Children's reasoning with schemes in the context of science education : studies of exemplification, analogy and transformation
It is clear from common experiences that abstract ideas are often difficult to understand, and that the use of concrete examples is often useful, perhaps always necessary. The research investigates some aspects of the relation between abstraction and examples: how 11-12 year old children move in their thinking between more and less generic levels; between greater and lesser degrees of abstraction; from example to generalization and vice versa, in the context of science education. The central interest is in how children use and modify concrete reasoning schemes. Its significance is in eliciting deep and implicit ideas which affect how children learn science. The empirical work consists of four related studies. The analysis is both qualitative and quantitative, in both cases looking for patterns in response. The first study explores the limitations of the boundaries of ontological categories in children's transformations of entities. Results provide evidence that ontological categories such as natural kinds and artefacts exist in thinking and that schemes are the "bridges" which can make possible even cross-ontological transformations. The second study explores the way that dimensions organise various entities and suggests a novel analysis of analogies. Results show that schemes appear in children's reasoning as packages. The presence of one scheme may predict the presence of another. Children use schemes such as "flow" and "path", which interact and modify one another. The use of examples in science teaching varies. The focus of the third study is on the analysis of examples of ideas in terms of objects which can be seen schematically. Results show that children are able to give consistent examples, in many cases different from the examples in their text books. Schemes that are used by children in the description of objects appear together across the various examples. Examples constrain the schemes children use to describe entities that take part in them. Examples work rather like metaphors. The fourth study shows that children are able to establish connections between concrete examples and generalizations. They think of some instances as better examples of ideas than others. The fit between examples and ideas is good when schemes such as `support', 'border', 'autonomous action' or better when several such anticipated schemes, are satisfied and poor when some are and some not.