Failure to understand could occur for a variety of reasons. There may be a failure to construct an adequate, coherent mental representation of the information in a situation. The learner may simply not know understanding is expected and so does not attend in a way that makes it possible. He or she may be unable to construct a mental representation because of a lack of relevant prior knowledge, excessive mental demand, not knowing what is relevant, or failing to notice relevant relationships within the new information and between it and prior knowledge. There could be a failure to manipulate a mental representation or relate it to others because of a lack of ‘rules’ for governing the relationship. There could even be a failure to recognize a mental representation as being the state that was to be understood or achieved, as when a solution to a problem is found but is not recognized as such. How to support understanding was the subject of earlier chapters but what if learners

develop understandings which satisfy them but are unacceptable to the academic community at large or are otherwise unsound? This kind of understanding ‘failure’ can exist in very different domains of thought. For example, in biological science, some believe that acquired characteristics, such as rough hands can be inherited (Clough and Wood-Robinson, 1985). As a child, Peter Ustinov avoided drinking water after eating fish in case the bits re-joined in his stomach (Ustinov, 1977). In physical science, a common belief is that a force is needed to maintain motion in the absence of friction. In history, children tend to consider earlier people as somewhat stupid (Knight, 1990). Misconceptions also arise from words which mean different things at different times. For instance, revolution, industry and middle class have changed in meaning over the years. Applying these conceptions anachronistically can lead to unacceptable understandings

of past events. This also applies to ethical and moral conceptions. In geography, Flat Earth misconceptions are well known but some people think of Africa as being totally in the southern hemisphere, Edinburgh as being directly north of London, that volcanoes release lava from the centre of the Earth (Bisard et al., 1994) and that lightning never strikes the same place twice, while accepting it strikes mountains more frequently than low lying areas (Aron et al., 1994). In mathematics, novel situations commonly cause difficulties in applying algorithms

(Dehaene, 1997). For example, errors in subtraction occur when children attempt to apply a half-understood rule to situations such as 27−19, resulting in the answer 12. So-called buggy arithmetic is not uncommon and is not confined to subtraction (Bruer, 1994; Woodward and Howard, 1994). In weighing probabilities, there is often an inability to consider events as independent, even when they are. In tossing dice, if a six and four come up this time, they are thought less likely next time. The result is that the gambler chooses different numbers (Savoie and Ladouceur, 1995). In environmental health, people may believe we are experiencing an epidemic of

cancer from exposure to synthetic chemicals. These chemicals are seen as inherently toxic while natural substances are benign. When widespread, public misconceptions of this nature can influence government policy (Hrudely, 1990). In public health, there are dietary misconceptions. For instance, saturated fats may be thought to have more fat than unsaturated fats; you may substitute margarine for butter and so reduce your fat intake, and you can tell by looking at foods whether or not they are high in fats (Auld et al., 1994). In popular psychology, there are common misconceptions like IQ does not predict

academic success and less academically able children are generally gifted in non-academic areas. There is also a belief that having convicts talk to children about the error of their ways persuades the children to go straight, in spite of evidence to the contrary (McCutcheon et al., 1993). In teaching, ‘authentic learning’ is a term used to describe learning in situations like

those in which the knowledge would be used. Cronin (1993) describes some teachers’ misconceptions about authentic learning. For example, some argue that approximations to the real world are not worthwhile (if you are learning to teach, then start by taking a big and difficult class for an absent colleague) or that the level of learning aimed for is not enough for the real world (to be a teacher, you need a diploma in social work) or that only complex situations are valid (to be a teacher, you have to start by running a whole-school assembly). Some failures to understand are simply due to errors of fact. For example, it seems

reasonable to believe that pencil lead contains lead so, like other metals, it will conduct electricity. In reality, pencil lead contains graphite, a non-metal so it is surprising that it conducts electricity. It is likely that an error of this kind is easy to correct: a statement of the correction and the reason for it is likely to suffice. Perhaps a little more difficult to correct are some law-like ideas, such as ‘all wild animals are dangerous’. After all, a belief of this kind has survival value and even when someone is given contrary examples, such as the butterfly, the frog and the sparrow, they may still feel a need for caution. Some personal theories about how the world works can shape a wide range of under-

standings. Misconceptions of this kind are generative in that they are frequently used to explain, predict or justify situations and events. For instance, the belief that a force is needed to maintain motion even in the absence of friction will make its owner expect

rocket engines to be kept on in space otherwise the rocket will slow and stop. On the Earth, too, such a student’s understanding of many situations in dynamics would lead to very significant errors. This means that the impact of misconceptions ranges from a minor and local failure to

a major and widespread disability, according to the nature of the misconception. No one is immune to misconceptions and not all are serious. Some, however, have the potential to underpin (mis)understandings across a wide field and so can have significant consequences. Probably most problematic are those that are deep rooted, work adequately in a limited range of circumstances and can be used across a wide domain. Unfortunately, these also tend to be the ones most difficult to change. How does someone come to have such conceptions?