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

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.

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

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The Verbal Component of Mathematical Problem Solving in Bilingual Contexts by Early Elementary Schoolers

“…At the same time, the student must create a model of the problem situation, that is, the mental representation that will later allow him to move onto the next decision-making stage. This can be seen in those constructivist intervention processes in which the child creates and invents his own problem-solving strategies [43].…”

Ethiopian Early Grade Mathematics Curriculum Organization

“…In learning progression responsive curriculum, it is expected that the sequence of contents be appropriate for students' developmental stage, age, and grade level. In addition, contents in a given curriculum is said to be appropriate if it is presented by considering the sense; from simple to complex, spiral, whole to part, children experience and real life condition, and order of events (Bermejo, Ester, & Morales, 2021;Sáez et al, 2013). The findings from this study indicated that the presentation of contents in early grade mathematics curriculum lacked appropriateness in relation to these lucidities.…”