Abstract
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.
Highlights
The emergence of research papers on the teaching-learning of mathematics is increasingly noticeable
It implies that our students learn in a meaningful way, building their own knowledge to permit them directly apply what they have learned in their daily life, and always starting from their previous knowledge
The idea that we propose in the PEIM is that the teacher, through individual interviews, can define the student’s mathematical profile in order to find out what developmental stage the student is at, what informal knowledge has been acquired and what type of proposals will allow the learner to progress adequately according to his rate of development
Summary
The emergence of research papers on the teaching-learning of mathematics is increasingly noticeable. Research results are frequently a long way from the classroom reality. In other words, it seems that research and educational practice are walking along different paths, and as a result, bridges should be built between the university and the school (Bermejo, 2018). Improving mathematical competence does not imply making faster calculations, or obtaining a better resolution in activities only when they are presented to students more or less regularly Instead, it implies that our students learn in a meaningful way, building their own knowledge to permit them directly apply what they have learned in their daily life, and always starting from their previous knowledge
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