Revistas Educational Studies in Mathematics

Descripción

Some errors in the learning of algebra suggest students have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing in order to analyze the students’ capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process depending on the characteristics of the algebraic statements given. We designed a written questionnaire composed of eight closed algebraic statements expressed symbolically, which was administered to 55 students who had finished their compulsory education and that had some previous experience in problem posing. In our analysis of the data, we examine both syntactic and semantic structures of the problem posed. We note that in most cases students posed problems with syntactic structures different to those given. They did not include computations within variables, and changed the kinds of relationships connecting variables. Students easily posed problems for statements with additive structures. Other differences in the type of problems posed depend on the characteristics of the given statements.

Lista de autores

Cañadas, María C., Molina, Marta y Del-Rio, Aurora

Fecha

2018

Autores

Descripción

In the context of early algebra research and as part of a classroom teaching experiment (CTE), we investigated fourth grade (9- to 10-year-old) students’ justifications of how they performed tasks involving the functional relationship y = 2x. We related their written justifications (part of the task) to the task characteristics, which included various semiotic systems (verbal, numerical and alphanumeric, among others) and the demand of different type of justifications. The role of classroom discussion in helping express the functional relationship orally in more sophisticated terms was also investigated. The findings showed that students’ written justifications changed with the semiotic system involved in the task. Oral discussion helped students generalize in more sophisticated terms than in their written justifications, in which they omitted information or used less precise language.

Lista de autores

Ayala-Altamirano, Cristina y Molina, Marta

Fecha

2021

Autores

Descripción

This paper describes the difficulties faced by a group of middle school students (13- to 15-year-olds) attempting to translate algebraic statements written in verbal language into symbolic language and vice-versa. The data used were drawn from their replies to a written quiz and semi-structured interviews. In the former students were confronted with a series of algebraic statements and asked to choose the sole translation, of four proposed for each, that was semantically congruent with the original. The results show that most of the errors detected were due to arithmetic issues, especially around the distinction between product and exponent or sum and product in connection with the notions of perimeter and area. As a rule, the error distribution by type varied depending on the type of task involved.

Lista de autores

Castro, Encarnación, Cañadas, María C., Molina, Marta y Rodríguez-Domingo, Susana

Fecha

2022

Autores

Descripción

Proving an existence theorem is less intuitive than proving other theorems. This article presents a semiotic analysis of significant fragments of classroom meaning-making which took place during the class-session in which the existence of the midpoint of a linesegment was proven. The purpose of the analysis is twofold. First follow the evolution of students’ conceptualization when constructing a geometric object that has to satisfy two conditions to guarantee its existence within the Euclidean geometric system. An object must be created satisfying one condition that should lead to the fulfillment of the other. Since the construction is not intuitive it generates a dilemma as to which condition can be validly assigned initially. Usually, the students’ spontaneous procedure is to force the conditions on a randomly chosen object. Thus, the second goal is to highlight the need for the teacher’s mediation so the students understand the strategy to prove existence theorems. In the analysis, we use a model of conceptualization and interpretation based on the Peircean triadic SIGN.

Lista de autores

Samper, Carmen, Perry, Patricia, Camargo-Uribe, Leonor, Sáenz-Ludlow, Adalira y Molina, Óscar

Fecha

2016

Autores