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Topic: hi school stats/zoology?
Replies: 1   Last Post: Dec 18, 1995 6:03 PM

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Joe H Ward

Posts: 743
Registered: 12/6/04
Re: hi school stats/zoology?
Posted: Dec 18, 1995 6:03 PM
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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 *
* *


On Mon, 18 Dec 1995, Thurman Wenzl wrote:

> Date: Mon, 18 Dec 1995 01:54:17 -0500
> From: Thurman Wenzl <>
> To: Multiple recipients of list <>
> 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,
> -


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


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

-- 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.


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

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
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


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

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",

-- 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,

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.

June 6 - July 1, 1994
Health Careers High School

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

** 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

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

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

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:___________
School: ___________________________ School grade Sept. 94 _________________

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