Matematical Language and Advanced Mathematics Learning

This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students’ linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students’ behaviors requires to take into account the role of context. Some ideas from functional linguistics are outlined and some features of the texts usually produced by students are discussed and compared to the corresponding features of standard mathematical texts. Some teaching implications are discussed as well

Language in argumentation and solution of problems with graphs

Il lavoro indaga le argomentazioni degli studenti universitari prodotte allo scopo di giustificare le loro risposte a problemi introduttivi di analisi matematica che richiedano il riconoscimento di relazioni fra grafici, testi verbali e formule. L'esame dei testi argomentativi prodotti in un ampio arco di tempo mette in luce serie difficolt\ue0 linguistiche e suggerisce che non possiamo escludere che il linguaggio possa essere un fattore determinante per la qualit\ue0 degli argomenti. L'obiettivo principale dello studio \ue8 il raggiungimento di una migliore comprensione di come le difficolt\ue0 linguistiche influenzino le argomentazioni

Developing language through communication and conversion of semiotic systems

This paper investigates the use of language by 2 classes of 7th graders in a context involving linguistic exchanges and conversions between representation systems in mathematical setting. The pupils were given tasks requiring the verbal description of a figure by means of a written text with no drawings for one class, and the interpretation of the text for the other. Both the tasks have been dealt with through discussion. The constraints involved in the experiment (communication with people not sharing the same context of situation; conversions between figures, written and spoken texts) have been designed in order to promote the acquisition of linguistic skills suitable for the learning of mathematics

Interpreting symbolic statements as texts: an exploratory study

This paper is devoted to the problem of the interpretation of mathematical texts . Some ideas on mathematical language are shortly discussed with the help of some constructs from functional linguistics. Some evidence regarding the interpretation processes of a symbolic text by groups of 10-graders, including both written answers and the transcriptions of spoken interactions is presented and discussed. The outcomes of this study show that students often try to interpret mathematical statements according to everyday-life schemes. This suggests that in school practice mathematical expressions should be dealt with as texts (rather than as abbreviations or local conventions) and that metalinguistic awareness should become one of the the goals of both linguistic and mathematical education

L'interpretazione dei testi matematici tra processi cooperativi e modelli logici: il caso dei connettivi

Il tema delle competenze logiche richieste per capire la matematica è stato quasi sempre oggetto di controversie sul piano educativo, tra i sostenitori dell'insegnamento della logica come disciplina e quelli che la guardano come una competenza trasversale. Il problema viene spesso sollevato nel corso della scuola secondaria di secondo grado e all'inizio dei corsi universitari. In questo contributo si discutono i processi di interpretazione dei testi matematici in linguaggio verbale, e il potenziale conflitto tra i meccanismi interpretativi propri delle notazioni simboliche della matematica e quelli usuali delle lingue. Viene affrontato in particolare il tema dell'interpretazione dei condizionali, anche attraverso l'esame di due teorie opposte. Vengono poi illustrati alcuni esempi a proposito di altri connettivi proposizionali. La conclusione è che la diversità dei processi interpretativi tra lingua e linguaggi della logica sconsiglia di proporre attività che richiedono l'interpretazione logica di testi verbali al di fuori dei contesti in cui questa sia giustificata

On prospective teachers' evaluations of freshman students' written arguments

n this paper we present a qualitative study in which we analyse how a group of prospective mathematics teachers evaluates written arguments produced by freshman students solving a problem involving graphs. The prospective teachers were attending a course of Mathematics Education for the second year of a master degree in Mathematics. In particular we focus on how prospective teachers in their evaluations look at mathematical content, language, and argumentative structure. The outcomes show, on the one hand, a certain attention to some linguistic aspects, on the other hand, a greater attention to the content than to the argumentative structure of the texts. We suggest that prospective teachers' models for linguistic education are often the standard ones, based on conformity to grammar or style rather than on adequacy with respect to goals

Toward Industry 4.0 With IoT: Optimizing Business Processes in an Evolving Manufacturing Factory

