Jose Navarro

This study tested a structural model of cognitive-emotional explanatory variables to explain performance in mathematics. The predictor variables assessed were related to students’ level of development of early mathematical competencies (EMCs), specifically, relational and numerical competencies, predisposition toward mathematics, and the level of logical intelligence in a population of primary school Chilean students (n = 634). This longitudinal study also included the academic performance of the students during a period of four years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test (ENT), and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence (TILE). The results of these tests were used to analyse the interaction of all the aforementioned variables by means of a structural equations model. This combined interaction model was able to predict 64.3% of the variability of observed performance. Preschool students' performance in EMCs was a strong predictor for achievement in mathematics for students between 8 to 11 years of age. Therefore, this paper highlights the importance of EMCs and the modulating role of predisposition toward mathematics. Also, this paper discusses the educational role of these findings, as well as possible ways to improve negative predispositions toward mathematical tasks in the school domain.

Educational interventions are necessary to develop mathematical competence at early ages and prevent widespread mathematics learning failure in the education system as indicated by the results of European reports. Numerous studies agree that domain-specific predictors related to mathematics are symbolic and non-symbolic magnitude comparison, as well as, number line estimation. The goal of this study was to design 4 digital learning app games to train specific cognitive bases of mathematical learning in order to create resources and promote the use of these technologies in the educational community and to promote effective scientific transfer and increase the research visibility. This study involved 193 preschoolers aged 57–79 months. A quasi-experimental design was carried out with 3 groups created after scores were obtained in a standardised mathematical competence assessment test, i.e., low-performance group, high-performance group, and control group. The results show that training with the 4 digital learning app games focusing on magnitude, subitizing, number facts, and estimation tasks improved the numerical skills of the experimental groups, compared to the control group. The implications of the study were, on the one hand, provided verified technological tools for teaching early mathematical competence. On the other hand, this study supports other studies on the importance of cognitive precursors in mathematics performance.

Despite both thinkers belonging to the tragic generation of 1914, Ludwig Wittgenstein (1888-1951) and José Ortega y Gasset (1883-1955) never actually met in their lives or in their texts (neither those they wrote nor those they read). Coming from very separate philosophical traditions -- the logical atomism of Wittgenstein and the neo-Kantianism and phenomenology of Ortega -- the works of these two philosophers nevertheless show latent conceptual affinities. We shall limit ourselves to suggesting three possible conceptual keys: limit, context and belief. We shall then finally take Wittgenstein"s distinction between sagen and zeigen in the light of the difference Ortega highlights between talking and saying, reflecting upon the limits of language and the meaning each thinker gives to silence