3 - The Process of Mathematical Agreement: Examples from Mathematics History and an Experimental Sequence of Activities

Summary

Introduction

Usually systematization processes are interpreted as processes beyond the processes of mathematical discovery. For example, Mariotti [9] establishes two moments for the production of mathematical knowledge: “…the formulation of a conjecture, as the core of the production of knowledge, and the systematization of such knowledge within a theoretical corpus.” In this same vein is to contrast the argumentation process of a conjecture with the process of a theorem proof [1].

We proceed from the consideration that, for purposes of learning, there are propositions whose validity can be established from the outset as true to the need to bring coherence to a system of knowledge. The truth of the statement can be interpreted as “agreed truth;” in the sense that it is set from the necessity to make a theoretical corpus.

The following intends to show a knowledge production process, that we have called the process of mathematical agreement, which has the characteristic of combining different moments in the production of mathematical knowledge. In this sense the process of mathematical agreement, can be interpreted as a process of systematization of knowledge.

We will present three examples from the history of mathematics that show the production of the meaning of: 1) fractional exponents, 2) the square root of negative numbers as precursor to the meaning of complex numbers and 3) the radian and the trigonometric functions. In order to validate the process of mathematical agreement we then present the results of an experimental sequence that has the objective of student acceptance of the square root of negative numbers and of the operations on them.