Re: hi school stats/zoology?

Joe H Ward (joeward@tenet.edu)
Mon, 18 Dec 1995 18:07:25 -0500


Hi Thurman --

Good to hear of your interest in working with high school students!

Where are you located?
------
Yes, there are many folks working with high school students who are
doing some "research" projects. Some of these certainly will respond
to your message.

Laura Niland (of MacArthur High School in San Antonio) and I
are working with high school students who do various research projects.

Laura teaches a "regular" half-year statistics course at MacArthur High
School each year. In her course each student is involved in some
type of research activity. Next year Laura will teach an AP-Statistics
course to prepare her students to take the AP-Statistics Exam in May, 1997.

I am a "volunteer teacher" at Health Careers High School, which is a
magnet school near our University of Texas Health Science Center at San
Antonio. Many of these students interact with researchers at the UTHSC.
At Health Careers HS we have a BIOSTATISTICS-RESEARCH CLUB which meets
each week to discuss and work on various aspects of research analysis.
Ms Nancy Dooley and I are co-sponsors of this club.

Our San Antonio Chapter of ASA distributes, throughout the San Antonio
area, a list of volunteer statisticians who will help students with their
science research projects.

The main change in our workshop activities is the use of STUDENT SYSTAT in
place of BUSINESS MYSTAT. Since STUDENT SYSTAT is MUCH closer to the FULL
SYSTAT, it seems better to use it in place of BUSINESS MYSTAT.

Laura has a list of some of her projects in "NON-ELECTRONIC" form. If
you send me your mailing address, I will ask Laura to mail you a copy.

You may not have seen the attachment below that describes some of Laura's
and my activities. We plan on having a session just for teachers who
will be teaching AP-Statistics in '96-'97. And we will have our summer
session described in the attachment below. Our emphasis for the science
research students is to use a Predicion Model (aka Linear Models,
Regression Models) approach to pursuing research studies. As you will
observe in the outline of the AP-Statistics announcement, their are some
good steps toward the use of computers for simulation studies, but the
"inference" activities involve mostly "pre-computer" approaches. But
progress is slow.

Keep in touch --

-- Joe

***********************************************************************
* Joe Ward 167 East Arrowhead Dr. *
* Health Careers High School San Antonio, TX 78228-2402 *
* Univ. of Texas at San Antonio Phone: 210-433-6575 *
* joeward@tenet.edu *
***********************************************************************

--

On Mon, 18 Dec 1995, Thurman Wenzl wrote:

> Date: Mon, 18 Dec 1995 01:54:17 -0500 > From: Thurman Wenzl <CZGA45A@prodigy.com> > To: Multiple recipients of list <edstat-l@jse.stat.ncsu.edu> > Subject: hi school stats/zoology? > > Does anyone have examples from efforts to introduce high school students > to statistics via practical projects? > I seem to recall that Joe Ward has mentioned such efforts in Texas, but I > couldn't figure out how to search for his notes in the archives. > I'd like to work with a math teacher at a small branch high school here > which is located at the zoo, to introduce his students to data collection > and analysis. Has anyone else besides Joe W. had experience with efforts > like these? > Thanks in advance, > - > THURMAN WENZL CZGA45A@prodigy.com > > >

**** HANDOUT FOR "ADOPT-A-SCHOOL" SESSION, ASA TORONTO, 1994 *************** **************************************************************************** EMPOWERING HIGH SCHOOL STUDENTS TO EXPLOIT STATISTICAL MODELS AND SOFTWARE FOR RESEARCH PROJECTS Joe H. Ward, Jr, Health Careers High School, Laura J. Niland, MacArthur High School Joe H. Ward, Jr., 167 E. Arrowhead Dr, San Antonio, TX 78228

Key Words: Adopt-a-School, Linear Models, Computers

Introduction

Activities of the San Antonio Chapter of ASA involving K-12 students and teachers are presented. These include (1) the Texas Prefreshman Engineering Program (PREP) designed to encourage females and minorities to enter science and engineering careers, (2) Student & Teacher Collaborative Projects in Problem Solving Using Data Analysis, and (3) Statistics Projects at MacArthur High School. These experiences are designed to strengthen the statistics and computer skills (using BUSINESS MYSTAT) of students who are involved in independent research projects for science fairs and statistics project/poster contests. A "top-down" approach is used which emphasizes starting with meaningful research questions and introducing new concepts as the need arises. The conceptual framework involves the Big Four Ideas of (1) Prediction, (2) Uncertainty, (3) Modeling, and (4) Optimization. A General Linear Model approach is used, starting with mutually exclusive categorical models with least-squares solutions that yield "cell means". Then more complex models are developed to investigate interactions among variables.

