The arithmetical machine Zero+1 in mathematics laboratory: instrumental genesis and semiotic mediation

This paper presents the analysis of two teaching experiments carried out in the context of the mathematics laboratory in a primary school (grades 3 and 4) with the use of the pascaline Zero  +  1, an arithmetical machine. The teaching experiments are analysed by coordinating two theoretical frameworks, i.e. the instrumental approach and the Theory of Semiotic Mediation. The paper focuses on the analysis of the semiotic potential of the pascaline and students’ instrumental genesis, on the functions of schemes and gestures of usage

Systems of Instruments for Place Value and Arithmetical Operations: an Exploratory Study with the Pascaline

This paper concerns the use of instruments in teaching and learning mathematics at primary and secondary school levels. It focuses on the introduction and use of the arithmetical machine Zero+1, called pascaline, and its relationships with other instruments used by students to write numbers and make operations, as spike abacus or calculator. The analysis of three teaching experiments shows that the instruments are related with respect to their utilization schemes, but also to their representations

The Laboratory of Mathematical Machines: Exhibitions, Educational Research and Sessions for Students

In this paper, we present the different kinds of activity involving the Laboratory of Mathematical Machines of the University of Modena e Reggio Emilia and its collection of instruments, the mathematical machines. They are copies of historical instruments, constructed with an educational aim but also used in the popularization of mathematics

Are mathematics students thinking as Kepler? Conics and mathematical machines

Our interest is the analysis of the thinking processes of some university students who worked on the design of a machine that uses a tightened thread to draw a hyperbola. Previously, the students worked with other machines for conics. We focus on the way past experience becomes part of a new experience, in which making of the machine is the end point of the task. This implies the presence of technological and scientific aspects, whose interplay is fundamental to shape thinking

University students at work with mathematical machines to trace conics

This paper aims to investigate the way past experience with some tools to draw conics becomes part of the experience of designing a new drawer. In particular, it centres on the thinking processes of a group of university students who have the following task: to design a hyperbola drawer. The analysis is carried out using the perspectives of transfer of learning and instrumental approach, and focuses on utilization schemes and the interplay between scientific and technological aspects

ICT, new insights on old problems

In our research works, we used to look at the way in which artefacts become, for teachers as well as for students, instruments of their mathematical work. The questions of tools and technologies in mathematical education are now widely considered in our communities. The 100th anniversary of the creation of ICMI is the occasion to go back to history, to think on the possible contribution to mathematics learning of old (but not dead) artefacts to mathematics learning and to the instruments’s geneses.http://www.unige.ch/math/EnsMath/Rome2008/WG4/Papers/TROUMAS.pd

Des scénarios portant sur l’utilisation d’artefacts dans l’enseignement et apprentissage des mathématiques à l’école primaire

Le texte présente deux exemples de scénarios pour l’apprentissage du nombre où le recours à des artefacts concrets joue un rôle clé. Ces scénarios ont été mis au point suivant la méthodologie du laboratoire de mathématiques, fondée sur les cadres théoriques de la médiation sémiotique et de l’approche instrumentale. L’objectif didactique est la construction, par les élèves, des mathématiques véhiculées par l’artefact sous la conduite de l’enseignant, qui a un rôle crucial de médiateur culturel. Les artefacts considérés sont un boulier géant à l’école maternelle et la machine arithmétique ‘Zero+1’ (appelée ‘pascaline’) à l’école élémentaire

APPROACHING CONIC SECTIONS WITH MATHEMATICAL MACHINES AT SECONDARY SCHOOL

This workshop aims to discuss the main steps of a teaching experiment focusing on the introduction of conic sections at secondary school level (16-17 years-old students) following the methodology of mathematics laboratory with mathematical machines