Fashion Trends in a Middle School

Supercomputing Challenge Summer Institute Final Report July 27, 2006 Capshaw Middle School - Team #01 Theresa Anaya Burney Peter Colehour Susan Gibbs Thansewi J. Martinez Makoena Monese

Introduction

 Middle school students arrive at school wanting both to conform to fashion norms and to be recognized as individuals. Each student also has a relative degree of shyness or sociability. These factors affect each student’s susceptibility to a fashion trend. The research supports the relative shyness and resistance levels of students, and tipping points in the spread of a trend.

Executive Summary

Our computational model:    Allows multiple trials of how the initial percentage of resistant students affects speed of a trend’s spread Imitates the real-world school environment: • • Shows relative shyness and susceptibility of students Recognizes that the relative percentage of resistant students determines the speed of the trend’s spread. Can be used to study relevant middle school topics: • • • bullying spread of disease the susceptibility of individuals to drug, alcohol, tobacco use, and sexual activities.

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The Project Hypotheses

The StarLogo model will graph the spread of a trend, comparable to an infection model. The lower the initial percentage of followers, the slower the trend will spread. A tipping point may exist in the initial percentage of followers, above which the trend spreads much more quickly.

Mathematica Model

 Our infection model set two contact rates (30% of agents have fewer contacts) and used an infection variable for the percentage of the population that was susceptible (infection after 2 exposures) or immune (after 4 exposures).

dP

I

/dt= rcP

I

(1-P

I

)

Expected number of susceptible individuals who will become infected in the time Δt, assuming rc = 1.

Starlogo Model

 Our STARLOGO model allows students to manipulate the original percent of students characterized as “followers” (susceptible) and “freethinkers” (relatively immune).

Results

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2.

3.

All 3 Hypotheses proved The StarLogo model is comparable to an an infection model. The lower the initial percentage of followers, the slower the trend will spread. Two tipping points exist in the initial percentage of followers, above which the trend spreads much more quickly

Recommendations

Students:    Expand model to apply to new issues Expand and refine model to show affect of advertising, new conflicting trends, and Conduct real-world experiments on the spread of trends Teachers: Create a StarLogo TNG model Use model to entice students into Challenge

Acknowledgements

 We appreciate:  STI Team - for all their support and patience.  Dylan Allegreti - for supporting the process and working with us.