Mathematics tests are undergoing a process of change. They used to be composed largely of closed, single-answer questions. Such questions are still found in some maths tests, but the introduction of the National Curriculum, with its emphasis on the development of processes of mathematical thinking rather than on the acquisition of knowledge as such, has done much to encourage a more open approach to the teaching, learning and assessment of mathematics. This has had a significant influence on the development of the National Numeracy Strategy introduced in all primary schools in 2000.
The development of mathematical thinking depends upon the pupils' ability to make links between the different aspects of mathematics that they understand. As far back as 1991, the National Curriculum encouraged an approach that would support this process:
Some activities have clear-cut results. Others may have several possible outcomes. These more open-ended activities can give scope for deploying a wide range of skills.
Mathematics in the National Curriculum (1991): Translating programmes of study into policy and practice. Para 5.9
The National Curriculum tests included questions that were designed to assess the pupils' ability to think mathematically, and to explain their thinking. This emphasis on 'explaining why', rather than just 'knowing how', helps to encourage a more exploratory, discursive approach in the classroom. Presenting mathematical concepts in a variety of ways supports the creation of conceptual links between related aspects of mathematics. It may also help to increase the accessibility of the questions, by offering pupils different routes in to a problem and supporting their use of a variety of thinking styles.
Presenting mathematical concepts in a variety of ways
Problems that present mathematical concepts in a variety of ways may help to make the mathematics more meaningful, and encourage pupils and teachers to understand the links between different aspects of the subject. For example, pupils may be asked to solve an algebraic equation presented in conventional terms:
3c + 2 = 2c + 6
Alternatively, a diagrammatic presentation may enable pupils to think their way through it, and develop a mental model of the abstract problem.
Again, a question might require the multiplication of two mixed numbers:
The same computation may be presented in the context of finding the area of a rectangle.
Here again, the diagram offers a model on which pupils may base their thinking, enabling them to grasp the meaning that underlies the process of multiplying a pair of mixed numbers.
Karen drew this rectangle on centimetre