1.      Overview

The Argentina v England game in the quarter-finals of the 1986 FIFA World Cup in Mexico City included two of the most famous goals in football history, both scored by the Argentinean player, Diego Maradona. The second of these was voted in 2002 as the Goal of the Century. Indeed, some claim this to be the greatest individual football goal of all time!

In this Case Study pupils investigate why this particular goal is so famous and admired. They create a simple mathematical model to explore the contention that it is best ever goal (so far!). At the conclusion of the three lessons, each pupil will have developed a personalized model for evaluating any football goal – either from the past or in the future. Pupils use their model to rate the Goal of the Century and compare it to some other famous goals, including some of their own choosing.

This is an engaging problem for pupils who are interested in football or sport in general. The opening story about the famous Maradona goal piques pupils’ interest and creates a vibrant point of discussion about ‘best ever’ events. People often make unsupported claims about these, and so pupils should readily relate to the context.

Although ranking the ‘greatness’ of football goals is not an activity that has huge social implications per se, the aim of this Case is to help pupils recognise that, in everyday life, opinions are often based on what can be quite flimsy, anecdotal or subjective evidence and that it is often  important to try to justify claims objectively. At one level of understanding, pupils learn that goals can be compared and ranked using a mathematical model, but the Case aims to develop the deeper understanding that good decision making is based on sound reasoning supported by objective and justifiable evidence.

 

2.      Mathematical Content

To create their model, pupils identify and select parameters (variables) whose values may be either measured or counted. They devise point scales to score each variable in their chosen model. A total score for each goal is obtained by summing the scores for the selected variables. This score then allows the goal to be ranked alongside other goals.

The task is rich with mathematical possibilities and has strong links to the KS3 (or KS4) curriculum (see below). As they progress through the lessons, pupils discover that in order to be able to make reasoned, informed judgements about the relative greatness of football goals they need to think and work mathematically – although pupils may not initially recognise some of the necessary thinking as being “mathematics”.   Mathematics lies in the critical understanding that a model should be created in order to decide whether a goal is, indeed, the ‘goal of the century’.

Research has shown that having pupils think qualitatively before quantitatively reduces ‘cognitive overload’ and allows them to focus on the core thinking without being distracted by numbers, units and formulae.

Pupils learn the concept of a mathematical variable and develop an understanding of the distinctions between opinion-based, measured and counted variables. They make decisions about what variables are important and think about how they can collect the data they need from each variable. The identification, categorization, choice and use of variables with which to develop a ranking system is part of mathematical modelling, as is elucidating and explaining any estimates, assumptions, restrictions and constraints that they believe they need to make in ranking/rating individual goals. The discussions that ensue as pupils justify their positions add to the richness of the task, especially as it is very likely that different scoring or ranking models will produce different outcomes.

The skill-based mathematics required is appropriate for pupils in the KS3 (or KS4) target range, being accessible to those with lower levels of ability yet challenging for more skilled and confident pupils, particularly if they incorporate the concept of weighted variables. Number, Geometry and Measurement are involved when pupils make estimates and direct and indirect measurements of distances and angles from the video clips. Statistical skills are needed when pupils collect and tabulate the primary data.