Fair competition?
Math Alympiad preliminary 2009
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The activity

Fair competition?

Usually, in competitions between sports clubs from different towns the clubs play against each other once. That means that, over the course of a season, each club will play several away matches, as well as home matches. In this assignment, we will take a closer look at a number of different competition setups. We will take a look at the UEFA Cup for the season 2004 - 2005. This is an international football competition, organised by UEFA (Union of European Football Associations), where the participating teams are divided into groups of five to play a mutual competition. In this competition the teams all play each other once. In addition all teams play two home matches and two away matches.
Background information

Math A-lympiad

The Mathematics A-lympiad is a real-world-mathematics-problem-solving competition for teams of students forom uppe secondary schooles, with open ended assignments.
The open assignments are designed by the A-lympiad committee, a committee residing at the Freudenthal Institute of Utrecht University in the Netherlands, that organizes the Mathematics A-lympiad since 1989. The aim is to elicit students to think mathematically, to solve open-ended unfamiliar problems in a creative way, to model, structure and represent problems and solutions, to work collaboratively and to communicate about mathematics. The task is set in a non-mathematical real life (often work related) situation that asks for mathematical modelling and problem solving. The final product is a report fitting the real-life context of the task.

Math in teams
During the Dutch Mathematics Day Contest students work in teams of about 3 to 4 members on an open mathematical problem solving task during a couple of hours. The product of this work is a report (and sometimes a presentation).
Using your skills in a new setting
  • The task gives the students the opportunity to show what they have learned from mathematics and how they can use the knowledge and skills in a new situation.
  • Students can try, analyze, reason, calculate en design;
  • The (context of the) task is authentic, while the mathematics knowledge is easy to (re)use in this new situation;
  • Different teams can work 'on their own level' and this gives opportunities for differentiation;
  • There is a structure in the task from 'easy first steps' to a more complex end task.
The assessment can be focused on:
  • The completeness and correctness of the answers for the various parts;
  • the representation of calculations and the method used;
  • the use of math;
  • the argumentation and the justifications of choices and decisions;
  • the depth to which the various assignments have been answered;
  • originality and creativity in methods and solutions;
  • elements like: lay-out, readability, language, illustrations etc.

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