How the Language of Instruction Influences Mathematical Thinking Development in the First Years of Bilingual Schoolers.

The present research study focuses on how the language of instruction has an impact on the mathematical thinking development as a consequence of using a language of instruction different from the students' mother tongue. In CLIL (Content and Language Integrated Learning) academic content and a foreign language are leant at the same time, a methodology that is widely used in the schools in the present times. It is, therefore, our main aim to study if the language of instruction in second language immersion programs influences the development of the first formal mathematical concepts. More specifically, if the learning of mathematical concepts in the early ages develops in a similar way if it is taught in the students' mother tongue and is not influenced by the language used for teaching. Or else, if it can influence the development of the first skills only in the students' general performance or in certain areas. The results of both the analysis of variance and multiple regression confirm how influencing the language of instruction is when mathematical thinking is developed teaching formal contents in a non-coincidence language. The second language is affecting the resolution of daily life problems, being more competent those students in 1st grades whose language of instruction matched with their mother tongue.

A Constructivist Intervention Program for the Improvement of Mathematical Performance Based on Empiric Developmental Results (PEIM).

Teaching mathematics and improving mathematics competence are pending subjects within our educational system. The PEIM (Programa Evolutivo Instruccional para Matemáticas), a constructivist intervention program for the improvement of mathematical performance, affects the different agents involved in math learning, guaranteeing a significant improvement in students' performance. The program is based on the following pillars: (a) students become the main agents of their learning by constructing their own knowledge; (b) the teacher must be the guide to facilitate and guarantee such a construction by being a great connoisseur of the fundamental aspects of the development of the child's mathematical thinking; (c) the mathematical contents must be sequenced in terms of the complexity and significance for the student as well as contextualized at all times; and (d) the classroom must have a constructivist climate highlighting cooperative work among students. The implementation of PEIM along with the empirical evaluation conducted in several centers in Madrid and Zaragoza (Spain) confirm how students improve their mathematical competence. Both first- and second-grade students in elementary education were far more effective in solving problems, highlighting the use of more advanced strategies in their resolution and a lower incidence of conceptual errors. Moreover, it was possible to verify how the students proving greater difficulty, experienced an evolution in learning similarly to those who did not present it. The program provides customized education to allow the teacher to know at all times how he should be more influential on the students' learning through mathematical profiles. Both teaching practice and teachers were observed, being that of the experimental group more prone to analyzing processes and allowing the construction of knowledge by students, due to their psycho-developmental training. As a result, we found several improvements through the implementation of the program that may serve, for upcoming years, as a basis for the necessary changes in the teaching of mathematics.

The degree of abstraction in solving addition and subtraction problems.

In this study, the incidence of the degree of abstraction in solving addition and subtraction problems with the unknown in the first term and in the result is analyzed. Ninety-six students from first grade to fourth grade in Primary Education (24 students per grade) solved arithmetic problems with objects, drawings, algorithms, and verbal problems. The participants were interviewed individually and all sessions were video-taped. The results indicate a different developmental pattern in achievement for each school grade depending on the levels of abstraction. The influence of the level of abstraction was significant, especially in first graders, and even more so in second graders, that is, at the developmental stage in which they start to learn these arithmetic tasks. Direct modeling strategies are observed more frequently at the concrete and pictorial level, counting strategies occur at all levels of abstraction, whereas numerical fact strategies are found at higher levels of abstraction.

The degree of abstraction in solving addition and subtraction problems

In this study, the incidence of the degree of abstraction in solving addition and subtraction problems with the unknown in the first term and in the result is analyzed. Ninety-six students from first grade to fourth grade in Primary Education (24 students per grade) solved arithmetic problems with objects, drawings, algorithms, and verbal problems. The participants were interviewed individually and all sessions were video-taped. The results indicate a different developmental pattern in achievement for each school grade depending on the levels of abstraction. The influence of the level of abstraction was significant, especially in first graders, and even more so in second graders, that is, at the developmental stage in which they start to learn these arithmetic tasks. Direct modeling strategies are observed more frequently at the concrete and pictorial level, counting strategies occur at all levels of abstraction, whereas numerical fact strategies are found at higher levels of abstraction (AU)

En este estudio se analiza la incidencia del grado de abstracción en la resolución de problemas de suma y resta con la incógnita en el primer término y en el resultado. Noventa y seis alumnos de primero a cuarto curso de Educación Primaria (24 escolares por curso) resuelven tareas aritméticas con objetos, dibujos, algoritmos y verbales. Los participantes se entrevistaron de manera individual y se registraron en vídeo todas las sesiones. Los resultados indican un patrón evolutivo diferente en el rendimiento para cada curso escolar según los niveles de abstracción.Resulta significativa la influencia del nivel de abstracción sobre todo en primero y más aún en segundo curso, es decir, en el momento evolutivo en que se inicia el aprendizaje de estas tareas aritméticas. Las estrategias modelado directo se manifiestan más en el nivel concreto y pictórico, las estrategias conteo ocurren en todos los niveles de abstracción, mientras que las estrategias hechos numéricos se encuentran en los niveles de mayor abstracción (AU)

Microgénesis y cambio cognitivo: adquisición del cardinal numérico / Microgenesis and cognitive change: cardinality acquisition

En el presente estudio se pretende caracterizar el análisis microgenético y evaluar su eficiencia como instrumento para estudiar el cambio cognitivo e intervenir en el desarrollo. Numerosas investigaciones confirman la eficacia de este procedimiento. Así ocurre, por ejemplo, en el siguiente trabajo de intervención sobre la adquisición del cardinal numérico. Los grupos experimental y control pasaron sendos pretest y postests. El grupo experimental siguió además un programa de aprendizaje específico. Los resultados muestran la existencia de diferencias significativas entre los dos grupos, de modo que la mayoría de los participantes del grupo experimental pasó del nivel cuarto al nivel seis en escasos días, cuando normalmente los niños requieren varios meses para llegar a este nivel evolutivo

This study pretends to characterise the microgenetic analysis and assess it efficiency for studying cognitive change and intervening in development. The effectiveness of this procedure has been confirmed by many researches. That is shown, for instance, in an intervention study about the acquisition of cardinality. The pretest and post-tests were administered to the control and experimental groups. The experimental group completed a specific learning program. Results show significant differences between the groups, so that the experimental group went from the forth level to the sixth level in a few days, when children in regular conditions require many months to attain this developmental level