Inquiry-Based Learning: An Educational Reform Based upon Content-Centred Teaching

The author of this paper posits that inquiry-based learning (IBL) enacted via a modified Moore method (MMM) is a content-driven pedagogy; as such it is content-centred not instructor-centred or student-centred. The MMM is a philosophy of education where student must master material by doing; not simply discussing, reading, or seeing it and that authentic mathematical inquiry relies on inquiry though constructive scepticism. We must commit to conjecture and prove or disprove said conjecture; we must do in order to learn; through real inquiry learning is achieved, and hence this paper proposes an archetype of mathematical pedagogy such that the experience of doing a mathematical argument is the reason enough for an exercise and inquiry-based learning (IBL) enacted via a modified Moore method (MMM) is an authentic way to actualise a learning environment where the content studied is the centre of the experience. The pedagogy of IBL is like no other pedagogy (for others focus on manner of exposition, recitation, activities, exercises, etc. and less with the content as oft content is secondary to the other method(s)) because in IBL content is primary. Many methods of instruction are not active but rather passive and some students wish to be passive and do the least (work) for the most (highest grade). IBL cannot be done passively. For a student to master material it is necessary for the instructor to be a master of the material so that the instructor may guide students through the content; hence, the IBL is in the tradition of a master-apprentice system. The major focus of the paper is on how the use of the MMM creates a more effective mathematical education for students; how use of the MMM established an atmosphere that created for many students firm and authentic understanding of many of the principles of mathematics; and, therefore is key in mathematics education reform. We will also discuss how inquiry-based learning (IBL) enacted via a modified Moore method (MMM) is rooted in a philosophical position of "positive scepticism." What binds and supports mathematics is a search for truth, a search for what works, and a search for what is applicable within the constraints of the demand for justification. It is not the ends, but the means which matter the most - - the process at deriving an answer, the progression to the application, and the method of generalisation. These procedures demand more than mere speculative ideas; they demand reasoned and sanguine justif