Toward a theoretical framework of teaching mathematics through an epistemic holistic-conceptual approach
Mathematics education has always had a special kind of complexity and has posed problems worldwide. Only a relatively few students come to have a proper understanding of mathematical concepts, while the wide majority of students develop a "mathematical anxiety", lose the battle with the conceptual base of mathematics, and strengthen in their minds the idea that mathematics is something merely instrumental and calculational.
Within the research on mathematical education, the ongoing debate concerning the conceptual approach versus the procedural one has always focused on the general goal of understanding mathematics and developing math skills, (somehow corresponding to 'learning' versus 'doing' mathematics); however, the debate still has not resulted in a conclusion as to a) what epistemological concept of "understanding" mathematical understanding does fall within, b) what the exact relation is between the two types of approaches, and c) whether and how can they be unified.
Given the epistemological nature of understanding and the special place mathematics does have as an object of study in an intersecting zone of epistemology, philosophy of mathematics, and philosophy of science and adjacently foundations of mathematics and history of mathematics, the necessary contributions for a theoretical framework within which to investigate these issues are expected to come from these domains. Their potential in this respect has already been acknowledged, but it was not explored from a practical-applicative educational perspective.
The goals of this project are these: 1) to define a holistic concept of mathematical understanding from the educational perspective, on epistemological grounds; 2) to delimit clearly the concepts and knowledge zones from philosophy that can contribute to the theoretical framework of an adequate conceptual approach toward mathematics education; 3) to develop this framework, explore the ways to unify the conceptual and procedural approaches at the methodological level, and provide the criteria for developing the content of the curricula so as to ensure a holistic understanding of mathematics.
Dr. Catalin Barboianu (Philosophy of Science, Epistemology, Philosophy of Mathematics, Mathematics), principal investigator
New openings will be announced with the development of the project.
Updates and outcomes
The project completed a first phase of the theoretical research and the results can already be applied in the math education realm. PhilScience initiated a web-based math tutoring service for the students of 6 to 12 grades dedicated to the adequate conceptual understanding of the mathematics taught in school. This experience and students' feedback will be used as empirical data in a further stage of research within the project. Click the links below to be directed to that resource:RO version