# Fulvia FuringhettiUniversità degli Studi di Genova | UNIGE · Dipartimento di Matematica (DIMA)

Fulvia Furinghetti

Professor

## About

207

Publications

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## Publications

Publications (207)

People have studied, learned and used mathematics for over four thousand years. Decisions on what is to be taught in schools,
and how, are ultimately political, influenced by a number of factors including the experience of teachers, expectations of
parents and employers, and the social context of debates about the curriculum. The ICMI study is posi...

The history of mathematics education is an interdisciplinary research area
that is experiencing a significant development and this book presents recent
work in this area. This book is the result of the seventh conference
ICHME (International Conference on the History of Mathematics Education)
that took place at Erbacher Hof, Mainz (Germany) from 19...

In this chapter, we first describe the Italian context when the proposals of reforms, generically indicated under the label of “new math” or “modern mathematics,” were developed all around the world. The current mathematics programs dated to 1945, the main topic was geometry, taught according to a rooted tradition based on Euclid. The conference of...

After a succinct description of the meeting opportunities for mathematics educators up to the 1950s, this chapter describes how, in the wake of the New Math/modern mathematics reform movement, meetings have become a fundamental tool for focusing on problems and potential of reform proposals. Bodies that have played the most relevant roles are ICMI,...

This Timeline is intended to point out the most significant moments in the history of
ICMI"– former CIEM/IMUK"– and to show how the activities of the Commission
broadened and differentiated during the second half of the twentieth century, in
order to provide a useful chronological framework for the chapters and the biographical profiles that make u...

The purpose of this volume is to understand and outline the evolution of the objectives and field of action of the International Commission on Mathematical Instruction (ICMI) from its creation in 1908 in Rome until 2008, through an analysis of the main events and protagonists of its history. It consists of three parts, each exploring different face...

This chapter contains the list of the participants in the first International Congress on Mathematical Education (ICME-1) held in Lyon from 24 to 30 August 1969.KeywordsParticipants in ICME-1

This Timeline is intended to point out the most significant moments in the history of ICMI – former CIEM/IMUK – and to show how the activities of the Commission broadened and differentiated during the second half of the twentieth century, in order to provide a useful chronological framework for the chapters and the biographical profiles that make u...

This chapter aims at giving an overview of the activities related to mathematics education presented during the International Congresses of Mathematicians (ICMs) from 1897 to 2006. Before mathematics education developed as a full-fledged academic discipline with its specific conferences and journals, the opportunities for international meetings in...

This chapter contains the biographical portraits of the 54 members of the Central/Executive Committee of ICMI who passed away in the first 100 years of ICMI.Each of these portraits consists of a section of general biographical information and a section containing contributions to education and dissemination of mathematical culture. In the same vein...

This chapter contains the biographical portraits of the scholars awarded the title of Honorary Member of the Commission on the occasion of the International Congress of Mathematicians in Oslo (1936) and the portrait of Charles-Ange Laisant, one of the founders of L’Enseignement Mathématique, the official organ of ICMI. Among the scholars awarded in...

This chapter lists the officers and the members of the Central Committees of CIEM (Commission Internationale de l’Enseignement Mathématique), IMUK (Internationale Mathematische Unterrichts-Kommission), and of the Executive Committees of ICMI (International Commission on Mathematical Instruction).KeywordsCIEMIMUKICMICentral CommitteeExecutive Commit...

This chapter analyses the evolution of ICMI after its establishment in 1952 as a subcommission of the International Mathematical Union (IMU). The changes in society and research, and movements such as New Math, made evident the need for new paradigms for approaching the problems of mathematical instruction. The collaboration with international bodi...

The history of mathematics education is an interdisciplinary research area that is experiencing a significant development and this book presents recent work in this area. This book is the result of the seventh conference ICHME (International Conference on the History of Mathematics Education) that took place at Erbacher Hof, Mainz (Germany) from 19...

In this paper, we describe an experiment in using history to work on problem-solving and the relationship between arithmetic and algebra. The students involved attended the first year of the Italian upper secondary school (grade 9). The original sources we used are problems from Italian treatises on arithmetic and algebra that appeared in the Middl...

