Collectives of humans-with-media in mathematics education: notebooks, blackboards, calculators, computers and … notebooks throughout 100 years of ICMI

The main aim of this study was to present evidence of the ways in which different media have conditioned and dramatically reorganized education, in general, and mathematics education, in particular. After an introduction of the theme, we discuss the epistemological perspective that provides the foundation for our analysis: the notion of humans-with-media. Then, we briefly illustrate how the medium is related to the scientific production of mathematical knowledge. We take a detour into the world of art to examine how devices and instruments have historically been associated with the production of mathematical knowledge. Then, we review studies on the history of education to show how traditional media were introduced into schools and have influenced education. In particular, we examine how devices such as blackboards and notebooks, which were novelties a 100 years ago, came to be accepted in schools and the mathematical activities that were promoted with their use. Finally, we discuss how information technology has changed education and how the Internet may have an impact on mathematics education comparable to that of the notebook over a century ago.

[2]  Celia Hoyles,et al.  Windows on Mathematical Meanings: Learning Cultures and Computers , 1996 .

[3]  F. R. Watson,et al.  The Influence of Computers and Informatics on Mathematics and Its Teaching , 1986 .

[4]  Kenneth Ruthven.  Mathematical technologies as a vehicle for intuition and experiment: a foundational theme of the ICMI, and a continuing preoccupation , 2008 .

[5]  Marcelo de Carvalho Borba,et al.  Humans-with-Media and the Reorganization of Mathematical Thinking: Information and Communication Technologies, Modeling, Visualization and Experimentation , 2006 .

[6]  A. G. Howson,et al.  The Influence of Computers and Informatics on Mathematics and its Teaching: Foreword , 1986 .

[7]  Keith Devlin,et al.  The logical structure of computer-aided mathematical reasoning , 1997 .

[8]  Anthony Ralston,et al.  The Influence of Computers and Informatics on Mathematics and Its Teaching. Science and Technology Education Series, 44. , 1986 .

[9]  Jean Hébrard.  Por uma Bibliografia Material das Escritas Ordinárias: o espaço gráfico do caderno escolar (França – Séculos XIX e XX) , 2012 .

[10]  Silvina Gvirtz.  El discurso escolar a través de los cuadernos de clase : Argentina 1930-1970 , 1996 .

[11]  Amy Ackerberg-Hastings,et al.  Tools of American mathematics teaching, 1800-2000 , 2008 .

[12]  H. O. Pollak.  Mathematics as a Service Subject: Mathematics as a service subject – Why? , 1988 .

[13]  J. P. Kahane,et al.  The Popularization of Mathematics: Frontmatter , 1990 .

[14]  Lucien Febvre,et al.  L' Apparition Du Livre , 1958 .

[15]  The International Commission on Mathematical Instruction , 1995 .

[16]  Donald W. Stover.  A Student's Construction. , 1973 .

[17]  Michael H. Price,et al.  Squared paper in the nineteenth century: Instrument of science and engineering, and symbol of reform in mathematical education , 1980 .

[18]  R. Brun.  Lucien FEBVRE et Henri-Jean MARTIN. L 'apparition du livre. Paris, Albin Michel, 1958. (Bibliothèque de synthèse historique. L'Évolution de l'humanité, n° 49.) , 1958 .

[19]  O. Skovsmose.  Humans-with-media and the reorganization of mathematical thinking , 2005 .

[20]  Sal Restivo,et al.  Theory of Mind, Social Science, and Mathematical Practice , 2007, Perspectives On Mathematical Practices.

[21]  Carolyn Kieran,et al.  Research Issues in the Learning and Teaching of Algebra , 1989 .

[22]  Olga de Sá,et al.  O futuro do pensamento na era da Informática , 2010 .

[23]  Daniel Bell.  New identifications in Raphael's School of Athens , 1995 .

[24]  Luciano Meira,et al.  Making Sense of Instructional Devices: The Emergence of Transparency in Mathematical Activity. , 1998 .

[25]  A. G. Howson.  Developments in mathematical education : proceedings of the second International Congress on Mathematical Education , 1973 .

[26]  Vinicio Villani,et al.  Perspectives on the teaching of geometry for the 21st century : an ICMI study , 1998 .

[27]  Paul Keys,et al.  OR as technology revisited , 1998, J. Oper. Res. Soc..

[28]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[29]  Jere Confrey,et al.  A student's construction of transformations of functions in a multiple representational environment , 1996 .

[30]  Renato Kraide Soffner,et al.  As tecnologias da inteligencia e a educação como desenvolvimento do potencial humano , 2005 .

[31]  Celia Hoyles,et al.  Windows on Mathematical Meanings , 1996 .