Solución estratégica a problemas matemáticos verbales de una operación. El caso de la multiplicación y la división

Alejandra García Alcalá, Jonathan Vázquez Maldonado
y Luis Zarzosa Escobedo

Abstract: Mathematical word problems are a common school practice for teaching meaningful mathematics. Based on a direct teaching strategy approach, the purpose of this study was to expand the external validity of the Xin, Wiles and Lin (2008) model for solving math word problems. Two boys and one girl about 9 years old, 4th graders struggling with mathematics, were instructed. The math problems were multiplication and division in the form of sentences. The students were taught to answer strategic questions and to use an algebraicoutline so that they could detect the common structure of the math problemsand solve them. The three students had great improvement from the pretest to posttest and two of them learned to solve division problems with fewer attempts.The significance, practical use and transfer to new problems are discussed.

Keywords: strategies; teaching; elementary school; basic math operations.


Estudio sobre el proceso de conceptualización de la función exponencial

Patricia Sureda y María Rita Otero

Abstract: This paper describes the process of conceptualization of four groups of pupils in high school (121 students around the age of 15-16 years), and the way they study the conceptual field of exponential functions with a dynamic of study, in which the first aim is the participation of the pupil in the construction of knowledge. The theoretical constructs proposed by Vergnaud’s Conceptual Fields Theory (1990, 1996, 2007a, 2007b, 2011) are specially used to describe the answers of some pupils when a problem that is solved through means of exponential models is proposed. The analysis of the protocols shows a process of conceptualization, linked to the different systems of representation of the exponential function, which is possible to describe by five stages.

Keywords: concept, systems of representation, exponential function, teaching, secondary.