Palo Alto H.S. Team Wins International Mathematical Modeling Competition

PHOTO: The winning team with Superintendent Dr. Max McGee and Palo Alto High Principal Kim Diorio.

-----

News from the Palo Alto Unified School District:

Competing against 17 teams from 10 countries in a week-long competition focused on using all types of mathematics to solve a real-world problem brought out the best in the four‑person team of student mathematicians from Palo Alto High School (Paly).

After earning a spot in this ultra‑competitive contest by winning the top award in the 17th Annual International High School Mathematical Contest in Modeling (HiMCM) earlier this year, team members Kathryn Li, Allison Zhang, Eric Foster, and Andrew Lee worked with Team Advisor and Palo Alto High Mathematics Instructional Supervisor Radu Toma to prepare for this competition.

Their perseverance, ingenuity, and hard work paid off. All international teams received a common problem in mid-April and had one month in which to participate. During that time teams chose five (5) consecutive days to work together on the problem. The Palo Alto High Team worked on their problem April 19-23.

In this competition, only four schools’ projects earned the highest standing of being recognized as “Outstanding,” and this is the highest mathematical honor that Paly has ever received. This recognition has earned the team the opportunity for an all-expenses paid trip to Hong Kong in early July to receive their award from the international expert committee who judged the entries and to join other team winners for cultural visits in Hong Kong.

Dr. Glenn “Max” McGee, Superintendent, commented, “These four students are quite literally ‘world class’ in every sense of the term. Not only are their mathematical accomplishments in winning this prize extraordinary, but also their teamwork, persistence, and creativity are exemplary. Being first in the world takes more than just formulaic knowledge. They must have a true, deep conceptual understanding of advanced mathematical principles and concepts as well as the resilience, drive, and resourcefulness to excel to develop novel solutions to modeling complex real-world problems.

“Also, since they had to work together for five days straight, they had to collaborate and to enjoy one another. What especially impresses me is they pursued this contest just for the learning experience. They received no grades and still had to keep up with their other assignments. This is what we mean when we talk about learning for learning’s sake. What a great example these students are for all of us.

“I am also grateful to the teachers and parents who taught, supported, and encouraged the students since their earliest years in school. I am confident these young men and women will continue to excel in mathematics and to use their intellectual and creative potential to solve some of our society’s most challenging problems.”

The team’s advisor and Palo Alto High Mathematic Instructional Supervisor Mr. Toma, shared, “It is so exciting to have earned this recognition; this is the highest award Paly students have ever earned in mathematics. I am absolutely blown away by their accomplishment and humbled to have had them as students. This award is a tribute both to these students’ exceptional talent, work ethic, determination, and love of mathematics and to all their past mathematics teachers who have taught, inspired, and mentored these students over the years.”

The IM2C is a new competition that strives to be a true team competition, held over a number of days with students able to use any inanimate resources. All competition problems emphasize working with mathematics in a way that mirrors the way the world works with mathematics. Students must use a variety of mathematics in order to find a solution. Utilizing various formulas, teamwork, and concepts from the various fields of mathematics gives the students experience with how mathematics can solve real-world problems. The IM2C provides students with a deeper experience both of how mathematics can explain the world and what working with mathematics looks like. The Palo Alto High School team was one of only four teams in the world to earn the highest ranking on this problem.

Below is the problem from this year’s competition.

Movie Scheduling

A great deal of preparation must take place before a movie can be filmed. Important sets and scenes need to be identified, resource needs must be calculated, and schedules must be arranged. The issue of the schedule is the focus of the modeling activities. A large studio has contacted your firm, and they wish to have a model to allow for scheduling a movie. You are asked to answer the questions below. You should provide examples and test cases to convince the movie executives that your model is effective and robust.

Question 1: Develop a model that will produce a filming schedule given the following constraints:

* The availability dates of the stars of the film.
* The time required to film at a list of specific sites.
* The time required to construct and film on a list of sets.
* The availability dates for specific resources. For example a war movie might require helicopters which are available only at specific times.
* Some scenes cannot be shot until after certain computer generated content is defined and other physical items are constructed. Your schedule must include extra time to allow for redoing some shots if they turn out to be inadequate after editing and review.

Question 2: Develop a model that will take the information and schedule generated from the first question and can adjust them in the event that some delay in one aspect or the availability of some asset changes. For example, if one of the stars has an accident and cannot film for a certain period of time, you should be able to adjust the schedule.

Question 3: Use the model developed in the first question to develop a way to determine the most important constraints. That is, identify the constraints that will cause the longest delays if a problem occurs.