The major goal of the activities described below is to empower high school students (and their teachers) to make effective use of the combined power of a prediction model (regression, linear model) approach and computers in data analysis for practical research. Probability, statistics and computer topics are introduced when needed. This approach possesses several important advantages over the traditional sequence in introductory statistics instruction:

-- Students will have less to learn, because many of the "standard" statistical analysis procedures developed before the availability of high-speed computers can be accomplished with fewer ideas.

-- Students will have more power to solve new problems, since they will be able to specify new models for unique problems.

-- Students will be able to solve more problems with less computational burden, since the use of statistical software packages allows for solutions to complex prediction problems.

Background

In the early 1960's Joe Ward began working with high school students and teachers, helping them to combine prediction (regression) models and computers for data analysis. One high school student was recognized by the Westinghouse Science Talent Search for his paper "A Vector Approach to Statistics". Ward served as a representative of the National Council of Teachers of Mathematics (NCTM) to the ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability from 1989-1991. During that time he inaugurated an "Adopt a Statistician" program by disseminating a list of San Antonio area statisticians who volunteered to assist students and teachers with design and analysis for research projects. In September, 1992 the San Antonio Chapter of ASA officially "adopted" the Health Careers High School under the ASA "Adopt-a-School" project. Experience has revealed that teachers and their students wait until the "last minute" to contact the statisticians for assistance. So present efforts are directed toward encouraging high school teachers and students to ask statisticians to advise early in the project planning stage.

During the summers of 1991 and 1992 Ward taught "Problem Solving Using Data Analysis" to third-year PREP (PRefreshmen Engineering Program) students. The PREP program is designed for students in grades 7-11, to encourage them to go into science and engineering careers. PREP is directed by Dr. Manuel Berriozabal, The University of Texas at San Antonio. In 1990 Ward and Laura Niland teamed to give presentations designed to "empower students and teachers to use prediction (regression) models and computer software for data analysis". Laura is the Texas, 1988 Presidential Awardee in Secondary Mathematics. She teaches statistics at MacArthur High School and was a staff member at the 1992 Quantitative Literacy Workshop at Clemson University.

During the summer of 1993 and again in 1994 a 20-day, 4 hours/day "Student & Teacher Collaborative Project in Problem Solving Using Data Analysis" was presented by Ward and Niland at Health Careers High School. Students from the 1993 Project applied their data analysis skills to research projects entered in Junior Academy of Science, Science Fairs and the ASA Project/Poster contests. The announcement for the 1994 Project is shown below.

Instructional Outline -- Introducing the "Top Down Approach".

The "Top Down Approach" starts with one or more "interesting" problems and introduces topics to address the problems ONLY as the topics are needed. This means, of course, that probability ideas are not introduced until much later than in a traditional course. Many "standard" courses still approach the subject with techniques that were appropriate BC (Before Computers) --- almost as if the computer is not available. And when the computer IS used it is used to process the algorithms of pre-computer days.

On the first day we try to show the students that they will be able to do things WITH THE COURSE OBJECTIVES that they CAN NOT DO WITHOUT THE COURSE. We try to get as quickly as possible to the question of: "How do we control for the uncontrollable"?

This approach STARTS where many one- semester statistics courses STOP. This means that the students move quickly to the "natural language" discussion of how to predict a dependent variable from ONE attribute, then "how to control for" a SECOND variable that might "confound", or "contaminate" the results. We try to let students pick a word that "describes" variables that might "mess-up" the conclusions.

We have used four different problem situations. Two or more of the problems are discussed briefly, and one particular problem is studied in great detail depending on the audience interests.

We start by discussing:

Real-World Problems:

1. To win a bet as to which basketball player will score more points in the next game.

2. To predict which Sea World (Texas or Florida) will earn the most profit next year.

3. To compare the effectiveness of teachers.

4. To compare the "sizes" of babies born to mothers who smoke and mothers who do not smoke.

Then we can discuss some

QUESTIONS OF INTEREST:

1. Is there a difference between the performance of player x and player y?

2. Is there a difference in profits between Sea World of Texas and Sea World of Florida?

3. Is there a difference between student performance measures for various teachers?

4. Is there a difference in birth weights between babies born to mothers who smoke and mothers who do not smoke?

>From here we "brain-storm" what might "bother you" about these questions. This leads to making a list of variables that might "confuse", "confound", "contaminate" , "mess up" our investigations.

We discuss how nice it would be to "control for the uncontrollable". Which leads to the idea "if you can't control it, then try to 'measure' it".

