Secondary School Students’ Errors in the Translation of Algebraic Statements

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

doi:10.1007/s10763-016-9739-5

Cited by 27 publications

(29 citation statements)

References 16 publications

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“…Despite of the importance given to algebraic symbolism internationally, many authors stress the limited mastery students' show of this representation system and question the comprehension that students develop (e.g., Fernández-Millán & Molina, 2016;Kieran, 2007). Many studies show frequent and persistent errors made by secondary and even university students when using algebraic symbolism (e.g., Booth, 1982;Cerdán, 2010;Kirshner, 1989;MacGregor & Stacey, 1993;Molina, Rodríguez-Domingo, Cañadas, & Castro, 2017;Ruano, procedural or conceptual (Star, 2005). Our approach attends to the conceptual component of knowledge of algebraic symbolism.…”

Section: Introductionmentioning

confidence: 99%

“…The translation from the symbolic to the verbal representation system has been paid less attention in previous studies (Molina, et al, 2017) and Molina et al (2006) have observed that it causes fewer difficulties to secondary students than the opposite translation. They suggest using this greater facility as a means to support (a) the development of students' understanding of algebraic symbolism and (b) the improvement of problemsolving skills.…”

Section: Introductionmentioning

confidence: 99%

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Meanings given to algebraic symbolism in problem-posing

2018

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Meanings given to algebraic symbolism in problem-posing

2018

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“…The studies suggest emphasizing the brackets while teaching operations to elementary level students (Hoch & Dreyfus, 2004;Marchini & Papadopoulos, 2011). However, it is important to note the understanding of the structural sense of algebraic expressions by focusing on quantitative relationships as operations and representations symbolically by using the same and different letters in order to prevent students" errors and improve conceptual understanding (Molina, Rodríguez-Domingo, Cañadas, & Castro, 2017). In the planning process, the teachers also stated common misconceptions which the students could have based on their previous experiences, such as the students" thinking of 4x as a two-digit number, and the teachers encountered these misconceptions which Seng (2010) identified.…”

Section: What Do Teachers Know and What Other Knowledge Types Do Theymentioning

confidence: 99%

“…Eda started by connecting the properties of arithmetical operations, which was one of the commonly suggested approaches for connecting arithmetic with algebra (Banerjee & Subramaniam, 2012;Livneh & Linchevski, 2007;Subramaniam & Banerjee, 2004). Molina et al (2017) also pointed out that the lack of understanding of the relationships in arithmetic expressions can cause errors in structuring algebraic expressions. Next, Eda emphasized the like term concept using different colored unit cubes to take the students deeper into addition and subtraction, as Filloy and Sutherland (1996) suggested.…”

Section: What Do Teachers Know and What Other Knowledge Types Do Theymentioning

confidence: 99%

Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Yıldız¹,

Akyüz²

2019

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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Teachers use their content and pedagogical content knowledge for teaching algebra. For this reason, the examination of how teachers use this knowledge may help shed light on how students learn algebra, especially in determining why they usually have difficulties. The aim of the current study is to reveal what teachers know, and propose what they actually need to know for teaching the simplification and equivalence of algebraic expressions. The multiple-case study design was used for this study to compare and contrast the two middle school teachers" lesson planning and instruction. The data corpus included lesson plans, actual instruction records, and post-observation interviews. Data analysis was conducted using the Mathematical Knowledge for Teaching (MKT) model. The findings indicated that both teachers had a lack of specialized content knowledge about mathematical representations such as algebra tiles. They did not use algebra tiles effectively and could not link algebraic and geometric representations that underlie the idea of multiplication. It was observed that both teachers generally used unknowns and variables interchangeably indicating the inadequacy of their common content knowledge. In the planning process, the two teachers were able to state the common misconceptions that the students generally had and the ways of addressing them. Through the cases of these two teachers, it was observed that teachers need to have a good conceptual mathematical understanding and also knowledge of students" thinking in order to design effective lessons. Based on the findings, the types of knowledge that the teachers need to have are outlined and the theoretical and practical implications of the study are discussed.

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“…Llama la atención la cantidad de investigaciones que abordan el estudio del conocimiento de las ecuaciones por parte de estudiantes de secundaria y de las dificultades que se ponen de manifiesto cuando los estudiantes trabajan con ellas. Algunas de estas dificultades se refieren a características del simbolismo algebraico que se emplea en las ecuaciones (e.g., Álvarez y Gómez-Chacón, 2015; Arnau y Puig, 2013; Fernández-Millán y Molina, 2016Molina, Rodríguez-Domingo, Cañadas y Castro, 2017;Resnick, Marmeche y Mathieu, 1987), y otras al concepto ecuación visto como un todo (Capraro y Joffrion, 2006;Filloy y Rojano, 1989).…”

Section: Pna 12(3)unclassified

Ejemplos y definiciones de ecuaciones: una ventana hacia el conocimiento conceptual de estudiantes de secundaria

Millán

Molina

2018

pna

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estudiantes para indagar en el conocimiento conceptual implícito y explícito del concepto ecuación que han adquirido en la Educación Secundaria. Los estudiantes mostraron facilidad para generar ejemplos de ecuaciones y determinar diferencias entre ellos, dando evidencias de su conocimiento conceptual implícito. En cuanto al explícito, manifestaron dificultades para definir el concepto ecuación. Generar ejemplos les ayudó a identificar elementos comunes, generalizar y expresar verbalmente, aunque con ciertas limitaciones, lo que para ellos es una ecuación. Palabras clave: Conocimiento conceptual; Definiciones; Ecuación; Generación de ejemplos Examples and Definitions of Equations: A Window to the Conceptual Knowledge of Secondary Students In this study, we use the generation of examples and the definition of concepts by students to study their implicit and explicit conceptual knowledge of the concept of equation acquired in secondary education. Students showed facility to generate examples of equations and to determine differences between them, giving evidences of their implicit conceptual knowledge. As for the explicit knowledge, they evidenced difficulties in defining the concept of equation. Generating examples helped them to identify common elements, to generalize and to express verbally, although with some limitations, what an equation is for them.

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Secondary School Students’ Errors in the Translation of Algebraic Statements

Cited by 27 publications

References 16 publications

Meanings given to algebraic symbolism in problem-posing

Meanings given to algebraic symbolism in problem-posing

Examining Two Middle School Mathematics Teachers’ Knowledge for Teaching Manipulation of Algebraic Expressions during Lesson Planning and Instruction

Ejemplos y definiciones de ecuaciones: una ventana hacia el conocimiento conceptual de estudiantes de secundaria

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