We Are Mathematical Beings

In this mathematical-poetical text, the author posits mathematical thought as fundamental to concepts of self and world. Mathematics is not something exterior to be learned, but basic to daily life. For example, object permanence is an abstract concept of multiple perspectives compiled in to the idea of one stable object. Such abstraction is mathematics. These concepts exist both socially and materially. A wooden cube is both a social concept and a material object. We exist in a mathematically determined world. We use mathematics to enact new reals. This is so common that often we are unaware of it.

On the Hermeneutics of Reading Historical Texts in the Mathematics Classroom

A hermeneutical substructure for the reading of historical texts in the mathematics classroom is described. It is organized according to the four transcendentals of unity, truth, beauty and goodness, each of which is considered internally –with respect to the text itself – and externally – with respect to both its relations to mathematical thought in general and other cultural manifestations. Lead questions are provided for each category as are also details regarding various ways in which the student’s interactions with the text can be organized in order to provide the student with a rich learning experience. Some attention is also given to questions relating to implementation.

Epistemological Notes on Mathematics

This chapter is an attempt to show how mathematical thought has changed in the last two centuries. In fact, with the discovery of the so-called non-Euclidean Geometries, mathematical thinking changed profoundly. With the negation of the postulate for “antonomasia,” that is the uniqueness of the parallel for Euclid, and the construction of a geometric theory equally valid on the logical and coherence plane, called non-Euclidean geometry, the meaning of the word “postulate” or “axiom” changes radically. The axioms of a theory do not necessarily have to be dictated by real evidence. On this basis the constructions of arithmetic and geometry are built. The axiomatic-deductive method becomes the mathematical method. It will also highlight the constant link between mathematics and the reality that surrounds us, which tends to make itself explicit through an artificial, abstract language and with clear and certain grammatical rules. Finally, you will notice the connection with the existing technology, that is the new electronic and digital technology.

The Role of Instinct in David Hume's Conception of Human Reason

This article investigates the role of instinct in Hume's understanding of human reason. It is shown that while in the Treatise Hume makes the strong reductive assertion that reason is ‘nothing but’ an instinct, in the First Enquiry the corresponding statement has been modified in several ways, rendering the relation between instinct and reason more complex. Most importantly, Hume now explicitly recognises that alongside instinctive experimental reasoning, there is a uniquely human intellectual power of intuitive and demonstrative reason that is not itself an instinct. At first sight it may look as if this intellectual reason, that is capable of grasping ‘relations of ideas’, is not even grounded in instinct but is a thoroughly non-natural element in human nature. On closer analysis, however, it is shown that intellectual reason, in its apprehension of ‘abstract’ and general relations, is dependent on language – the use of ‘terms’ – and that language itself is grounded in instinctive associations of ideas. Thus, Hume's overall view is that even the intellect is an outgrowth of instinct and his conception of human nature is, therefore, shown to be fully naturalistic. Yet this naturalism can still make room for the ‘exceptionalism’ of human mathematical thought, which has no counterpart in the animal kingdom where language is lacking.

Modeling The Use of History of Mathematical Thought in Mathematics Instruction

Mathematics is a human creation, which has been developing for more than four thousand years. It emerged as a response to different social and economic needs of civilizations. Historical development of mathematics stresses that mathematics as a science has always been connected to economic and social context and development of society. There is little or no research that promotes using historical content in mathematics lessons in the Nigeria context. In this paper, we model the use of history of mathematical thought (HMT) in mathematics instruction and solved the formulated model equation using integrating factor. The rate at which HMT is used by teachers in mathematics instruction is assumed to be proportional to the number of teachers that do not use HMT. The analysis suggests that with time, only a fraction of teachers can use HMT in teaching mathematics due to the fact that they will not remember to use it, and additional recruitment of teachers will result in only marginal improvement in the usage of HMT.

Mathematical Forms in the Look about the Human Body: Thought, Technique, Art and Education

This article is an analytical exercise on a way of thinking in which mathematics operates in the ways of representing and speaking about human body drawing. With a problematic attitude, one asks: how and where does a technique that colonize ways of representing and looking at the body in art and math activities in the classroom come from? This means analysing a modulation of look and thinking that organizes the imagetic representation of the human body, shapes the image, and orders thought, in which mathematics operates as the agent and effect of a mode of colonization. Therefore, it takes different ways of representing the body in art history, operating in a theoretical-methodological movement, with “the perspective of visuality for visualization in Mathematical Education”. Thus, other possibilities of (re) thinking with images are raised, analysing them under the bias of a decolonial mathematical thought, that is, a thought that questions and denounces the effects of truth and the hegemonic mathematical visualities. From this, then reinventing itself to re-exist in Mathematical Education.