And why does the penny drop?
More fundamental failures in maths and science teaching exist than those highlighted by university maths specialists last week, two research teams have concluded. The university academics complained about a lack of basic skills among student entrants to degree courses. They blamed both progressive teaching methods and the national curriculum for poor maths performance in schools.
The two research teams taking part in the Innovation and Change project (see panel) studied how children perform in maths and science lessons and talked to groups of primary and secondary children. Both teams found that even where children became good at, for example, measurement, or drawing graphs to illustrate scientific experiments, they did not grasp the concepts underlying what they were doing. Without the concepts, progress in both subjects is put at risk, the researchers claimed.
In a study of how six to 12-year-olds were taught about measures in maths and forces in science, a topic fundamental to later work in physics, a research team at King's College, London, found that between 15 per cent and 25 per cent of six and seven-year-olds were performing at the same level as 70 per cent of 11 and 12-year-olds in the study. This, in itself, presents serious practical problems for curriculum designers and teachers, they said.
When children in Years 2, 4, 6 and 8 undertook experiments intended to help them understand forces, just over half of the Year 8 pupils could identify the opposing forces which establish equilibrium and few could use or define the scientific terms involved. Few understood how weight was related to gravity, or understood terms such as friction, balance or distortion. A grasp of scientific vocabulary was essential to children's progress, the researchers suggested.
"Teaching about forces at secondary level usually begins with assumptions about children's thinking that cannot, according to our results, be justified, " they said. They came to similar conclusions about mathematics after experiments involving measurement. Children, they found, were being taught how to measure length, weight, area, volume, angle and temperature, but with little or no emphasis on the underlying common concepts.
"If pupils were asked to devise a measuring system for length or temperature or time that they could use on a desert island it is not clear they would know what is required."
Talking to the researchers helped some of the children to understand these concepts. It therefore seems important, the team said, to pay continuous attention to the quality of pupils' reasoning as well as their ability to come up with the "right answers".
While expertise was important, the team concluded, generalisation and abstraction will help children remember what they know and demonstrate the processes which characterise mathematics.
At secondary level, a team from Durham and York universities examined pupils' ability to make use of evidence in science. They found pupils being told how to use instruments or draw graphs, but lacking any clear grasp of what these tools were for or what results they were likely to provide.
They suggested that experimental science should be seen as having a distinct "content" of its own. The aim should be to teach concepts such as repeatability and validity, and the significance of variables and "controls", which were not widely or well understood. Graphs were being produced without the right axes, and pupils had little idea of what pattern to look for in their practical results.
The King's College team argued that it was possible to establish stages by which children progress in understanding mathematical and scientific concepts, and that it should therefore be feasible to provide schemes of work to help. They said this should be addressed in national curriculum Orders which might help to focus teaching and assessment on conceptual learning. If nothing was done, children's progress in maths and science may be blocked by problems not instantly apparent to their teachers.
It is profoundly disappointing, the team concludes, that ideas which bright pupils can work out for themselves at the age of six or seven are still not understood by some older pupils after six more years in school. But whether programmes can be developed which can alter this unsatisfactory outcome remains to be seen.
Progression in learning - issues and evidence in mathematics and science, Paul Black, Margaret Brown, Shirly Simon and Ezra Blondel. Evidence in Science Education, Sandra Duggan, Richard Gott, Fred Lubben and Robin Millar.
INNOVATION AND CHANGE
Researchers have been monitoring the effects of the revolution that erupted in schools in the early 1990s. Ten project teams, from a dozen universities, brought together academic educationists, psychologists, sociologists and experts in linguistics to investigate fundamental classroom issues.
The research project, entitled Innovation and change in education: the quality of teaching and learning,was funded by the Economic and Social Research Council. The researchers' conclusions are brought together for the first time in Teaching and learning in changing times, edited by Professor Martin Hughes of Exeter University, to be published by Blackwell at the beginning of next month.