3.      Organisation and pedagogy

The lesson descriptions provide suggestions as to how the problem can be tackled, but there is flexibility for both the pupil and the teacher. Whichever approach is adopted, the nature of this problem is that it encourages pupils to explore a variety of creative solutions and then to contrast them with other models in the class.

A strong feature of this Case Study is its accessibility to pupils of differing abilities. The problem posed is an ‘open’ one with no ‘correct’ solution. This allows pupils the freedom to investigate possibilities without being concerned that they may be ‘wrong.’ Indeed, a motivating factor of this Case is the opportunity it allows each pupil to devise a model of their own design.

After viewing video clips of several famous football goals, every pupil will be able to make an initial judgement about the greatness of this Maradona goal compared with other goals. Opinions are likely to differ, and this in itself makes an interesting starting point. Some pupils may disagree and want to suggest other goals as the ‘best ever’. The Case allows pupils to think of different models, some of which may be quite sophisticated. For example, some pupils may come up with a weighting system.

For the teacher there is flexibility:

• in the manner in which the concepts are translated into actual classroom activities;

• in the balance achieved between control of the activity and pupil decision making;

• in deciding whether tasks should be done individually, in groups or as a whole class;

• in deciding the level of difficulty appropriate for the class in question;

• in allowing the pupils to explore ideas of interest in more detail; and,

• in determining how the pupils’ work on the tasks should be assessed.

4.    General Advice

Keep the Aim of the Case Study (using variables and constraints to design a model) and the final task (applying and justifying the model) in mind at all times. Remind the pupils of them frequently to ensure that individual lessons have a focus and the entire case study has a clear and meaningful purpose.

Learn with the pupils. Work the task in preparation for the lessons. Measure the relevant parts of the video clip and form your own opinion. One approach is to create spreadsheets using Excel, and explore the variables yourself.

Allow the pupils the amount of freedom you are comfortable with. Discussions can be guided in a directed and ordered manner or in a less structured way with pupils exploring areas of interest on their own.

At all points where mathematical skills are required, quietly raise the pupils’ awareness of the fact that this is happening, but do not introduce the skill before the need is apparent and clear.

Suggested Extensions:

 

5.   Assessment

Assessment of pupils’ work should be based on their performance in the tasks themselves. Some suggested methods of assessment are:

• Portfolio of Lessons: The worksheets can be collected and assessed at the conclusion of the Case. It is suggested that criteria be established before the task begins. For example:

1. accuracy (of measurements, calculations, etc);

2. work habits (cooperation, responsibility for own tasks, etc);

3. effectiveness of presentation (of graphs, summary charts, etc); 

4. selection of appropriate strategies and mathematical and ICT skills for the analysis.

• Pupils explain their model using a written justification and/or an oral presentation. They should explain the features of goals they most admire (i.e. their variables) and justify their inclusion in their model. They should also explain any restrictions/constraints/assumptions they made in the development of their model. For example, they may have decided to compare only goals kicked from within a certain distance from the goal-mouth or only goals kicked off the ground.