Rupture or continuity: The arithmetico-algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment

Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés

doi:10.1007/s10649-016-9717-4

Cited by 20 publications

(8 citation statements)

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“…Today, a change of paradigm purports that cognitive difficulties can be overcome (by a majority of students) with appropriate teaching. The discussion is one of a continuum rather than a rupture (Hitt, Saboya, and Cortés, 2017a). In this new paradigm, three types of approaches have emerged:…”

Section: Local Theoretical Framework and First Elements Of Arithmetic...mentioning

confidence: 99%

“…Step 3: studies of the concepts of variable and covariation between variables and of the generalization (in the transition from primary to secondary levels) related to arithmetic-algebraic thinking among 6th grade elementary students with learning difficulties in Mexico (11-12 year-old pupils, K6) (Hitt, Saboya & Cortés, 2017a, 2017bSaboya, Hitt, Quiroz & Antoun, 2019). Páez's (2004) doctoral thesis worked on teacher training with a teaching method based on collaborative learning, scientific debate, self-reflection, and the process of institutionalization (ACODESA) (see Hitt, 2007).…”

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confidence: 99%

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Educação: Saberes em Movimento, Saberes que Movimentam III

Cardoso¹

2023

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O terceiro volume da Educação: Saberes em Movimento, Saberes que Movimentam, publicado pela Editora Artemis, convoca a inovação enquanto denominador comum. Uma inovação em torno de diversos cenários digitais, que hoje, mais do que nunca, populam os nossos quotidianos, em diferentes níveis de ensino. Mas também uma inovação em torno de competências de literacia ditas básicas, tradicionais, como a leitura e a escrita, todas inerentes ao direito universal à educação e à aprendizagem ao longo da vida, desígnios que a UNESCO nos estimula a concretizar, dia após dia. Celebrar o dia internacional da educação, assinalado precisamente há um mês, é ir ao encontro desta inovação – curricular, pedagógica, tecnológica – que permita contribuir para atender às necessidades dos nossos alunos, estudantes, professores, formandos, enfim, numa palavra, dos educadores em todo o mundo. Uma inovação contextualizada, holística e transformadora, que permita contribuir para assegurar, aos indivíduos e aos coletivos, o desempenho consciente de um papel ativo, crítico e interventivo na sociedade. Nos Saberes em Movimento, Saberes que Movimentam aqui reunidos, há ainda espaço e tempo para recordar que a Educação mudou significativamente, em alguns pontos do globo, mais do que noutros, durante a COVID-19. Esta pandemia, a par de outras situações atuais de grande adversidade, continua a provocar mudanças com impacte no nosso presente e futuro. Importa, pois, (re)imaginar direções positivas para a educação1; importa, portanto, (re)imaginar os nossos futuros em conjunto2. E que os Saberes plasmados nestes capítulos possam ser o ponto de partida para (re)iniciar esta conversa, tão essencial quanto vital3! Teresa Cardoso

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Section: Local Theoretical Framework and First Elements Of Arithmetic...mentioning

confidence: 99%

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confidence: 99%

Educação: Saberes em Movimento, Saberes que Movimentam III

Cardoso¹

2023

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“…In addition, children are seldom placed in situations that lead to debate [9], to the analysis of expressions, to generalization or to the search for different solutions. To these causes, we should add the fact that classrooms, especially in the Spanish context, have neither concrete or well-structured manipulative resources to support verbalization and reasoning, nor a process of translating the experience to symbolic language [10].…”

Section: Introductionmentioning

confidence: 99%

“…This paper aims to develop and illustrate a didactic proposal, implemented in a classroom of first year of primary education, that develops algebraic thinking through an arithmetic that transcends the mere knowledge of numbers and operations to pay attention to a deep understanding of the number system, relationships and mathematical structures. In other words, this proposal addresses the development of number sense by considering "an arithmetic-algebraic thinking, a new approach which underpins the construction of a cognitive structure that links both types of thinking" [9]. The proposal is based on the use of manipulative materials, rigorously structured, that act both as numerical and arithmetic supports; and the activities are presented as problematic situations to promote the reasoning and analysis.…”

Section: Introductionmentioning

confidence: 99%

Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

et al. 2021

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Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

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“…El objeto de estudio en la investigación fue la fase de validación de una conjetura geométrica, con el propósito de analizar el proceso de construcción y reformulación de justificaciones elaboradas por estudiantes al trabajar en un entorno sociocultural propiciado por el método de enseñanza de ACO-DESA: aprendizaje colaborativo, debate científico y autorreflexión (Hitt y González-Martín, 2015;Hitt, Saboya y Cortés, 2017)in progress since 2005, related to modelling mathematical situations in Qu\u00e9bec secondary schools (grades 8 and 9. Por lo tanto, nuestro objetivo fue analizar las formas de justificar de los estudiantes y determinar cómo evolucionan durante el desarrollo de una actividad organizada con ACODESA, en la cual se les solicita justificar matemáticamente.…”

Section: Introductionunclassified

Desarrollo y cambios en las maneras de justificar matemáticamente de estudiantes cuando trabajan en un ambiente sociocultural

Rubilar

Badillo

2019

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RESUMEN • En este artículo reportamos cómo se promovió un acercamiento desde la fase preformal hacia la fase formal en la manera de justificar de estudiantes. Se implementó una actividad diseñada bajo los principios del método de enseñanza de aprendizaje colaborativo, debate científico y autorreflexión (ACODESA), con el fin de generar un ambiente sociocultural en la clase de matemáticas y así promover las interacciones sociales entre los estudiantes. Exponemos el caso de un alumno que cambió su manera de justificar tras intercambiar ideas y discutir con sus pares durante el análisis de las justificaciones construidas por cada uno de ellos. PALABRAS CLAVE: Demostración; Justificación; Proceso de validación matemática; Niveles y tipos de prueba; ACODESA. ABSTRACT • In this article we report how an approach was promoted from the pre-formal to the formal stage regarding the students' way of justifying mathematical reasoning. We implemented an activity based on the ACODESA teaching method to create a sociocultural environment in the mathematics class and to promote social interactions between the students. We present the case of a learner who changed his way of justifying after exchanging ideas and discussing with peers during the analysis of the justifications generated by each of them.

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Rupture or continuity: The arithmetico-algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment

Cited by 20 publications

References 17 publications

Educação: Saberes em Movimento, Saberes que Movimentam III

Educação: Saberes em Movimento, Saberes que Movimentam III

Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Desarrollo y cambios en las maneras de justificar matemáticamente de estudiantes cuando trabajan en un ambiente sociocultural

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