Hardcore Hardball

Baseball is our national pastime, a sport which engages many high school students as fans and as players. Its rich lore and amenability to quantification make it a natural topic for statistical analysis. Although the modern game has existed for decades, there are many open questions of game strategy which can be examined using simple, mathematically rich models that draw on the basic tools of high school algebra. The recent bestseller Moneyball describes the increased reliance on quantitative analysis that is revolutionizing professional baseball. Meanwhile, fantasy leagues have turned millions of fans into amateur mathematical analysts, for whom the question of player evaluation has clear import. The topic of player evaluation leads in turn to questions about the biological limits of human performance. What makes one player faster or stronger than another? What are the physiological origins of those differences? What are the ethical and physical ramifications of using steroids to stretch those limits?

All too often, high school students doubt the importance of mathematics and science to their future lives. All too often, they fail to make connections between the learning they encounter in the classroom and the problems they encounter in the outside world and in other subjects. We would like to prepare a semester-long curriculum, coordinated between an algebra and a biology course, in which students explore the deep questions that arise as they operate a virtual baseball team. We will share our results with the broader teaching community by making our lesson plans, materials, and teaching journals publicly available on the web. Students will work in small ownership groups whose “standings” in the league will rise and fall based on the results of their analysis. Baseball provides a rich enough problem domain that students will master a full spectrum of algebra and biology topics, in accordance with state and national standards. We believe that this project will motivate students who may not have previously excelled in math and science. By applying mathematics and science in a natural context, it will help students see these subjects’ relevance to their future lives, and help students come to identify themselves as mathematically and scientifically adept.

This project will use baseball as a central theme to develop a high school curriculum for a mathematics and a biology course. Students will work in small ‘ownership groups’ to investigate focused questions facing the owners of a professional baseball team., questions chosen to cover the full range of algebra/biology topics described in state and national standards. These investigations involve significant mathematical and scientific content, yet provide a clear relevance to engage students. We believe that the richness of this subject, its engaging topic, and a spirit of healthy competition will inspire students to a deep mastery of the subject knowledge. This approach will invite students to make connections between math, science, and everyday life, and to change their attitudes towards mathematics and science.

We would like to request a grant that will cover the cost of the technology resources and the specialized equipment required to implement this curriculum. Not only will current and future classes benefit from this innovative curriculum, but we also plan to make the results available on the internet to the teaching community.

The ownership groups will be chosen to provide a heterogeneous mixture of prior expertise in baseball, mathematics, and science. They will choose a team identity and name and view, as a class, an anchor video which introduces the topic and raises many questions for investigation (http://kromerica.com/PBI/PBI-BaseballVideo.mpg). To ensure that everyone knows the rudiments of the game, we will work with the Physical Education faculty to schedule a class softball game. One goal of this project is to draw in students who may have never excelled in mathematics or science; we hope that by positing a real-world exploration such students will find areas in which they can appear as an expert for the class or their team. Even if some students have a weak baseball background, they will be motivated by the mathematical questions and can learn the baseball from their teammates, just as those with a previously weak mathematical or scientific background will be motivated by the context.

Students will also investigate questions of in-game strategy. For example, even now the question of when and how often to attempt a stolen base rages among professional baseball experts. (In 2005, the LA Angels attempted more than four times as many steals as the Oakland A’s – a huge spread for such a significant statistic.) Students will use linear functions to model the path of the ball (from pitcher to catcher, the reaction time of the catcher, and then from catcher to baseman) and of the runner (who has an initial lead, a ‘jump’ or starting time, and a given rate of speed). Students will be asked to develop a ‘stolen base’ strategy: for a fixed pitcher and catcher (and thus time to the base) and given the speed, lead and jump of the runner, when is a steal justified? The teachers will enter this stolen base strategy in a computer simulation, and the results will affect the class league standings.

Baseball hitters often talk about a ‘rising’ fastball – one that seems to elevate as it approaches the plate. Is such a pitch possible? What would its path look like? To answer these questions, students will investigate the path of a falling object. They will use motion detectors to plot the (quadratic) distance vs. time of a ball falling straight down. They will later be given selected frames from video capture of several pitched and batted balls. Students will use image display software to track the path of the ball in flight, and graphing software to display its path and horizontal speeds.

Any overhead shot of a baseball field will reveal a worn patch where the outfielder stands at the beginning of a play. How do the speed and final height of a pop fly interact with the running speed and reaction time of an outfielder to determine her starting position? Building on the linear functions used to model the stolen base problem and the quadratic functions that model the path of a baseball in flight, students will develop a rule for positioning their outfielders. (Again, results from empirical tests of that strategy will enter the league standings).

