Teaching Practice
Mathematical teaching usually requires the use of several important teaching pedagogies or components. Most GCSE, A-Level and undergraduate mathematics require the following components:
- Textbooks or lecture notes which display the mathematical material to be covered/taught within the context of the teaching of mathematics. This requires that the mathematical content being taught at the (say) undergraduate level is of a well documented and widely accepted nature that has been unanimously verified as being correct and meaningful within a mathematical context.
- Workbooks. Usually, in order to ensure that students have an opportunity to learn and test the material that they have learnt, workbooks or question papers enable mathematical understanding to be tested. It is not unknown for exam papers to draw upon questions from such test papers, or to require prerequisite knowledge of such test papers for mathematical progression.
- Exam papers and standardised (and preferably apolitical) testing methods. Often, within countries such as the US, the UK (and, in all likelihood, China) there are standardised qualifications, examinations and workbooks that form the concrete teaching materials needed for secondary-school and pre-university courses (for example, within the UK, all students are required to sit or take Scottish Highers/Advanced Highers, A-levels or their equivalent in order to ensure that a certain minimal level of mathematical competence in a wide variety of topics has been obtained). Note, however, that at the undergraduate, post-graduate and doctoral levels within these countries, there need not be any standardised process via which mathematicians of differing ability levels can be tested or examined. Other common test formats within the UK and beyond include the BMO (which is a multiple-choice test competition paper used in order to determine the best candidates that are to represent countries within the International Mathematical Olympiad).
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