Teaching of Advanced Mathematics - Essay Example

But before that, we must delve further into the importance of the questioning mechanism, thus I shall bring out opinions presented by established mathematicians in relation to this study, as applied to classroom teaching of Mathematics. Ainley, J. as mentioned above, interprets her findings about questioning techniques, on the premise that, when, applied to classroom study, everytime the teacher asks a question, it merely implies her underlying desire in testing the student's learning outcome.

Therefore, a teacher's questioning style is described as "guess what is in my mind" tactics. Some of the frequent techniques of mathematical questioning range from using open questions, not commenting on answers but waiting for more, bringing in other people, collecting a range of responses on the board, seeking agreement, alternatives and dissent, using or not using "hands-up", using names to generate particular response, remaining silent until something else is said, and eventually all efforts culminating towards a successful learning outcome.

Jim Smith, in his article "Questioning Questioning" (1986) in the same study as Ainley, advises to maintain a balance between saying too much so that things become repetitive, to saying nothing at all. Suggesting that students be encouraged to talk enthusiastically about how they have helped other students, be allowed to interrupt teachers with relevant questions, and thereby, enable them to take part in the scheme by Skemp called "relational" learning (1976 & 1993), which is a flexible methodology that imparts in the student, a genuine interest in the deeper aspects of learning Mathematics, not only through methods and formulae but also by developing in them the much-needed grasping power to form powerful connections, interpretations, eliminate unnecessary fear of complex figures and symbols (such as surds, integrands, graphs, tables, etc.) and a chain of unbroken knowledge to further advance their learning capabilities.

Both mathematicians have affirmed the potent power of "testing" methodologies over simple "seeking" questions. As discussed in relevant examples above, upon our own close introspection, we can find that several of these questioning techniques are already followed by us in enhancing day-to-day learning activities whatever be the subject of study. In the course lesson example mentioned in this paper, I have designed my scheme to accommodate this very school of thought.

In an effort to understand the constructive ideas behind methods of questioning, we have at our disposal, a