A third major fork of the course will have students design their own ballpark. They will be granted significant freedom to design any park they desire, but it will have to meet constraints of budget, crowd size, major-league regulations, and fan demands. They will use mathematical modeling and reasoning to evaluate their ballpark – Based on the height and distance of the fences, what do you expect your park’s home run percentage to be? Based on the area and slope of the seating sections, what is the park’s capacity? Does that slope meet architectural and handicapped accessibility requirements? We will invite a professional architect to introduce these questions and to evaluate the final results.

At the same time, students will use baseball and the question of human performance as a starting point for wide-ranging questions in biology. For example, how does the internal biology of the human muscle and nervous system act when we run, hit or throw? Students will explore the cell biology of muscles by quantifying the action potential response of the squid giant axon. After dissecting a squid, teams use an oscilloscope to display the strength and shape of the axon’s electrical impulse. This leads in turn to discussions of how stimulus and inhibition affect response time and endurance.

We plan to bring in a sports nutritionist to discuss how the physical exertion of an athlete affects his nutritional requirements. This motivates an investigation of the cell energy cycle and of nutrient and byproduct transport. Furthermore, it brings students to consider the ethical and physiological ramifications of performance-enhancing drugs. (The question of how to detect cheaters is both biological and mathematical and allows for significant interplay between the courses.)

In each investigation, our goal is to take a real and straightforward question from the world of baseball, one that draws on standards-aligned topics and methods. We supply students with the tools and procedures that a researcher might use to answer that question. Students in turn prepare an answer that is evaluated both subjectively (by how well they understood and communicated their findings) and, whenever possible, empirically (by subjecting their answer to competitive test). We plan to have students see the real-world import of the material by frequently inviting outside experts in nutrition, medicine, architecture, and sports to discuss their work and lead investigations.

Each ownership group will turn in a final ‘Report to the Commissioner’ containing the final design of their ballpark; an analysis of their draft (with revisions to their ultimate statistic); a nutrition and conditioning plan for their players; and the results of their class investigations. Each group will give a brief presentation on their ownership decisions and how the mathematical and scientific decisions they made were influenced by the players they chose. These portfolios will be reviewed by a panel of experts (the ones that visited the class over the semester) and will have a significant influence on the final league standings.

It is a sad reality that today, more than ever, generations of students in the United States are falling behind the international accomplishments of their peers in mathematics and the sciences. Numerous educational studies indicate that, among other factors, a lack of motivation from students and their perceived notions that mathematics and sciences are not beneficial to the real world contribute to such low interest and abilities in these fields.

To address this national concern, we have designed a project that is rich in mathematical and scientific content, is considered a worthwhile interest of study to an overwhelming majority of the population, and most importantly, provides a bridge clearly tying mathematical and scientific principles to real-world scenarios. In designing, managing and maintaining a professional baseball team, students will investigate topics such as statistics and probability in game management, biological, chemical and ethical issues stemming from performance enhancing drugs, the construction of professional ballparks, and modeling the motions of balls using computer based technologies. Students will work with professionals in fields such as athletics, medicine, and architecture to create a professional baseball organization that includes a player roster, ballpark design, a medical staff, and the necessary business plan to ensure a profitable return.

This is a project that will unite students from all ability levels, race, religion, and socioeconomic status together to work for a common goal. What better opportunity will students have to realize the usefulness and necessity for mathematics and science in our world than to see it in use with a sport such as baseball, which is recognizable and loved throughout the world? We believe that this project will engage students, provide them with a playground in which to explore the beauty of mathematics and science in our everyday life, and perhaps plant a seed from which the next generation of great mathematicians and scientists shall grow.

(As our assessments are designed around our educational goals we have combined these sections)

Our primary goal is to have students master standards-aligned mathematical and scientific topics. We will measure our success in meeting state and national content standards using students’ performance on the state exam. We will also assess domain-specific mastery by having our community experts review the students’ final project portfolios. Whenever possible, we will ask students to distill the result of an investigation into a simple ‘manager recommendation’ that can be subjected to direct empirical test.

Almost as important a goal is to use the natural appeal of baseball and the spirit of friendly competition to motivate students’ interest in this project. We would like to involve all students regardless of their prior background in math, science, or sports, and would especially like to involve students that may not have previously excelled in math and science classes. Ideally, we would like to have all students come to identify themselves as mathematically and scientifically adept, and to recognize that mathematic and scientific concepts have relevance and importance to their future lives. To measure our success, we will compare the results of an intake questionnaire (self-assessing their background and attitudes towards math, science, and baseball) with both an exit project evaluation questionnaire and the subject mastery tests. We will also pre- and post-test students with the standard “Attitudes Toward Mathematics Inventory” (http://www.rapidintellect.com/AEQweb/cho25344l.htm) to see if this approach to learning changes their perceptions towards mathematics and science.

We plan to make this project a permanent component of the biology and algebra curriculum at our high school. In the first year, four algebra classes (two teachers, ~120 students) and three biology classes (one teacher, ~90 students) would follow this curriculum. In future years, the full faculty of algebra and biology instructors would use project-based instruction, amounting to several hundred students across both subjects.

