International Mathematical Modeling Challenge

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  • Pilot 2015
  • Deelnemers: vrijwilligers uit 9 Wiskunde A-lympiade finalisten en 10 finalisten Wiskunde B-dag
  • Dit leidt tot ongeveer 10 teams voor deze pilot (5 A en 5 B).
  • Uitvoering door scholen: in principe: woensdag 15-4
  • Een jury selecteert twee IMMC winnaars: opdracht en winnende uitwerking in het Engels naar centrale organisatie sturen.
  • Overall winnaar wordt juni 2015 bekend gemaakt.

The purpose of the IMMC is to promote the teaching of mathematical modeling and applications at all educational levels for all students. It is our firm belief that students and teachers need to experience the power of mathematics to help better understand, analyze and solve real world problems outside of mathematics itself - and to do so in a realistic context. We are launching this challenge in the spirit of promoting educational change.

For many years there has been an increased recognition of the importance of mathematical modeling from universities, government, and industry. Modeling courses have proliferated in undergraduate and graduate departments of mathematical sciences worldwide. Several university modeling competitions are growing and flourishing. Yet at the high school level there are only a few such competitions with many fewer students, even amid signs of the growing recognition of modeling’s centrality. We believe that it is time to change the secondary school culture. And we believe that one important way to do this is to institute a high-level, prestigious new secondary school contest – one that will have both national and international recognition. We therefore propose to found the International Mathematical Modeling Challenge (IMMC). We intend this to be a true team competition, held over a number of days with students able to use any inanimate resources. We can’t emphasize enough that we want students to experience working with mathematics in a way that mirrors the way the world works with mathematics. Real mathematical problems are messy. Real problems don’t come after chapters in a mathematics text so that you know what techniques to use. Real problems require a mix of different kinds of mathematics to analyze and solve. And real problems take time and teamwork. We intend that the IMMC will provide students with a deeper experience of both how mathematics can explain our world and what working with mathematics looks like.

This competition will be inspired by other major international contests, with two rounds of competition, namely national rounds to pick teams from each participating country and an international round hosted each year by a different country, in which the national winners are judged against each other At the first meeting of the IMMC Planning Committee several key decisions were made. First, each country will choose two (2) teams of up to four (4) students each to participate. The countries will be free to choose their teams in any way they deem appropriate, including as winners of local contests.

In April the IMMC will send out one problem that all selected teams will work on in their home countries. This will be a true open-ended modeling problem, with no single correct answer. IMMC problems will be chosen so as not to reward students simply for knowing more or higher- level mathematics, but rather to test their ability to use the modeling process (Sample problems are appended). Teams will be given five (5) consecutive days to work on the problem. However, we will permit teams to choose when within the month to begin. Each team will have an advisor who will attest that their team has followed the rules. Students will be allowed to use any and all resources with the exception of asking non-team members for help.

Papers will be sent in English, electronically and in print, to the IMMC central office. These papers will be read by a distinguished panel of experts. In late July/early August all of the participating teams will come to a host country where they will spend some time touring and enjoying new cultural experiences. Each team will be accompanied by one advisor. Teams will then present and defend their solutions before the judging panel. The panel may ask other modeling related questions. Outstanding teams will be recognized based on their presentations and their panel interviews. Our plans call for beginning the contest in 2015. We will select the judging panel, set the exact dates of the contest, and select the first host country in the coming months. What is most important at this time is a willingness to participate – to help us mold this contest into the beacon for educational change that we hope it will become. Please join with us as we move forward to make this plan a reality.

IMMC Planning Committee:

  • Solomon Garfunkel, COMAP, USA
  • Keng Cheng Ang, National Institute of Education, Singapore
  • Fengshan Bai, Tsinghua University, China
  • Alfred Cheung, NeoUnion ESC Organization, Hong Kong
  • Vladimir Dubrovsky, Moscow State University, Russia
  • Henk van der Kooij, Freudenthal Institute, the Netherlands
  • Zbigniew Marciniak, Warsaw University, Poland
  • Mogens Allan Niss, Roskilde University, Denmark
  • Ross Turner. Australian Council for Educational Research, Australia
  • Jie “Jed” Wang, University of Massachusetts, Lowell, USA

Sample Problem: City Planning

Major thoroughfares in big cities are usually highly congested. Traffic lights are used to allow cars to cross the highway or to make turns onto side streets. During commuting hours, when the traffic is much heavier than on any cross street, it is desirable to keep traffic flowing as smoothly as possible. Consider a two-mile stretch of a major thoroughfare with cross streets every city block. Build a mathematical model that satisfies both the commuters on the thoroughfare as well as those on the cross streets trying to enter the thoroughfare as a function of the traffic lights. Assume there is a light at every intersection along your two-mile stretch. First, you may assume the city blocks are of constant length. You may then wish to generalize to blocks of variable length

==Sample Problem: How Many Taxis? You are standing in the rain trying to hail a cab in a large city. While waiting, seven cabs pass by that already have a passenger. The numbers on the cabs are 405, 73, 280, 179, 440, 301, 218. Suppose that you want to estimate the number of taxis in the city. Assuming that all of the taxis are numbered 1 through N and are all in service, how can you use the observed numbers to estimate N, the total number of cabs? How can you test your method for estimating N?


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