Journal ArticleDOI

El Uso de Las Letras como Fuente de Errores de Estudiantes Universitarios en la Resolución de Tareas Algebraicas

01 Dec 2014-Bolema (Universidade Estadual Paulista / Pró-Reitoria de Pesquisa / Programa de Pós-Graduação em Educação Matemática)-Vol. 28, Iss: 50, pp 1545-1566
TL;DR: In this paper, a study with 194 students of the Centro Universitario de la Costa Sur in Autlan, Mexico, found that more than half of the students at this level of education do not show difficulties in evaluating letters, handling them as objects or considering their presence, however, it does reveal deficiencies in the discernment to understand the use and meaning of the letters as unknown of specific value, numbers, and variables such as widespread.
Abstract: The present investigation is a study with 194 students of the Centro Universitario de la Costa Sur in Autlan, Mexico. It aims to analyze the most common mistakes that first semester students show in the productions, to operate with different meanings that may have letters in algebra and, based on these results, establish its location within one of the four categories of understanding in the use and meaning of letters in algebra proposed by Kuchemann (1980). The results show that more than half of the students at this level of education do not show difficulties in evaluating letters, handling them as objects or considering their presence, however, it does reveal deficiencies in the discernment to understand the use and meaning of the letters as unknown of specific value, numbers, and variables such as widespread.

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Dissertation
03 Jul 2019
TL;DR: In el presente trabajo se propone contribuir en el fortalecimiento de los procesos relacionados con the generalización, uso de representaciones and el uso of the letra, asociados al pensamiento variacional, in estudiantes de grado 5° a partir del diseno y aplicacion of actividades de aprendizaje basadas en problemas.

5 citations

Cites background from "El Uso de Las Letras como Fuente de..."

• ...(citado en García et al., 2014, p.1550) Capítulo 2 51 2.2.6.2 Signo igual Diversos estudios5 muestran que las interpretaciones que hacen los estudiantes del signo “=” y de las ecuaciones pueden diferir de las que se pretende en la enseñanza....

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Journal ArticleDOI
TL;DR: In this paper, a trabajo focused on analysing, clasificar, and interpreting the errores algebraicos presenta un grupo de 38 matriculados en el curso Matematica General de la Universidad Nacional en Costa Rica.
Abstract: Este trabajo tiene como objetivo general analizar, clasificar e interpretar los errores algebraicos que presenta un grupo de 38 estudiantes matriculados en el curso Matematica General de la Universidad Nacional en Costa Rica, que se oferta a diversas carreras. En este estudio, que constituye una replica de investigacion, empleamos un cuestionario centrado en el uso de las letras con diferentes significados, desde etiquetas a variables. Se desarrollo desde el enfoque cuantitativo durante el periodo 2018-2019. Como resultado del analisis se ha detectado que los errores mas frecuentes en las respuestas de los items responden al uso de la letra como incognita de valor especifico, letra como numero generalizado o en el manejo de la letra como variable.

2 citations

Journal ArticleDOI
12 Jul 2021
TL;DR: In this article, the authors present a self-assessment of mathematics teachers' competencies, considering the socio-training approach, using the definition of Perrenoud, who refers to competence as the capacity to act effectively in a situation of a defined type, a capacity that is supported by knowledge.
Abstract: Evaluating competencies is not an easy task since they encompass knowledge, attitudes, and skills. The most realistic approach is through a self-assessment where the person who answers it is aware of its purpose. For the construction of this article, the definition of Perrenoud was considered, who refers to competence as the capacity to act effectively in a situation of a defined type, a capacity that is supported by knowledge. The purpose of this study was to design and validate a reliable and pertinent instrument that allows the self-assessment of mathematics teachers’ competencies, considering the socio-training approach. Content validation was carried out with a group of twelve expert judges, applying Aiken’s V and the degree of relevance with a pilot of twenty-eight participants, determined by Cronbach’s Alpha. As a result, adequate levels were reached with minimal observations and a reliable and relevant instrument was concluded.

1 citations

Journal ArticleDOI
30 Jun 2020
TL;DR: In this paper, the authors diagnose previous knowledge of the parabola in engineering freshmen at a university through the conceptual framework of Duval's semiotic representations, in order to develop a didactic proposal that improves their learning.
Abstract: The purpose of this work was to diagnose previous knowledge of the parabola in freshmen at a university through the conceptual framework of Duval's semiotic representations, in order to develop a didactic proposal that improves their learning. For this purpose, an instrument was designed to assess whether a student understands the main characteristics of the parabola in its various representations, as well as the ability to perform conversions between verbal, algebraic and graphic registers. It was applied to a sample of 55 engineering freshmen before receiving instruction on the topic. It was found that the most difficult treatment activities were the graphic and algebraic records, while in the Conversion activities the lowest performance was observed from the graphic to the algebraic and from the verbal to the graphic. On the other hand, the Treatment activities in the verbal register, and the conversions from the graphic to the verbal, from the algebraic to the graphic and from the verbal to the algebraic were found to be strengths. Therefore, students' prior knowledge of the parabola was diagnosed which will contribute to support a didactic proposal aimed at improving the learning of this topic.

1 citations

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Journal ArticleDOI
TL;DR: The authors found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names.
Abstract: Research studies have found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names The principal explanation given in the literature has been a general link to levels of cognitive development In this paper we present evidence for specific origins of misinterpretation that have been overlooked in the literature, and which may or may not be associated with cognitive level These origins are: intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in mathematics, and the effects of misleading teaching materials Recognition of these origins of misunderstanding is necessary for improving the teaching of algebra

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TL;DR: Evidence is presented that some common misinterpretations can be explained by considering factors more accessible than cognitive level to diagnosis and possible remediation, and that difficulties in learning to use algebraic notation have several origins.
Abstract: Research studies have found that the majority of students up to age 15 seem unable to interpret algebraic letters as generalised numbers or even as specific unknowns. Instead, they ignore the letters, replace them with numerical values, or regard them as shorthand names. The principal explanation given in the literature has been a general link to levels of cognitive development. In this paper we present evidence for specific origins of misinterpretation that have been overlooked in the literature, and which may or may not be associated with cognitive level. These origins are: intuitive assumptions and pragmatic reasoning about a new notation, analogies with familiar symbol systems, interference from new learning in mathematics, and the effects of misleading teaching materials. Recognition of these origins of misunderstanding is necessary for improving the teaching of algebra. The Concepts in Secondary Mathematics and Science (CSMS) research project (Hart, 1981) provided evidence linking students' levels of under- standing of algebraic letters to Piagetian stages of cognitive development and to IQ scores. It was concluded that most of the 13 to 15-year-olds tested were unable to cope with items that required interpreting letters as generalised numbers or even as specific unknowns. In the many years since the CSMS project, it has been widely accepted that cognitive level is a suf- ficient explanation for the way in which algebraic notation is interpreted. If cognitive level is viewed as a barrier to the construction of certain concepts, it explains why students cannot do certain algebraic tasks. However, it does not explain why they misinterpret the notation in different ways and why they make certain errors. In this paper we take this next step. We show that some common misinterpretations can be explained by considering factors more accessible than cognitive level to diagnosis and possible remediation. We present evidence that difficulties in learning to use algebraic notation have several origins, including:

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