Mathematical Competence Scale (MCS) for Primary School: The Psychometric Properties and the Validation of an Instrument to Enhance the Sustainability of Talents Development through the Numeracy Skills Assessment

Abstract

The adequate development of the numeracy skills is a target of the fourth of the Sustainable Development Goals and is considered the basis for a financial literacy: both are competences needed for successful social and professional inclusion. Building on these goals, we carried out a unidimensional Mathematical Competence Scale (MCS) for primary school. The aim of this study was to present the psychometric properties and the validation process of MCS, designed basing on Item Response Theory. The final version of the scale, which measures different domains of mathematical knowledge (Data Analysis and Relationships, Geometry, Dimensions and Measurements, Numbers and Calculations), was validated on the entire population of 2935 fourth graders in Ticino Canton, Switzerland. The results reveal the high level of correlation between the six mathematical dimensions and confirm the assumption of a latent “mathematical construct”. However, even the multidimensional model could be considered a good model because it fitted the data significantly better than the one-dimensional model. In particular, the differences of the deviance between the two models are significant (χ2 (20) = 642.66, p < 0.001). Moreover, findings show a significant gender effect and a positive correlation between students’ actual school performance during the same academic year and MCS scores. MCS allows a reading of the learning and teaching process in the perspective of the psychology of sustainability and sustainable development and helps a teacher to sustain student talent through the development of numeracy skills; in fact, the scale is intended both as an assessment tool and an innovative approach for shaping the development of curriculum, and therefore has potential to serve as a bridge between empirical research, classroom practice and a positive (school and professional) career development.