Abstract:

Knowledge-based economy and knowledge-based society are currently common key term in most of the discussions involving education and especially higher-education. My paper focuses on the relation between the knowledge-based society and mathematics, especially mathematical education and mathematical thinking. The treaty of Lisbon says at article 179 that “The Union shall have the objective of strengthening its scientific and technological bases by achieving a European research area in which researchers, scientific knowledge and technology circulate freely.”, hence the importance of fostering (at least in Europe) a scientific knowledge-based society, especially a mathematical knowledge-based society.
Both scientific reasoning and scientific culture play an important role in shaping the modern world, and in constructing the so-called knowledge-based society. In this “scientific knowledge-based society” mathematics plays in fact a dual role. On one hand, it helps us securing and deductively organizing our reasoning, and, on the other hand, it provides us the theoretical basis for all scientific domains. We may say that something counts as science depending on how much mathematics comprises in it.
Mathematics offers us a way of dealing epistemically with the world, a mode to tackle the world from a certain angle. But, in fact, does our world have a mathematical structure or is mathematics just a creation of our mind? This is a very important question which has been bothering the philosophical minds for centuries. Yet, regardless of the ontological status of mathematical entities, we should acknowledge the fact that mathematics is an important part on our world. Besides counting and making certain current calculations, mathematics teaches us how to solve problems, and perhaps this important aspect should be more cultivated by us.
In 17th century mathematics has been seen as a medicine of the soul (medicina mentis). In this sense, I advocate a teaching methodology based on project-based learning instead of the classical ex cathedra way of given to our students just mathematical results and proofs. First, the student should be taught how to see the world mathematically, and to see the advantages of this point of view, and only after to pour in it mathematical knowledge per se. In this sense the student is stimulated to be creative, and to discover certain mathematical patterns of thought, which may help him to better understand various problems. In order to make sense of numerical data, and to learn how to mathematize and understand quantitatively a phenomenon, one should be first trained to think algorithmically. For instance, after visualizing the Fibonacci series in the disposition of the petals of a flower, one could better understand and master the techniques of series in general.

Keywords:

Mathematical education, knowledge-based society.