Thematic Working Group 1

Role of Metaphors and Images in Learning and Teaching Mathematics

Bernard Parzysz

IUFM Orléans-Tours & DIDIREM (université Paris-7), France

Christer Bergsten

Linköpings Universitet, Sweden

José Manuel Matos

Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal

Angela Pesci

Dipartimento di Matematica, Università di Pavia, Italy


Twenty-five researchers (which appeared a suitable number) participated in our group, and 12 papers were discussed. In order to make the discussion easier and more efficient, we first decided to organize 4 sessions of 3 papers, each session being devoted to a particular theme, namely:

For people not familiar with the field, it may perhaps be of some use to begin with some words about embodied cognition and metaphors. The notion of ‘embodied cognition’ has been developed by Lakoff & Nuñez from two main ideas :

Concerning ‘conceptual metaphors’, Lakoff & Nuñez distinguish three main types (Ferrara):

— grounding metaphors

— linking metaphors

— redefining metaphors


But within our group the word ‘metaphor’ was used in a broad sense, which embraced notions such as:

We can take ‘metaphor’ to mean the transfer of a ‘sign’ or a set of ‘signs’ which are proper to one domain (source) to another domain (target) (Potari et al.). In fact, metaphorical language is a ‘natural’ way of speaking about things. Examples :




During the sessions, several questions posed by current research were discussed :

And, since metaphors cannot match all the properties of the source with those of the target :


Finally, we left CERME 3 with some ideas for future research, and more especially the need for comparative studies which might identify different practices in various areas (problem solving, calculation, graphical representations, geometry…) through:

N.B.: An e-mail list (or web-site) for ´ Metaphors ª (opened to all) will be created for:



List of contributions

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