For example 1 above we might generate a list of variables we might like to "control" such as:

-- Home vs Away games -- Who is guarding the players -- Injury status

For example 2 above:

-- Weather conditions (Rainfall, Temp) -- Other events in the area -- Special attractions

For example 3 above:

-- Quality of the students (Pretest Scores) -- Socio-economic status (Free lunch) -- Ethnic category For example 4 above: -- Gestation period -- Ethnic background -- Age of Mother

After introducing two predictor attributes (or factors) into our models, it is important to investigate the presence or absence of INTERACTION between the two attributes. Detailed discussions are introduced regarding the various conclusions that can be made based upon the analysis of possible INTERACTION. For example 3 above, if it is found that there is a "STRONG INTERACTION" between Teachers and Pretest Scores, then better student performance might be obtained by assigning a particular teacher to a specific student. And, if it is concluded that there is "NO INTERACTION", then it may be appropriate to assign any student to any teacher.

We indicate to the student that there are some powerful things to be accomplished by combining a PREDICTION MODEL approach with the COMPUTER to answer questions of importance.

--Prediction, Uncertainty, Modeling and Optimization

The motto for our approach is PUMO, which represents THE BIG FOUR IDEAS of:

Prediction Uncertainty Modeling Optimization

With these four ideas we can systematically investigate interesting real-world problems.

The students discuss various ways of making PREDICTIONS of variables of interest. This leads to the use of "averages" or "means" of subsets of data as useful for making predictions.

This discussion includes reasons for UNCERTAINTY in the accuracy of predictions: measurement errors, unknown information that might improve prediction, sampling errors, inadequate ways of combining the predictor information, etc.

This leads to a more formal idea of a MODEL to represent the relationship between the variable to be predicted (dependent variable) and the relevant predictor information.

Examples of such representations are:

Dependent Variable = Function of Predictor Information + Error

Data = Fit + Residual

Data = Model + Error

Y = Prediction + Error

Y = P + E

After reasonable prediction models are developed it is important to use those predictions to make practical decisions. This leads to attempts to OPTIMIZE some "value indicator" (objective function). These indicators might involve one or more indicators such as "cost", "satisfaction", "profit", "pollution", etc.

-- Computer Software

Almost any appropriate software package can be used to carry out the computational requirements for the analyses. The ones that have been used in the past have been MYSTAT, then BUSINESS MYSTAT and now STUDENT SYSTAT.

Selected References

American Association for the Advancement of Science. Science for All Americans. Washington, D.C.: AAAS, 1989. American Statistical Association. Guidelines for the Teaching of Statistics K-12 Mathematics Curriculum. Alexandria, VA: ASA, 1991.

Burrill, G., and J. Burrill. (Eds.). Data analysis and Statistics Across the Curriculum. Reston, VA: National Council of Teachers of Mathematics, 1991.

Corwin, R., and S.J. Russell. Used Numbers: Real Data in the Classroom. Palo Alto, CA: Dale Seymour Publications, 1990. Foerster, Paul A. Precalculus with Trigonometry: Functions and Applications. Menlo Park, CA: Addison-Wesley, 1986.

Fountain, Robert L. and Joe H. Ward, Jr. Regression Models and Software Packages: Synthesizing Traditional Procedures in a One-semester Statistics Course. Presented at ASA Winter Conference at Louisville, KY, 1992. Hale, Robert L., and Jeffrey W. Steagall. Business MYSTAT Statistical Applications (DOS Edition). Cambridge, MA: Course Technology, Inc., 1990. Laughlin, Margaret A., H. Michael Hartoonian, and Norris M. Sanders. From Information to Decision Making: New Challenges for Effective Citizenship. Washington, D.C.: National Council for the Social Studies, 1989.

Moore, David S., and George P. McCabe. Introduction to the Practice of Statistics, Second Edition, New York, NY: W.H. Freeman, 1993. (This book and supplementary materials accompany the Telecourse videotape series Against All Odds: Inside Statistics available from The Annenberg Project, 1-800-LEARNER. These 26, 30-minute tapes are excellent and are frequently shown on PBS.)

National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematics. Reston, Va.: NCTM, 1989.

Ward, Joe H., Jr., and Paul A. Foerster. Integrating Statistics into the Secondary Curriculum. Proceedings of the Third International Conference on Teaching Statistics. ISI Permanent Office, 428 Princes Beatrixlaan, PO Box 950, 2270 AZ Voorgburg, The Netherlands, 1991.

Ward, Joe H., Jr., and Earl Jennings. Introduction to Linear Models. Englewood Cliffs, NJ: Prentice-Hall, 1973. Ward, Joe H., Jr. Problem Solving Through Data Analysis. San Antonio, TX: Texas Prefreshman Engineering Program (TexPREP), 1991.

Quantitative Literacy Series

Gnanadesikan, M., R.L. Scheaffer, and J. Swift. The Art and Techniques of simulation. Palo Alto, CA: Dale Seymour Publications, 1987. Landwehr, J.M., and A.E. Watkins, Exploring Data., Palo Alto, CA: Dale Seymour Publications, 1986. Landwehr, J.M., J. Swift, and A.E. Watkins, Exploring Surveys and Information from Samples. Palo Alto, CA: Dale Seymour Publications, 1987. Newman, C.M., T.E. Obremski, and R.L. Scheaffer, Exploring Probability. Palo Alto, CA: Dale Seymour Publications, 1987.

