MEANING EQUIVALENCE: A METHODOLOGICAL TOOL FOR ASSESSING DEEP UNDERSTANDING
MERLO (Meaning Equivalence Reusable Learning Objects) is a methodological tool originally developed by U. Shafrir and M. Etkind (Ekind, Kenett, Shafrir, 2010). MERLO items (Arzarello, Kenett, Robutti, Shafrir, to be submitted) are structured activities with supporting pedagogical issues, covering appropriate concepts within a discipline through multi-semiotic representations in multiple sign systems. Each item includes five different statement representations that can share or not share the same meaning.
MERLO is an adaptable tool quite different from traditional ones, which can be employed for different disciplines and purposes, both for enhancing teaching and learning the discipline using a new methodology. For example, MERLO has been implemented by Masha Etkind in teaching architecture as an assessment tool to evaluate students’ deep understanding of concepts. It has also been recently adopted in mathematics education (Arzarello et al., 2015a; 2015b) in an international project, which involves researchers in Canada, Israel, Italy, and Australia. MERLO items can be used in teaching, as a methodological tool to organise activities for discussing mathematical concepts through multi-semiotics representations. Of course they can also be an important tool for learning with students engaged in individual or group activities, aiming at enhancing deep understanding. The trigger point is that these items are made of different representations (graphical, verbal, symbolic, or numeric) among which the students have to recognise which share a common meaning of a concept. The innovation in MERLO consists in directly challenging students in discovering relations among different representations, and not in stating if they are true or false, as in traditional items.
This proposal aims to present: the design of MERLO items in mathematics education; their use as tool for group activities stimulating discussions and argumentations; their use as formative assessment tool in education, aiming at the evaluation of deep understanding of concepts; insights in research provided by MERLO creation processes; the transversal potentiality of MERLO pedagogy and methodology, applicable in every discipline.
 Arzarello, F., Kenett, R. S., Robutti, O., Shafrir, U. (to be submitted). The application of concept science to the training of teachers of quantitative literacy and statistical concepts.
 Arzarello, F., Kenett. R.S., Robutti, O., Shafrir, U., Prodromou, T., Carante, P. (2015a). Teaching and Assessing with New Methodological Tools (MERLO): a New Pedagogy? 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.
 Etkind, M., Kenett, R.S., Shafrir, U. (2010). The evidence based management of learning: diagnosis and development of conceptual thinking with meaning equivalence reusable learning objects (MERLO). In 8th International Conference on Teaching Statistics (ICOTS). Ljubjana, Slovenia.