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

The energy of craftsmanship – In the era of digitalization: PTTX Putian Group success story

PTTX Putian Group is pioneering a green energy transformation in the electric power sector. With a fully integrated mill and a unique example of vertical integration, they are expanding their core manufacturing capabilities to meet the growing demand. This article showcases how PTTX Group is driving advancements in electrical steel material technology to create a greener and more low-carbon future

Artifacts for geometrical transformation and drawing curves in the classrooms, workshops and exhibitions

This contribution focuses on the use of some instruments, called “mathematical machines”, in teaching and learning mathematics

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

Exploring a new geometric-mechanical artefact for Calculus

We introduce a geometric-mechanical artefact designed for laboratory activities related to Calculus topics (3D models and construction instructions are freely available online). With new capabilities and a new design, this instrument adopts some mechanisms historically introduced to solve inverse tangent problems (that analytically correspond to solving differential equations). By such an instrument, besides materially revealing the tangent to a curve (tangent mode), it is possible to trace the graph of exponential functions and parabolas starting from the geometrical properties of their tangent (curvigraph mode). Furthermore, one can perform transformations as derivatives and integrals (transformation mode). Our research project aims to study the use of this artefact mainly for secondary school students. In this paper, we present the analysis of its semiotic potential, referring to the instrumental approach and the Theory of Semiotic Mediation. We also focus on a secondary school teacher manipulating the artefact to identify exploration processes and gestures of usage. The analysis supports the choice of starting the exploration in the tangent mode and suggests that the artefact fosters the emergence of the idea of the tangent line

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