Research advances in the last decades have allowed the introduction of Internet of Things (IoT) concepts in several industrial application scenarios, leading to the so-called Industry 4.0 or Industrial IoT (IIoT). The Industry 4.0 has the ambition to revolutionize industry management and business processes, enhancing the productivity of manufacturing technologies through field data collection and analysis, thus creating real-time digital twins of industrial scenarios. Moreover, it is vital for companies to be as “smart” as possible and to adapt to the varying nature of the digital supply chains. This is possible by leveraging IoT in Industry 4.0 scenarios. In this paper, we describe the renovation process, guided by things2i s.r.l., a cross-disciplinary engineering-economic spin-off company of the University of Parma, which a real manufacturing industry is undergoing over consecutive phases spanning a few years. The first phase concerns the digitalization of the control quality process, specifically related to the company's production lines. The use of paper sheets containing different quality checks has been made smarter through the introduction of a digital, smart, and Web-based application, which is currently supporting operators and quality inspectors working on the supply chain through the use of smart devices. The second phase of the IIoT evolution—currently on-going—concerns both digitalization and optimization of the production planning activity, through an innovative Web-based planning tool. The changes introduced have led to significant advantages and improvement for the manufacturing company, in terms of: (i) impressive cost reduction; (ii) better products quality control; (iii) real-time detection and reaction to supply chain issues; (iv) significant reduction of the time spent in planning activity; and (v) resources employment optimization, thanks to the minimization of unproductive setup times on production lines. These two renovation phases represent a basis for possible future developments, such us the integration of sensor-based data on the operational status of production machines and the currently available warehouse supplies. In conclusion, the Industry 4.0-based on-going digitization process guided by things2i allows to continuously collect heterogeneous Human-to-Things (H2T) data, which can be used to optimize the partner manufacturing company as a whole entity

Toward Industry 4.0 With IoT: Optimizing Business Processes in an Evolving Manufacturing Factory

Research advances in the last decades have allowed the introduction of Internet of Things (IoT) concepts in several industrial application scenarios, leading to the so-called Industry 4.0 or Industrial IoT (IIoT). The Industry 4.0 has the ambition to revolutionize industry management and business processes, enhancing the productivity of manufacturing technologies through field data collection and analysis, thus creating real-time digital twins of industrial scenarios. Moreover, it is vital for companies to be as "smart" as possible and to adapt to the varying nature of the digital supply chains. This is possible by leveraging IoT in Industry 4.0 scenarios. In this paper, we describe the renovation process, guided by things2i s.r.l., a cross-disciplinary engineering-economic spin-off company of the University of Parma, which a real manufacturing industry is undergoing over consecutive phases spanning a few years. The first phase concerns the digitalization of the control quality process, specifically related to the company's production lines. The use of paper sheets containing different quality checks has been made smarter through the introduction of a digital, smart, and Web-based application, which is currently supporting operators and quality inspectors working on the supply chain through the use of smart devices. The second phase of the IIoT evolution - currently on-going - concerns both digitalization and optimization of the production planning activity, through an innovative Web-based planning tool. The changes introduced have led to significant advantages and improvement for the manufacturing company, in terms of: (i) impressive cost reduction; (ii) better products quality control; (iii) real-time detection and reaction to supply chain issues; (iv) significant reduction of the time spent in planning activity; and (v) resources employment optimization, thanks to the minimization of unproductive setup times on production lines. These two renovation phases represent a basis for possible future developments, such us the integration of sensor-based data on the operational status of production machines and the currently available warehouse supplies. In conclusion, the Industry 4.0-based on-going digitization process guided by things2i allows to continuously collect heterogeneous Human-to-Things (H2T) data, which can be used to optimize the partner manufacturing company as a whole entity

Two techniques for the preparation of cell-scaffold constructs suitable for sinus augmentation: steps into clinical application.

The objective of this clinical trial was the analysis of 2 methods for engineering of autologous bone grafts for maxillary sinus augmentation with secondary implant placement. Group 1 (8 patients, 12 sinuses): cells of mandibular periosteum were cultured in a good manufacturing practice laboratory (2 weeks) with autologous serum and then transferred onto a collagen matrix. After another week, these composites were transplanted into the sinuses. In group 2A (2 patients, 3 sinuses), cells of maxillary bone were cultivated with autologous serum for 2 weeks, seeded onto natural bone mineral (NBM, diameter [Ø] = 8 mm) blocks, and cultivated for another 1.5 months. These composites were transplanted into the sinuses. Group 2B (control, 3 patients, 5 sinuses) received NBM blocks alone. In the course of implant placement 6 (group 1) and 8 (group 2) months later, core biopsy were taken. Clinical follow-up period was 1 to 2.5 years in group 1 and approximately 7 years in groups 2A and 2B. New vital bone was found in all cases at median densities of 38\% (n = 12) in group 1, 32\% in group 2A (n = 3), and 25\% in group 2B (n = 5). Differences between group 1 and 2B as well as 2A and 2B were statistically significant ( p = 0.025). No adverse effects were seen. All methods described were capable of creating new bone tissue with sufficient stability for successful implant placement