The book entitled Connecting Mathematics and Mathematics Education. Collected Papers on Mathematics Education as a Design Science is based on works of Erich Wittmann and his colleagues. The unifying elements of the book are on the one hand the underlying idea expressed by the author of a systematic rethinking of the gradual development of the desig...

Short biography and Contributions to mathematics education of Paul Henri Cartan

Short biography and Contributions to mathematics education of Ram Behari

Short biography and Contributions to mathematics education of Gino Loria

Short biography and Contributions to mathematics education of Shōkichi Iyanaga

Short biography and Contributions to mathematics education of Yukiyosi Kawada

This contribution is a short description of the experimentations carried out in the Italian upper secondary school on developing didactic units based on real situation.

This preface is a short presentation of the Conference and the the themes of research developed in the various activities,

At present there are some opportunities for innovation: rapid development in technology over the last few years has offered a concrete stimulus for the modification of both teaching methods and content.
In this belief we are working at a project consisting of a gradual introduction of Computer Science into the Mathematics course for students at the...

The years after WWII up to the late 1960s were crucial in the evolution of ICMI (International Commission on Mathematical Instruction) for both the settlement of some institutional aspects (mainly concerning the relationship with mathematicians) and the establishment of new trends of the activities. By referring to unpublished documents, this paper...

The history of mathematics education is an interdisciplinary research area that is experiencing a significant development and this book presents recent work in this area. The relation to the history of mathematics is of prime importance since the history of mathematics and the history of mathematics education have very much in common. For the early...

Emma Castelnuovo was an Italian mathematician known for her contributions to mathematics education. Biography The International Commission on Mathematical Instruction (ICMI) has decided in the past to create two awards to recognize outstanding achievements in mathematics education research: the Felix Klein Award, honouring a lifetime achievement, a...

This text is the transcription of the registration of the plenary talk delivered in the Seminar addressed to teachers entitled “Matematica? No problem”. it treats the difficulties of students and the image of mathematics held by students, some suggestions for teacher sto overcome the students difficulties.

NOTE: "THE PRIVATE FULL TEXT IS NOT THE FULL TEXT OF THE PROCEEDINGS, IT IS JUST A PRESENTATION OF THE PROCEEDINGS CONTAINING THE COVER, THE COLOPHON, THE TABLE OF CONTENTS, THE INTRODUCTION BY THE EDITORS, THE SHORT ABSTRACTS OF ALL THE CHAPTERS, AND THE INFORMATION ON HOW BUY THE BOOK FROM THE PUBLISHER."
ABSTRACT:
The history of mathematics educ...

Alcuni insegnanti del Gruppo ricerca educazione matematica di Genova (Ivana Chiarugi, Anna Cuttica, Silvia Focardi, Graziana Gazzolo) hanno elaborato un questionario destinato ai colleghi insegnanti di matematica nel biennio e nel triennio della scuola secondaria superiore; esso è stato poi ulteriormente revisionato e distribuito a cura dell’IRRSAE...

The various chapters concern the innovation of mathematics programs and mathematics teaching in Italy

the article is published in the journal Epsilon. It is a short presentation of some famous women mathematicians

Since long-time mathematics educators have shown interest in the use of history of mathematics in mathematics teaching. In many countries, curricula mention the need of introducing a historical dimension in mathematics teaching. This article discusses some interesting reasons put forwards by the supporters of this use and their epistemological assu...

Sommario. In questo articolo espongo alcune mie riflessioni sulla storia dell'insegnamento della matematica ispirate dalla lettura dei due libri di Paolo Linati: Maestri di matematica. Anna Zofia Krygowska-Hans Freudenthal-Arthur Engel-Henry O. Pollak. Teorie e problemi. L'algoritmo delle occasioni perdute. La matematica nella scuola della seconda...

Intervista all'Iprase (Istituto Provinciale per la Ricerca e la Sperimentazione Educative) pubblicata nel sito https://www.iprase.tn.it nel 2002 in occasione della presentazione (2002, 17 aprile) del libro: Furinghetti, F. (2002). Matematica come processo socioculturale. Trento: Studi e ricerche IPRASE Trentino. (Accesso 19 gennaio 2003)

Among all the mathematical journals of the nineteenth century L’Enseignement Mathématique plays a particular role. It was founded in 1899 by Charles-Ange Laisant and Henri Fehr and is still published today. To understand why its role is so interesting I analyse the first years of its life, in which it made a strong contribution to the birth of an i...

