Socio-Economic and Cultural Context in the Development of Early Mathematical Competencies: A Comparative Study of Specific Educational Contexts in Chile and Spain.

This research presents the findings of a comparative study of mathematical competence among 130 students (M = 54.08 months; SD = 2.57) from vulnerable school contexts in Chile and the Spanish public school system. The study analyses a set of general and specific domain precursors for which evidence of socioeconomic background exists. Using multivariate regression and discriminant analysis techniques, we calculated similarities and differences between groups by comparing these precursors. Significant differences were found between the Spanish and Chilean groups (p < .05); however, no differences were observed in non-symbolic comparison and receptive vocabulary. Possible reasons for the existence and extent of these differences are discussed in terms of socio-cultural and educational contexts.

The Open Algorithm Based on Numbers (ABN) Method: An Effective Instructional Approach to Domain-Specific Precursors of Arithmetic Development.

This article presents the results of a comparative study regarding the impact and contribution of two instructional approaches to formal and informal mathematical reasoning with two groups of Spanish students, aged four and five. Data indicated that for both age groups, children under the ABN method [Open Algorithm Based on Numbers (ABN)] (n = 147) achieved better results than the group under the CBC approach (Closed Algorithms Based on Ciphers) (n = 82), which is the widespread approach in Spanish schools to teach formal and informal mathematical reasoning. Furthermore, the comparative analyses showed that the effect is higher in the group of students who received more instruction on skills considered domain-specific predictors of later arithmetic performance. Statistically significant differences were found in 9 of the 10 dimensions evaluated by TEMA-3 (p < 0.01), as well as on estimation tasks in the number-line for the 5-year-old-group. However, the 4-year-old group only presented significant results in calculation and concepts tasks about informal mathematical reasoning. We discuss that these differences arise by differential exposure to specific number-sense tasks, since the groups proved to be equivalent in terms of receptive vocabulary, processing speed, and working memory. The educational consequences of these results were also analyzed.

Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school.

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 4 years as a variable. The sampled students were initially assessed by means of an Early Numeracy Test, and, subsequently, they were administered a Likert-type scale to measure their predisposition toward mathematics (EPMAT) and a basic test of logical intelligence. 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 and 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.