Number and magnitude: discussing the concept of measurement by means of a sixteenth-century mathematical instrument

Abstract: This paper presents some results of a study that valued manipulative conditions in the process of knowledge construction by handling a sixteenth-century mathematical instrument. The study was based on a problem-situation elaborated by epistemological and mathematical questions, which emerged from an interface built between the history of mathematics and teaching. The handling of this instrument triggered a series of actions that led teachers to reflect and discuss the very notion of magnitude, number and measurement. The results of the study suggest an epistemological gap between the observer who measures, the instrument that mediates the measuring, and the measured object. This gap compromises the proper understanding of measuring and the relationship between number and magnitude in measurement process.