An approach to testing and teaching
'Consider the problems of acquiring new knowledge; two ideas are particularly important. The first is that existing knowledge and conceptual structures affect the way that new materials are perceived and learned; the second is that new experiences bring about changes in our knowledge and conceptual structures. These two processes are referred to as assimilation (analogous to the way in which the stomach digests food, whose later structure cannot be recognized as being similar to its earlier structure) and accommodation (analogous to the way that the pupil of the eye adjusts itself different light levels). Biological analogies make it easier to understand these concepts but leave unresolved the question of when one accommodates and when one assimilates. In general, one accommodates (i.e. changes one's conceptual structures) when fresh knowledge provides strong challenges to what is in mind; so dramatic counter-examples to currently held beliefs, or coherent patterns in the world, which cannot be explained by existing beliefs are both likely to bring about accommodation. Assimilation (interpreting new events in terms of old ideas) can be made to work when the number of counter-examples to predictions made from old beliefs are rather low. It follows, therefore, that if misconceptions are to be remedied (i.e. the mechanism of assimilation is overcome and the mechanism of accommodation stimulated) a representative sample of questions in the domain of interest is unlikely to have the desired effect because the number of cases which violate pupils' misconceptions and which therefore might cause accommodation, will be relatively small. To foster accommodation it is necessary to provide dramatic examples which violate current conceptions and to provide these examples in quantity. Examples which are most likely to be dramatic are those in which it is obvious to pupils that the results they are obtaining using particular misconceptions are at variance with what they 'know to be true' from everyday experience.' pp.46-47.
Jim Ridgway (1988). Assessing Mathematical Attainment. Chapter 3, Using Test Results.Windsor Berkshire. NFER-NELSON. pp.40-52. [Ack. length of quote - See also: https://www.nfer.ac.uk/ ]
Thanks to Lancaster Univ. Library.