This paper deals with two aspects of Luigi Campedelli’s activity in the mathematical community at the end of the second world war. As a mathematician interested in didactic themes and as a President of the CIIM (Italian commission for the teaching of mathematics) he dealt with the problem of refreshing Italian mathematics teaching in the light of t...

In this report we describe how a team of five teachers have realized a longitudinal evaluation of students aged from 14 to 19 in order to analyse the evolution of their abilities and the causes affecting it. The need for this activity arises from the observation of the gap between the remarkable amount of synergism employed by the teachers and the...

The years after WWII up to the late 1960s were crucial in the evolution of ICMI (International Commission on Mathematical Instruction) for both the settlement of some institutional aspects (mainly concerning the relationship with mathematicians) and the establishment of new trends of the activities. By referring to unpublished documents, this paper...

To celebrate the centennial of the foundation of ICMI, an international symposium was held in Rome from 5 to 8 March 2008. As it did a hundred years ago, Palazzo Corsini, home of the Accademia Nazionale dei Lincei, provided the splendid venue for the congress. The final session was held in Palazzo Mattei di Paganica, home of the Enciclopedia Italia...

On the occasion of the Queen’s birthday in 2019, Peter Howard Ransom has been appointed a Member of the Order of the British Empire (MBE). This is an acknowledgment for HPM community and, in general, of mathematics educators. As a matter of fact, the motivation for the appointment is “For voluntary service to Mathematics Education.”
The present not...

This book contains the Proceedings of the Fifth International Conference on the History of Mathematics EducationSeptember 19-22, 2017, at Utrecht University, the Netherlands

Two facts mark the emerging of the new status of mathematics education as a scientific discipline: the inauguration in 1969 of the tradition of International Congresses on Mathematical Education (ICMEs), and the contemporary launch of journals related to mathematics education research. The early ICMEs acted as catalysts for new ideas that have thei...

Two facts mark the emerging of the new status of mathematics education as a scientific discipline: the inauguration in 1969 of the tradition of International Congresses on Mathematical Education (ICMEs), and the contemporary launch of journals related to mathematics education research. The early ICMEs acted as catalysts for new ideas that have thei...

The International Commission on the Teaching of Mathematics can be considered the parent of the International Commission on Mathematical Instruction (ICMI). This chapter describes the activities and major ideas of this Commission from its foundation in 1908 through the First World War. A brief account of the events in the community of mathematician...

Mi sembra che in epoche e contesti diversi sia sempre stata sentita la necessità di avvicinare la matematica a una qualche forma di ‘senso comune’ da parte di chi doveva insegnarla, quasi a giustificare l’esistenza di questa disciplina come materia d’insegnamento. In questa nota si presentano alcuni esempi (presi prevalentemente da testi del passat...

Before the establishment of the tradition of ICMEs in 1969, the community of mathematics educators had very few occasions to meet on an international level. Practically this was happening only during the quadrennial International Congresses of Mathematicians, in the section reserved for education (often together with other subjects such as history...

For a long time, mathematics educators have shown interest in the use of history of mathematics in mathematics teaching. This article discusses some interesting reasons put forwards by the supporters of this use and their epistemological assumptions. The initial part of the article provides a short account of the setting in which the first discussi...

We can see maths teaching at the ages 14-16 as a passage between two different levels of learning: on the one hand a completion of the first stage, and on the other hand a gradual passage to the successive stages of formalization and application.
The aim of this paper is to analyse the way in which teachers face some of the problems related to this...

The article illustrates the underlying philosophy of an in progress book in which pictures taken from historical books are used to hint some fundamental ideas of the history of mathematics. Both epistemological and disciplinary issues are taken into account. The aim of the book is to let its potential readers know different aspects of mathematics a...

Instead of offering an overview of the different domains where the pedagogical use of the history of mathematics is now ramified, we want, in this chapter, to focus on something that Cajori initiated many years ago. That is, seeing history not only as a window from which to draw a better knowledge of the nature of mathematics but as a means of tran...

