Mathematics & miss

Every student wants to pass his/her exams. Unfortunately, there are students who fail. One reason for this failure is that the student simply has not committed the necessary information to memory. This, in turn, can be ascribed to the prevalent bias in education against memorisation. Memorisation – so the charge runs – stifles originality. Instead of memorising facts, it is said, true, meaningful learning depends on understanding.

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There is, of course, an element of truth in this. True, meaningful learning does depend on understanding. Understanding is, however, only the beginning of learning. Understanding something does not mean that one has learnt it, that is, that one knows it and has confidence in applying it. When one understands something one has taken the first step in learning; the next step is to commit it to memory, that is, to memorise it. Then, and only then when something has been committed to memory, has one learnt it.

With only understanding, without committing the subject content to memory, one is simply not prepared for an exam, and one is also insufficiently prepared for the profession for which one is studying. Not only in an exam but also in the everyday practise of one’s profession, one needs a mass of detailed information (knowledge) stored in the mind.

Furthermore, higher order thinking skills, such as independent, critical thinking and problem solving, are always conjoined to relevant, domain-specific information, and therefore such skills cannot be gained and subsequently exercised without having committed the associated information to memory (Hirsch 1996:254, 264). The denigration of memorisation is in fact a denigration of knowledge, and ultimately a defeat of the educational ideal of stimulating problem solving and independent critical thinking. As Hirsch (1996:247) points out:

“Independent-mindedness is always predicated on relevant knowledge: one cannot think critically unless one has a lot of knowledge of the issue at hand. Critical thinking is not merely giving one’s opinion.” In fact, common sense tells one that the person who can think critically and who can solve problems is, without exception, one who has sufficient knowledge of the relevant issue or problem.

Thus, to attain success in an exam, both in questions that are straightforward and questions that require independent critical thinking and problem solving one must, first, understand the subject content and, second, one must commit the subject content to memory.

understand what a scientific theory is and what the difference between a valid and a speculative theory is, one must understand exactly what natural science involves, as well as its purpose and its limits. Study the explanations in the study guide.

Scientific theories are explanations of observed facts. Such theories tie the observed facts together, and the best theories are those which achieve this with the least number of inconsistencies. An example of a scientific theory is Newton’s theory of gravity which explains why falling objects always fall towards the centre of the earth.

Valid scientific theories give consistent results when tested in the laboratory and can be applied technologically. Valid theories, however, are open to modification and/or expansion if newly discovered factual data makes it necessary. For example, we know the theory of aerodynamics is valid because it is applied in aeroplanes.

Additional information: If a theory is verified repeatedly, it is regarded as fixed and universally valid; in other words, it is a natural law. The laws of nature cannot change. Every technical construction and measuring apparatus is a practical application of the laws of nature. If the laws of nature changed, bridges and tower blocks, for example, calculated correctly taking the laws of nature into account, could collapse. As all physiological processes are also dependent on the laws of nature, a change in these laws would have catastrophic consequences. For these reasons no patent office will accept an ‘invention’ that contradicts a natural law.

A speculative theory is a theory which considers matters that (1) are not physically observable and/or measurable and/or (2) are not repeatable events. Such theories should not be taught as facts because the data on which they are based can be interpreted in a different but also logical way.

The interpretations depend on the scientist’s presuppositions. In other words the presuppositions of the scientist determine the way in which data/facts are interpreted. Scientists always interpret evidence in terms of presuppositions and if such presuppositions of scientists differ then their interpretations of the evidence will also differ. Children must learn that presuppositions determine the path of reasoning.

Only when one knows the undergirding presuppositions of an untestable, speculative theory can one evaluate it and weigh it up against another theory that is based on different presuppositions. By teaching children to delve into the presuppositions undergirding speculative theories, they will learn the importance of forming informed opinions rather than simply endorsing the accepted, majority opinion. True critical thinkers are people who strive to discover truth and they value truth above majority opinion and group acceptance.