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:
 

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 (Prefreshman 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:
 

-- 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