## Abstract

The objective of this paper is to study students’ difficulties when they have to ascribe the same meaning to different representations of the same mathematical object. We address two theoretical tools that are at the core of Radford’s cultural semiotic and Godino’s onto-semiotic approaches: objectification and the semiotic function. The analysis of a teaching experiment involving high school students working on the tangent, shows how students’ difficulties in ascribing sense to different representations of a common mathematical object can be traced back to the kind of objectification processes and semiotic functions they are able to establish.

## Keywords

Mathematical objects Semiotics Meaning Activity Objectification Semiotic function## Notes

### Acknowledgments

I wish to thank the three anonymous reviewers as well as Norma Presmeg for their valuable and insightful comments on a previous version of this paper. A special thank to Bruno D’Amore for everything I have learned from him during his supervision of my Ph.D thesis, both at personal and scientific level. I would like to thank him also for his important contributions and revisions of this paper. I also would like to thank Raymond Duval, Juan Godino, and Luis Radford for the fruitful discussions, the thorough explanations, and their infinite kindness and generosity during my visits in Lille, Granada, and Sudbury. Last but not least, I wish to thank the teacher, Carmen Tabellini, and her students of the Liceo “E. Fermi”, Bologna, for their kind hospitality and their committed collaboration during the experiment.

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