(note web hosting from district)

Education:

The University of Texas at Austin August 2002-present

B.S., Mathematics with secondary teaching certification

Expected graduation May 2006

GPA: 3.51, received university honors, recipient of Austin ISD scholarship

Sam Houston State University August 2001-May 2002

B.S., Mathematics

Teaching experience:

McNeil High School November 2005

Bedichek Middle School October 2003-May 2005

Crockett High School March 2004-May 2004

Porter Middle School February 2004-May 2004

Pillow Elementary School September 2003-November 2003

Work experience:

Bedichek Middle School January 2004-May 2005

Y.M.C.A. May 2003-August 2003

Town of Flower Mound Summer Day Camp May 2002-August 2002

dlfitzpatrick@mail.utexas.edu

(469) 441-8144

1333 Arena Drive, Apartment 229

Austin, Texas 78741

Resume for Philip F Kromer

612 Park Pl #201 Tel (512) 659-6846

Austin, TX 78705 Fax (847) 792-4020

flip@mrflip.com Web mrflip.com/resume

------------------------------ Education --------------------------------

Graduate School in Physics - University of Texas, Austin. 1996-99, 2001-04

Bachelor of Arts, Computer Science - Cornell University, Ithaca NY. 1992-96

------------------------------ Employment -------------------------------

MCAT Instructor, Princeton Review Austin and San Antonio, 2000-2002

Modern Physics Lab, Assistant Instructor - UT-Austin, 1998-99

Quantum mechanics lab for physics majors. Spearheaded redesign:

Engineering Physics II Lab, Teaching Assistant - UT-Austin, 1996-97

Digital Systems Course, Teaching Assistant - Cornell CS Dept, 1995-96

Resolution Independent Video Language Project - Cornell CS Dept, 1994-95

Undergraduate research project developing a resolution-independent video and audio editing language.

---------------------------- Volunteer Work -----------------------------

Equal Ground Project - Austin TX. Fall 2002 - Spring 2003

Taught free SAT prep class to underserved high-school students.

AVID Program, Reagan High School - Austin TX. Spring-Fall 2000, Spring 2002

Tutored math for underserved college-bound students.

Community Technology and Training Center - Austin TX. Spring 2000

Taught a web design course for people seeking additional job skills.

Pediatric AIDS League

Daycare for two- to five-year-old children of parents with AIDS.

Texas State Science and Engineering Fair - Austin TX, 1998, 1999, 2000

Divisional and Grand Prize judge at state-level high school science fair.

Eagle Scout Project (Boy Scouts of America) - Washington, DC. 1990

Ran a one-year weekly science club, and coordinated construction of ascience resource center, for underprivileged elementary school students.

------------------------------- Computers -------------------------------

Programming Languages Scientific/Engineering Web Experience

C/C++ LabView HTML/CSS

Perl Mathematica PHP

Python Matlab DBI (MySQL)

Pascal Excel, incl. VBA CGI

Extensive experience in

* Full range of standard programming languages.

* Collaborative programming. Published free software online.

* Building and maintaining informative, well-visited web pages.

* System and network administration.

------------------------------ Projects ---------------------------------

Texas Triathletes Club Officer, Webmaster

Maintain club website and Worked with others to expand club membership.

Endurance Racing

2003 Ride for the Roses (century), 2002 & 2003 Dog Ridge Triathlon, 2002

& 2003 Sea World Triathlon, 2003 Dirty Duathlon, 2004 3M Half Marathon.

PC-Based Lock-in Analyzer

Designed a lock-in analyzer (an extremely sensitive amplifier) that is

freely available for download and widely utilised.

( http://mrflip.com/papers/LIA )

Computer-Controlled Nonlinear Pendulum

Worked with an undergraduate to develop computer instrumentation and control of a chaotic dynamics, allowing rapid, precise data collection. ( http://www.ph.utexas.edu/~phy453/GroupProjects/Chaos/lapdog.pdf )

Hybrid Electric Vehicle Team, Cornell University

Headed the engine group in a team of forty students who designed, built, and raced an energy-efficient passenger car. Redesigned and rebuilt the car's engine. Personally responsible for attracting several thousands of dollars in-kind donations from seventeen sponsors. ( http://www.hev.cornell.edu )

----------------------------- Publications-------------------------------

"Fact, Sir, Not Fiction: A Fraction of Frictions Obey Strictures of Fracture." Masters' Thesis, May 2004 (expected).

"Atomistic Simulation of Single Asperity Contact," 2003 APS March Meeting.

"Software-Based Lock-in Amplifiers," Advanced Imaging, Nov 2002.

"PC-Based Digital Lock-In Detection of Small Signals in the Presence of Noise," 1998 AAPT Apparatus Competition.

Through this program, I have had the opportunity to teach in a variety of settings teaching many different subjects.