This work examines the major directions of research in the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The history of mathematics education is viewed here as a part of social history, but possessing its own distinctive features. A sur...

This chapter examines the first non-ephemeral journal on teaching mathematics and sciences in primary school, which appeared at the beginning of the twentieth century in Italy. The project of publishing such a kind of journal is set in the context of the initiatives launched in the new Italian nation for creating a course of studies specifically ad...

This book offers insights into the history of mathematics education, covering both the current state of the art of research and the methodology of the field. History of mathematics education is treated in the book as a part of social history. This book grew out of the presentations delivered at the International Congress on Mathematics Education in...

The Fourth International Conference on the History of Mathematics Education was hosted by Academy of Sciences and University of Turin (Italy) from 23 to 26 September 2015. About 50 senior and junior researchers from 16 countries met for four days to talk about one topic: the history of mathematics education. In total 44 contributions were presented...

The Topic Study Group on the history of the teaching and learning of mathematics was formed in 2004 at ICME-10. Its work reflects the growing interest in the history of mathematics education. At ICME-13 in Hamburg, this TSG had more participants than in previous years, but the procedure at the main meetings followed established tradition -- short r...

This work examines the major directions of research in the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The history of mathematics education is viewed here as a part of social history, but possessing its own distinctive features. A sur...

HPM is one of the affiliate groups of ICMI — the International Commission on Mathematical Instruction. HPM 2016 is a satellite meeting of the corresponding ICME International Congress on Mathematical Education (ICME) organized by ICMI.
The quadrennial satellite meetings are a major activity of HPM. They bring together individuals with a keen intere...

The celebration of the Centennial of the International Commission on Mathematical Instruction offered the occasion to look back at the history of ICMI and outline the evolution of mathematics education until it achieved its present status as an academic discipline. The years after WWII up to the late 1960s were crucial in this evolution for both th...

This work examines the main directions of research conducted on the history of mathematics education. It devotes substantial attention to research methodologies and the connections between this field and other scholarly fields. The results of a survey about academic literature on this subject are accompanied by a discussion of what has yet to be do...

History of mathematics teaching and learning is a subject that concerns two domains of research and may generate fruitful synergies between them. In 2000, during the International Symposium celebrating the centenary of the first international journal on mathematics teaching (L’Enseignement Mathématique), the interplay between the present educationa...

From 25 to 28 September 2013 the third International Conference on the History of Mathematics Education (ICHME-3) was held at the Department of Education, Uppsala University, Sweden. The Scientific Program Committee was composed by Kristín Bjarnadóttir (University of Iceland), Fulvia Furinghetti (University of Genoa, Italy), Johan Prytz (Uppsala Un...

In this paper we present the main lines of a course on the history of
mathematics for prospective secondary school (students' age range 14-19) mathematics teachers, enrolled on a 2-year postgraduate teacher preparation program. In order to integrate the historical objectives with the educational objectives of the program we adopted the following st...

Emma Castelnuovo (1913–2014) was an Italian mathematics teacher of grades 6 to 8 in secondary school. During the crucial period of the 1950s and 1960s, when important reforms were proposed, she was involved in significant events such as the first CIEAEM meetings and the Royaumont Seminar. She was an active contributor to the development of internat...

According to some researchers one of the ways of using history in mathematics teaching is the hermeneutic approach. In this paper we report on a classroom experiment where the teacher (A. D.) tried to apply this procedure in teaching the topic “exponential and logarithms” to 18-19 year-old students attending the final year of an Italian high school...

This chapter outlines the evolution of international cooperation in mathematics education from its beginning in the nineteenth century, when an international perspective entered the world view, until the post-Second World War origin of the present structured network of activities aimed at mutually helping people. Cooperation is treated by following...

This chapter takes a historical view of the development of mathematics education, from its initial status as a business mostly managed by mathematicians to the birth of mathematics education as a scientific field of research. Starting from the acknowledgement that research in mathematics education demands more than the traditional focus on discussi...

Since longtime mathematics educators have shown interest in the use of history of mathematics in mathematics teaching. In many countries curricula mention the need of introducing a historical dimension in mathematics teaching. This chapter discusses some interesting reasons put forwards by the supporters of this use and their epistemological assump...