*************************************************************************** The following is the announcement for A Student & Teacher Collaborative Project conducted at the Health Careers High School which has been adopted by the San Antonio Chapter of the ASA. ***************************************************************************

ANNOUNCING: A STUDENT & TEACHER COLLABORATIVE PROJECT IN PROBLEM SOLVING USING DATA ANALYSIS June 6 - July 1, 1994 Health Careers High School

From: Joe Ward 167 East Arrowhead Dr., San Antonio, TX 78228-2402, (210) 433-6575 joeward@tenet.edu

** Have you ever had students enter research projects into competition and be marked down because of insufficient data or student's inability to explain the data analysis?

** Have you had students doing research projects come to you with a "pile" of data and not know what to do with it?

** Have you had a problem finding statistical computer programs to support data analysis for research projects?

** Have you had a problem locating someone to help with the statistical aspects of student research projects?

If you answered yes to any of the above, then this project may be for you!

It provides an unusual opportunity for teachers and students to acquire capabilities for data analysis using statistical software not available elsewhere.

This project is designed to strengthen the skills of students who are already in or about to begin independent science research initiatives. In the past, students who work on science fair or research projects have had a difficult time collecting, sorting, analyzing and interpreting numerical data. Few students or teachers have experienced any real-world problem solving using modern computer-based data analysis procedures.

Past experiences have indicated that innovative approaches in education can be introduced effectively by involving students and teachers in a collaborative learning experience. This project will bring together teachers, students and statisticians in an enriching experience to increase the students' and teachers' capability to investigate research questions using powerful data analysis techniques. The curriculum will consist of broad "real-world" research infusing the four major concepts of Prediction, Uncertainty, Modeling, and Optimization. The four major concepts will be integral to hands-on experiences involving problem solving processes, integration of statistics into other curriculum areas, exploration of laboratory data, new data analysis techniques and appropriate computer software.

This project will empower students to: (1) Identify and express real-world problems in natural language in preparation for creating formal mathematical/statistical models, (2) Translate the natural language problem statement into a mathematical model appropriate for analysis using a statistical software package, and (3) Interpret and present the results in both written and verbal form appropriate to assist in real- world decisions.

A maximum of six teachers will be selected to serve as mentors for a maximum of eighteen students. Student participants will be selected by their mentor teachers and will be those who have been identified by their teachers as students who are committed to conducting a research project to completion. Monitoring and evaluation of the project will consist of testing of skill acquisition during the formal learning sessions; but, of most importance, are the students' performance in the conduct and completion of research projects. The focus of evaluation in this project is the short-term performance of the students who apply their new skills in research projects. The teachers' success will be indicated by the quality of their students' research project analysis.

The project director is Dr. Joe Ward, assisted by Ms. Laura Niland. Dr. Ward has had much experience in introducing high school students and teachers in the applications of computers and statistics in research. He has developed curriculum and taught Problem Solving Through Data Analysis in the San Antonio PREP program. He is a past member of the American Statistical Association-National Council of Teachers of Mathematics Joint Committee on the Curriculum in Statistics and Probability. Ms. Niland has been recognized as a Texas Presidential Awardee in Mathematics and is actively teaching MacArthur high school students to use quantitative methods of data analysis.

Phase 1 -- Students and their mentors will meet at Health Careers High School for four hours per day (8:30 am to 12:30 pm), 5 days per week, for four weeks beginning Monday, June 6 and ending Friday, July 1.

Phase 2 -- Follow-up meetings will be conducted in the Fall of 1994 and Spring of 1995 to insure completion of student research projects. Statisticians from the San Antonio area will be available during this project to assist teachers and students with the design and analysis of their research. A major objective of this project is active participation by students in the Junior Academy of Science, Science Fairs, and National Statistics Contests. Each teacher who completes both phases of the project will receive a stipend of $300. Each student who completes both phases of the project will receive $50 for expenses associated with their research projects. One- half of the payments will be made after completion of Phase 1 and the final payment will be made after completion of Phase 2.

(Some students may wish to consider receiving credit in STATISTICS for this project).

Teacher & Student Application Form Each teacher should choose 2 or 3 students who are committed to the Project objectives. (If you have more than 3 qualified and interested students please call Joe Ward). **************************** Teacher Name:_____________________________________________________________ (Last Name) (First, Name) (MI) Home ______________________________________ Home phone:_______________ Address: ______________________________________ School: _________________ Subjects taught: _______________________ *************************** Student Name:_____________________________________________________________ (Last Name) (First, Name) (MI) Home ______________________________________ Home phone:___________ Address:______________________________________ School: ___________________________ School grade Sept. 94 _________________