Dipartimento di Matematica "Giuseppe Peano"

Descrizione del progetto

Altri collaboratori

T. Prodromou (Univ. of New England)

G. Aldon (ENS Lyon)

U. Shafrir (Toronto Univ. )

Insegnanti ricercatori: Susanna Abbati, Alberto Cena, Arianna Coviello, Santina Fratti, Luigia Genoni, Germana Trinchero, Fiorenza Turiano. 

MERLO (Meaning Equivalence Reusable Learning Objects) is a didactical and methodological tool developed and tested by Uri Shafrir and Masha Etkind (Shafrir & Ekind, 2010). MERLO (Arzarello, Kenett, Robutti, Shafrir, to be submitted; Etkind, Kenett, Shafrir, 2010) is a database that involves an organized collection of MERLO activities covering appropriate concepts within a discipline, through multi-semiotic representations in multiple sign systems. Each element of the database is a structured MERLO activity that includes one target statement TS and four other statements linked to the target statement because they:

- share or do not share meaning equivalence with the target statement,

- share or do not share surface similarity with the target statement.

The term meaning equivalence designates a commonality of meaning across several representations. The term surface similarity means that representations “look similar”.

Based on these two categorization criteria, it is possible to create four types of statements, called Q1, Q2, Q3, Q4, depending on the fact that they share or not share equivalence of meaning and/or surface similarity with the target statement.

MERLO is a very adaptable tool that can be used for subjects. For example, MERLO is used by Masha Etkind in architecture as an assessment tool to assess students’ deep understanding of concepts. MERLO was also used in mathematics education by Arzarello et al. (2015b) who applied the MERLO in mathematics tertiary education.

The project is a fall out of a Teach-Mob course given by Ron Kenett at Master Course in Mathematics in 2014-2015.

The aim of the project is the application of the MERLO approach in teachers’ education programs, the analysis of teachers’ processes while elaborating MERLO items for their classrooms and the analysis of students’ answers to such items.  A first study has been developed in 2013-2015 with the participants to the Master “Formatori in Didattica della Matematica” in the Department (Arzarello et al., 2015a, 2015b).

The study will be developed in Italy and in Australia, in collaboration with prof. Theodosia Prodromu (School of Education, University of New England, Armidale, NSW 2351, Australia)

 with in-service teachers of Mathematics who work in Secondary/Senior Secondary schools and pre-service teachers who study B.Sc (Year 2, 3) or M.Sc in Education.

The research work will be developed jointly by teachers of secondary schools and researchers, elaborating MERLO items and testing them in the schools. Specifically, the researchers will analyse the way teachers become involved in the MERLO philosophy and in the way they are able to include it in their teaching practices and the way students of secondary schools answer to the MERLO items.

We will use the Meta-Didactical Transposition model (Arzarello et al., 2014; Aldon et al., 2013) to analyse teachers’ professional development in terms of a dynamic point of view. This study will provide us with opportunities to observing the initial praxeologies of the two groups and how they evolve over time, giving birth to new shared praxeologies.

Risultati e pubblicazioni

Shafrir, U., & Etkind, M. (2010). Concept Science: Content and Structure of Labeled Patterns in Human Experience. Version 31.0.

Aldon, G., Arzarello, F., Cusi, A., Garuti, R., Martignone, F., Robutti, O., Sabena, C., & Souvy-Lavergne, S. (2013). The Meta-Didactical Transposition: A model for analysing teachers’ education programmes. In A.M. Lindmeier & A. Heinze (Eds.), Proceedings of  37th Conerence. of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 97-124). Kiel, Germany: PME.

Arzarello, F., Cusi, A., Garuti, R., Malara, N., Martignone, F., Robutti, O., & Sabena, C. (2014). Meta-Didactical Transposition: A theoretical model for teacher education programmes. In A. Clark-Wilson, O. Robutti & N. Sinclair (Eds.), The Mathematics Teacher in the Digital Era: An International Perspective on Technology Focused Professional Development (pp. 347-372). Dordrecht: Springer.

Arzarello, F., Kenett. R.S., Robutti, O., Shafrir, U., Prodromou, T., Carante, P. (2015a). Teaching and Assessing with New Methodological Tools (MERLO): a New Paradigm? In M.A. Hersh & M. Kotecha (Eds.), Proceedings of the IMA International Conference on Barriers and Enablers to Learning Maths: Enhancing Learning and Teaching for All Learners, pp. 1-8. Glasgow, Scotland, June, 10 -12.

Arzarello, F., Robutti, O., & Carante, P. (2015b). A new tool and a new challenge in mathematics teaching and learning. In Beswick, K., Muir, T., & Wells, J. (Eds.). Proceedings of 39th Psychology of Mathematics Education conference, Vol. 2, pp. 57-64. Hobart, Australia: PME.

Susanna Abbati, Paola Carante, Alberto Cena, Arianna Coviello, Santina Fratti, Luigia Genoni, Germana Trinchero, Fiorenza Turiano (2015c). MERLO Meaning Equivalence Reusable Learning Object. Atti del XIX Convegno GRIMED “Il laboratorio è la buona didattica per tutti”. Lucca, 10-12 aprile 2015

Ferdinando Arzarello, Ron S. Kenett, Ornella Robutti, Paola Carante, Susanna Abbati, Alberto Cena, Arianna Coviello, Santina Fratti, Luigia Genoni, Germana Trinchero, Fiorenza Turiano (2015d). Teaching and learning with MERLO: a new challenge for teachers and an opportunity for students. Proceedings of CIEAEM67 Aosta, Italy. 20-24 July 2015 (to appear).

F. Arzarello, O. Robutti, S. Abbati, P. Carante, A. Cena, A. Coviello, S. Fratti, L. Genoni, G. Trinchero, F. Turiano (2015 e). MERLO: Meaning Equivalence Reusable Learning Object. PROPOSTA INVIATA E ACCETTATA a: XX Congresso U.M.I. Siena, 7–12 settembre 2015