devoted to statistics, probability and data analysis. Two all day "conferences within a conference" devoted to elementary and secondary statistics were held at the 1995 Annual NCTM Meeting in Boston. Many of the examples used to illustrate the NCTM Assessment Standards are based in statistics. The council has, indeed, supported efforts to promote statistics as a component of the curriculum.

    The critical question, however, is what is actually happening in classrooms? Are we preparing students to deal with data and chance in meaningful ways? There are several issues that seem to need addressing before our efforts can begin to be successful. First, despite the existence of statistics and probability strands in the curriculum, there is no guarantee that they are being taught. And even then, in many instances, only the procedures have become a part of the curriculum. Despite being embedded in context, textbook exercises ask process questions, independent of the context and devoid of interpretation: what is the mean; make a box plot. The problems provide data on high school drop out rates but ask students only to "find the median," which can be done without any context. There is little attempt to make "sense" out of a situation or to use data to help advance an argument or to make a decision.

    The statistical view put forth is often limited. Little attention is paid to the concept of variability, to enable students to develop a sense of how important it is to capture not only measures of center but measures of how things vary, and what patterns in this variation might indicate. Little attention is paid to thinking carefully about how to design an experiment or to collect data. The emphasis is shifting from teaching students to think statistically about situations to teaching a prescribed and limited list of procedures.

    A further issue is the current "rush" to teach "real" statistical concepts. Even at the elementary level, probability is introduced on page one; on page two students learn to use "and" and "or," and at the middle school, on the third page they use combinations and permutations to answer probability questions. There is little opportunity nor curriculum provisions that allow students to investigate, to experiment with different probability situations, to look at results over many trials, to develop an understanding of probability rather than memorizing rules and formulas.

    Because the graphing calculator has become readily available, curve fitting has recently become a part of the curriculum. Instead of carefully building student understanding of what it means to choose a line to "best fit" a set of data, students are taught to punch a button. In grade 7 students with little or no preparation for thinking about what it means to fit a line to data and use their line to describe a relationship are finding a least squares regression line. Just because we can do something is not necessarily a reason for doing it! Without the mathematical foundation, a concept is likely to be used incorrectly. Repeatedly in texts and in publications, the concept of correlation is misused and misunderstood. A high correlation does not mean a line (or curve) is the "best fit" for a set of data. Fitting curves to data involves careful analysis of the context for clues about the relationship.

    (Contextually, the diameter of a tree and the volume of wood might be related by a cubic; if they are not, you might want to raise a question.) The context, graph, residuals and their graphs as well as numerical summaries are all part of the process of finding a "good" fit for data.

    The Standards paint a picture of statistics that is not yet a reality in classrooms. There is progress, but there is a long way to go. Technology is now readily available to allow students to explore statistical situations. Materials are being developed through the curriculum projects of the National Science Foundation that will provide teachers with exemplars. In particular, Data Driven Mathematics, a series of modules designed to integrate statistics into standard mathematical topics in the secondary curriculum and the elementary series, Elementary Quantitative Literacy, (both to be published by Dale Seymour) are designed to help teachers understand and incorporate statistics into their classes.

    Making statistics a true component of the curriculum presents a challenge for 1996 and beyond -- an even greater challenge, however, is to help teachers, students, and textbook writers understand that "statistics is the art of making numerical conjectures about puzzling questions," an exciting and fascinating way to think about numbers and mathematics and to ensure that it is this view of statistics that takes root in the classroom.

    Gail Burrill
    University of Wisconsin, Madison
    President-elect of the National Council of Teachers of Mathematics
    PHONE: (608) 263-4288
    gburrill@macc.wisc.edu

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