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.

Taking notes is a common strategy among higher education students, and has been found to affect their academic performance. Nowadays, however, the use of computers is replacing the traditional pencil-and-paper methodology. The present study aims to identify the advantages and disadvantages associated with the use of computer (typing) and pencil-and-paper (handwriting) for taking notes by college students. A total of 251 social and health science students participated in the study. Two experimental conditions were chosen: taking notes by hand (n=211), and taking notes by computer (n=40). Those that used computer-written notes performed better on tasks based on reproducing the alphabet, writing sentences, and recognizing words (p<.05). However, those using handwritten notes performed better on free recall tasks (p<.05). Differences between the two conditions were statistically significant rejecting the hypothesis of equality between groups (X2=60.98; p<.0001). In addition, the discriminant analysis confirmed that 77.3% of students were correctly classified by the experimental conditions. Although the computer allowed for greater velocity when taking notes, handwriting enhanced students’ grades when performing memory tasks. La toma de apuntes es una estrategia generalizada del alumnado de Educación Superior y se ha constatado su influencia en el rendimiento académico. El uso del ordenador está desplazando al método tradicional de lápiz y papel. El presente estudio pretende arrojar luz sobre las ventajas y los inconvenientes derivados del uso de uno u otro método en la toma de apuntes en las aulas universitarias. Un total de 251 estudiantes universitarios de ciencias sociales y ciencias de la salud participaron en el estudio. Se plantearon dos condiciones experimentales: toma de notas de forma manual (n=211) y de manera electrónica (n=40). Se hallaron diferencias a favor del grupo que usó el ordenador en las tareas basadas en completar el abecedario, escribir frases y reconocer palabras anotadas previamente (p<.05). Sin embargo, en la tarea de recuerdo libre los resultados reflejaron un mejor desempeño del grupo que tomó notas manualmente (p<.05). Se rechazó la hipótesis de igualdad entre los grupos (X2=60,98; p<.0001). Además, el análisis discriminante confirmó que el 77,3% de los alumnos fueron clasificados correctamente según su condición experimental. El uso del ordenador resultó muy útil cuando se trataba de anotar datos con rapidez; sin embargo, en las tareas de recuerdo los alumnos de escritura manual obtuvieron mejores puntuaciones que los de escritura electrónica.

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.

The main goal of this study was to analyse, using structural equation modeling, the contribution of predictors of both domain-general (working memory, processing speed and receptive vocabulary) and domain-specific (estimation and magnitude comparison) processes to informal mathematical performance (numbering, comparison, calculation and understanding of concepts) in preschoolers. A total of 158 preschool students (ages ranging from 52 to 64 months) participated in the investigation. Students were assessed with informal tasks measuring mathematical thinking, numerical estimation, symbolic and non-symbolic comparison-making, coding, receptive vocabulary, and backward digit span. Results showed that a structural equation model for multiple indicators and several factors could explain informal mathematical thinking capacity in young children. The model reduced specific-domain factor effects such as magnitude comparison. In conclusion, the effect of working memory was found to be less than the straight impact of the general-domain predictors considered in the study.

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