Look at a situation: where is the maths?
Look at the photographs called Building a school with bottles in Honduras on handout 1. This is presented as a context - no problems are posed. Make a list of things you notice about the situation. What mathematical questions occur to you? You might begin by asking questions that start:
- How many ...?
- What would happen if ....?
Now set yourself a problem and use mathematics to tackle it.
Look at the Key Stage 3 Key Processes
Try to relate the work you have just done to the modelling cycle flowchart on Handout 2 . How well does it fit? Simplify and represent the situation
- What specific problems did you pose?
- What simplifications and representations did you create?
- What choices did you make of information, methods and tools?
Analyse and solve the model you've made:
- What variables did you use?
- What information did you collect, or estimate?
- What relations between them did you formulate?
- What did you need to calculate, and how?
Interpret and evaluate the results:
- What did you learn about the situation? Were the results plausible?
Communicate and reflect on your findings:
- How could you best explain your analysis to someone else?
- What connections can you see to other problems?
Discuss some pedagogical implications
- How can you help pupils to become more aware of the Key Concepts in the Programmes of Study?
- How can you help pupils become more aware of the importance of the Key Processes shown in the modelling cycle on Handout 2?
- Should you explicitly discuss these goals with pupils?
- Should you gradually introduce pupils to the modelling cycle in pupil-friendly language?
Observe a lesson
Now watch Frank's lesson on Building a School with plastic bottles. As you watch the lesson, ask yourself: Which Key Processes can you see in the work of these pupils? Can you see them: Simplifying and representing the situation?
- What problems did they identify?
- What simplifications and representations did they create?
- What choices did they make of information, methods and tools?
Analysing and solving the model they've made?
- Which variables did they consider?
- What information did they collect, or guess?
- What relationships did they formulate?
- What calculations did they make?
Interpreting and evaluating the results?
- What did they learn about the situation?
- Were their results plausible?
Communicating and reflecting on the findings?
- How did they explain their analyses?
- What connections did they see to other problems?
Plan a lesson using one of the problems
Now it is your turn to plan a lesson using the Building a School situation. Discuss how you will:
- introduce the situation to pupils;
- introduce the idea of the modelling cycle;
- organise the classroom and the resources needed;
- answer the question "Why are we doing this in maths?";
- conclude the lesson in a way that gives pupils a better understanding of the nature of mathematical processes.
This is the end of the Introductory session. After you have tried out your lesson with your own pupils, return for the Follow-up session . Resources to support the lesson, and a suggested lesson plan, can be found in the Into the classroom session .