Cross Curricular Links - Numeracy

The benefits of linking mathematics with design and technology

The advantages of linking the two subjects are readily apparent for pupils and teachers.

For pupils:

• A real need – D&T activities offer pupils a real purpose, for example, to measure accurately or to cost a product.
• Relevant contexts - Only when pupils encounter real problem situations can they be expected to fully develop their strategic mathematical problem-solving skills.
• The opportunity to apply mathematics – D&T offers opportunities to apply a range 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 that suggests that pupils can achieve higher levels in mathematics through design and technology, as they are well motivated.

For teachers:

• Planning within meaningful contexts - When planning the numeracy session, it is useful to use real contexts. This help reinforce learning in both curriculum areas.
• Assessment opportunities - Teachers can identify opportunities where they can assess pupils in real situations during designing and making activities rather than through 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 - Careful planning should ensure that work is either built on or reinforced and not duplicated.

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.

Problem solving

An important application of mathematics is its role in problem-solving. Many authors have given an explanation of the role of mathematics in the process of problem solving in terms of a cycle.
The problem to be solved could be how to arrange furniture to enable all pupils to see the board whilst maintaining enough space for adequate movement around the room.

Creating a model

A representation of the situation is created. It could be a scale plan of the outline of the classroom on a sheet of paper with smaller card shapes representing the furniture. 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. Here 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. Trying it out which may reveal further problems with the arrangement, causing the problem solving cycle to run again.

This mirrors the way in which a child might work through a design and make assignment. S/he 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

These 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 understanding 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.

A difficulty in mathematics is that pupils do not have many real opportunities through which to practise and to develop their mathematical skills. Even the ‘problem’ situations pupils are given can be quite contrived and simplistic compared to the solving of real problems. This can lead to them failing to develop the strategic thinking skills that they require and even to think that mathematics is not of great use outside of mathematics lessons.