In their Introduction to the Proceedings of the first Conference on On-going Research in the History of Mathematics Education, held 20 to 24 June 2009 in Garðabær (Iceland), the editors expressed their conviction, given the variety of themes, the number of countries involved and the presence of experienced scholars alongside with young researchers,...

This paper traces the evolution of the profession of mathematics teacher in Italy during the transition of the country from a cluster of small, individual states to a single, unified nation. Our focus will be on the plans carried out for teacher training in the period from 1810, when the Scuola Normale Superiore in Pisa was created to train prospec...

The Special Issue of ZDM is an opportunity for the guest editors to organize a volume which will be particularly revealing also for the broader community of mathematics educators. The starting point for the issue was not to review the state of the art for some specific countries, nor to aspire to some completeness either chronologically or geograph...

Following the already established tradition of research in history of mathematics
education, the International Program Committee of ICME-12 included in the scientific
program a TSG 35 entitled “The history of the teaching and learning of mathematics”. The chapters reports on the activities of TSG35 and related activities.

This article first analyses and compares mathematicians’ and mathematics educators’ different conceptualisations of proof and shows how these are formed by different professional backgrounds and research interests. This diversity of views makes it difficult to precisely explain what a proof is, especially to a novice at proving. In the second secti...

This paper reports on a research project concerning the difficulties met by undergraduate students in mathematics during the first year of university. Our aim is to provide elements for studying the transition from secondary to tertiary level as perceived by the students who live it. The combination of different analytical tools (questionnaires, in...

This article relates to a project that has been developed in various classrooms of secondary school. The main assumptions inspiring this project are the following: students’ motivations to learn Mathematics are enhanced if they develop an image of Mathematics that encompasses the ‘social sense of Mathematics’ (that is they see Mathematics as a huma...

In this paper, we report on a study aimed at describing the way secondary school teachers treat proof and at understanding
which factors may influence such a treatment. This study is part of a wider project on proof carried out for many years. In
our theoretical framework, we combine references from research on proof with those from research on tea...

This article deals with the activity of example generation as a special case of problem solving. We asked university students in the scientific-technological area to produce examples (which may exist or not) of mathematical objects fulfilling given requirements. For the analysis of students’ performances, we have developed a model that attempts to...

In this paper we consider beliefs that intervene during the process of proving. At the beginning we reflect on the relationship between beliefs and knowledge. After we outline some examples that show how the process of proving carried out by students may be shaped by their beliefs. In particular, we see that the concept of leading beliefs that we u...

On the occasion of the ICMI centenary the authors of the present paper built the website “The First Century of the International Commission on Mathematical Instruction (1908-2008). History of ICMI,”(http://www.icmihistory.unito.it/) which contains information and documents about people, events, and bodies intervening in the first century of this Co...

The article illustrates the underlying philosophy of an in progress book in which pictures taken from historical books are used to hint some fundamental ideas of the history of mathematics. Both epistemological and disciplinary issues are taken into account. The aim of the book is to let its potential readers know different aspects of mathematics a...

Research into the history of teaching and learning mathematics began to develop into a genuine disciplinary area when mathematics education had transformed into an internationally scientific discipline, from the 1970s. Since mathematics education investigates a broad range of issues and cooperates with neighbouring disciplines, it is able to give c...

In this note I outline some elements of the history of mathematics education in Italy. Initially the chief characters were mathematicians who played a role in designing curricula and in editing textbooks. The development of the Italian community of mathematics educators towards the present day trend in research was fostered by participation in inte...

In this article, I consider the history of the International Commission on Mathematical Instruction (ICMI) from its inception
until the International Congress on Mathematical Education (ICME) held in 1969. In this period, mathematics education developed
as a scientific discipline. My aim is to study the presence and the contribution of women (if an...

It is widely recognized that purely cognitive behavior is extremely rare in performing mathematical activity: other factors,
such as the affective ones, play a crucial role. In light of this observation, we present a reflection on the presence of
affective and cognitive factors in the process of proving. Proof is considered as a special case of pro...

In this article I single out some events and chief characters of the first hundred years of ICMI that fostered the emergence of mathematics education as an academic discipline. This new discipline did not spring out of the blue: Its roots are in the environment of the ICMI (International Commission on Mathematical Instruction) and of the community...