Cross Curricular Links - Numeracy

The benefits of linking mathematics with design and technology

Through linking the two subjects, the advantages for pupils and teachers are readily apparent.

For the pupils, the benefits include:

- A real need - Design and technology activities offer pupils a real purpose, for example, to measure accurately or to cost a product.
- Relevant contexts - Only when pupils encounter real (as opposed to contrived) problem situations can they be expected to fully develop their strategic mathematical problem solving skills.
- The opportunity to apply mathematics - There are opportunities to apply a variety of aspects of mathematics and to gain practice in areas in which a child has difficulties such as shape, time or measurement.
- Enjoyment- There is evidence (see the case studies) that suggests that pupils can achieve higher levels in mathematics through design and technology, as they are well motivated.

For teachers, the benefits include:

- Planning within meaningful contexts - When planning the numeracy session, it is useful to use real contexts with the pupils. This help to reinforce learning in the two areas of the curriculum.
- Assessment opportunities - During the designing and making activities, teachers can identify opportunities where they can assess pupils in real situations, rather than during paper and pencil exercises. For example, as pupils use construction kits to make a shelter the teacher can talk with them about the shapes they can see and check their use of appropriate mathematical vocabulary.
- Best use of time - There are always time constraints in the primary curriculum and unnecessary duplication is wasteful. Careful planning should ensure that work is either built on or reinforced.

Aspects of the nature of mathematics

By exploring the nature of mathematics in more detail, the value of the links between the two subjects should become clearer.

Problen solving

An important application of mathematics is its role in the solving of problems. Many authors have given an explanation of the role of mathematics in the process of problem solving in terms of a cycle. A simple version of the cycle appears in figure 1.

One way of explaining the cycle is by means of an example:

At this stage a "real" problem is identified. The problem to be solved could be how to arrange furniture to enable all pupils to see the blackboard whilst maintaining enough space for adequate movement around the room.

Creating a model

At this stage a representation of the situation is created. In this case it could be a scale plan of the outline of the classroom on a large sheet of paper with various smaller shapes of card cut to the same scale representing the furniture in the room. However, in other situations, the model does not have to be physical, it could be a mathematical equation.

Analysing the model

This involves manipulation of the model to produce possible solutions. In the case of the classroom plan, this would involve arranging the shapes representing the furniture and checking whether all pupils would see the board from their tables and whether there would be enough room for adequate movement around the room. If the model created had been an equation, this stage would involve solving the equation.

Interpreting the solution

This involves looking at the mathematical solution in the previous stage and making sense of it in the "real" situation. In the case of the classroom plan, this would mean looking at the proposed solution and seeing whether it really makes sense in the real classroom. It could then be tried out. This trying out may reveal further problems with the arrangement, in which case the problem solving cycle can be encountered again.

This mirrors the way in which a child might work through a design and make assignment. He / she will not necessarily go through each stage in a linear or a cyclical path. The process will almost certainly be iterative.

Mathematical skills involved in the problem solving cycle

The many mathematical skills used in the problem solving cycle can be classified as being either technical or strategic.

- Technical skills are those that involve the performance of mathematical techniques. For example: calculating, measuring, producing scale drawings, solving equations, etc.
- Strategic skills involve the understanding of a task or problem and deciding on the appropriate technical skills to use. Choosing to use a scale plan to help solve the above problem is an example of the use of strategic skills

It is fairly obvious to see where technical skills from mathematics can be used in the designing and making process: measuring the length of materials when making a model, addition, subtraction, multiplication and division when costing materials for a project, and so on. There is equally a significant place for the use of strategic skills, from mathematics, in the designing and making process for example, as pupils generate ideas, plan or make decisions.