Pensamiento numérico-algebraico avanzado: construyendo el concepto de covariación como preludio al concepto de función.
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| Title: | Pensamiento numérico-algebraico avanzado: construyendo el concepto de covariación como preludio al concepto de función. |
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| Authors: | Hitt, Fernando1 hitt.fernando@uqam.ca, Morasse, Christian2 morasse.christian@gmail.com |
| Source: | Electronic Journal of Research in Educational Psychology. 2009, Vol. 7 Issue 1, p243-260. 18p. 1 Diagram, 2 Charts. |
| Subject Terms: | *Problem solving, *Collaborative learning, *Primary education, Algebra problems & exercises, Functional representation, Mathematical models, Introspection |
| Abstract (English): | Introduction. In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We offer a detailed critique of a research group who promote the movement of introducing algebra in primary school ("Early Algebra"). Method. In this collaborative research, we show how to promote advanced numericalalgebraic thinking through experimentation with certain activities (problem situations) in two groups of secondary students (grade 9), with 24 and 36 students, respectively. We use a specific methodology for collaborative learning, scientific debate and self-reflection (ACODESA methodology). Results. The pupils in this study constructed covariational reasoning as a prelude to the function concept. They also developed control elements that helped them in the process of solving problem situations. Discussion. Numerical reasoning is essential to giving meaning to the syntactic processes that, if manipulated or conceived of incurrectly, can lead to an error in a given situation. Advanced numerical-algebraic thinking helps us develop sensitivity to contradiction, enabling us to detect error. We believe that working with manipulative materials and producing functional representations that can evolve into institutional ones, and using collaborative learning with scientific debate and self-reflective reasoning (ACODESA methodology), can help pupils to more easily retain their mathematical concepts over time. [ABSTRACT FROM AUTHOR] |
| Abstract (Spanish): | Introducción. En este documento enfatizamos la importancia de desarrollar en los niños un pensamiento numérico-algebraico avanzado, que pueda proporcionar un elemento de control en los procesos de resolución de situaciones matemáticas. Se analizan concepciones de algunos alumnos que los induce a cometer errores en álgebra, por una falta de control por no recibir apoyo de su pensamiento numérico. Hacemos una crítica puntual a un grupo de investigación que se identifica con el movimiento acerca de la introducción del álgebra en la escuela primaria ("Early Algebra"). Método. En esta investigación, en colaboración, mostramos que es factible promover un pensamiento numérico-algebraico avanzado, en una experimentación de actividades (situaciones problema) con dos grupos de secundaria (grado 9), respectivamente con 24 y 36 alumnos, utilizando una metodología específica sobre aprendizaje en colaboración, debate científico y auto-reflexión (metodología ACODESA). Resultados. Los alumnos en este estudio, lograron construir el concepto de covariación como preludio al concepto de función, y desarrollar elementos de control que les sirvió en la resolución de las situaciones problema propuestas en esta experimentación. Conclusiones. El pensamiento numérico es esencial para proporcionar a los alumnos significados sobre sus procesos sintácticos que, por una mala manipulación o por una concepción, en una situación dada, puede guiarlos a error. El pensamiento numérico-algebraico avanzado, nos ayuda en el desarrollo de una sensibilidad a la contradicción para detectar el error. El trabajo con materiales, un aprendizaje colaborativo, debate científico y auto-reflexión (metodología ACODESA) permite una construcción más sólida de los conceptos matemáticos y posiblemente proporcionará una mayor retención de esos conceptos a largo plazo. [ABSTRACT FROM AUTHOR] |
| Copyright of Electronic Journal of Research in Educational Psychology is the property of Editorial of the University of Almeria (Spain) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 117083721 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Pensamiento numérico-algebraico avanzado: construyendo el concepto de covariación como preludio al concepto de función. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hitt%2C+Fernando%22">Hitt, Fernando</searchLink><relatesTo>1</relatesTo><i> hitt.fernando@uqam.ca</i><br /><searchLink fieldCode="AR" term="%22Morasse%2C+Christian%22">Morasse, Christian</searchLink><relatesTo>2</relatesTo><i> morasse.christian@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Electronic+Journal+of+Research+in+Educational+Psychology%22">Electronic Journal of Research in Educational Psychology</searchLink>. 2009, Vol. 7 Issue 1, p243-260. 18p. 1 Diagram, 2 Charts. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Problem+solving%22">Problem solving</searchLink><br />*<searchLink fieldCode="DE" term="%22Collaborative+learning%22">Collaborative learning</searchLink><br />*<searchLink fieldCode="DE" term="%22Primary+education%22">Primary education</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra+problems+%26+exercises%22">Algebra problems & exercises</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+representation%22">Functional representation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Introspection%22">Introspection</searchLink> – Name: Abstract Label: Abstract (English) Group: Ab Data: Introduction. In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We offer a detailed critique of a research group who promote the movement of introducing algebra in primary school ("Early Algebra"). Method. In this collaborative research, we show how to promote advanced numericalalgebraic thinking through experimentation with certain activities (problem situations) in two groups of secondary students (grade 9), with 24 and 36 students, respectively. We use a specific methodology for collaborative learning, scientific debate and self-reflection (ACODESA methodology). Results. The pupils in this study constructed covariational reasoning as a prelude to the function concept. They also developed control elements that helped them in the process of solving problem situations. Discussion. Numerical reasoning is essential to giving meaning to the syntactic processes that, if manipulated or conceived of incurrectly, can lead to an error in a given situation. Advanced numerical-algebraic thinking helps us develop sensitivity to contradiction, enabling us to detect error. We believe that working with manipulative materials and producing functional representations that can evolve into institutional ones, and using collaborative learning with scientific debate and self-reflective reasoning (ACODESA methodology), can help pupils to more easily retain their mathematical concepts over time. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Abstract (Spanish) Group: Ab Data: Introducción. En este documento enfatizamos la importancia de desarrollar en los niños un pensamiento numérico-algebraico avanzado, que pueda proporcionar un elemento de control en los procesos de resolución de situaciones matemáticas. Se analizan concepciones de algunos alumnos que los induce a cometer errores en álgebra, por una falta de control por no recibir apoyo de su pensamiento numérico. Hacemos una crítica puntual a un grupo de investigación que se identifica con el movimiento acerca de la introducción del álgebra en la escuela primaria ("Early Algebra"). Método. En esta investigación, en colaboración, mostramos que es factible promover un pensamiento numérico-algebraico avanzado, en una experimentación de actividades (situaciones problema) con dos grupos de secundaria (grado 9), respectivamente con 24 y 36 alumnos, utilizando una metodología específica sobre aprendizaje en colaboración, debate científico y auto-reflexión (metodología ACODESA). Resultados. Los alumnos en este estudio, lograron construir el concepto de covariación como preludio al concepto de función, y desarrollar elementos de control que les sirvió en la resolución de las situaciones problema propuestas en esta experimentación. Conclusiones. El pensamiento numérico es esencial para proporcionar a los alumnos significados sobre sus procesos sintácticos que, por una mala manipulación o por una concepción, en una situación dada, puede guiarlos a error. El pensamiento numérico-algebraico avanzado, nos ayuda en el desarrollo de una sensibilidad a la contradicción para detectar el error. El trabajo con materiales, un aprendizaje colaborativo, debate científico y auto-reflexión (metodología ACODESA) permite una construcción más sólida de los conceptos matemáticos y posiblemente proporcionará una mayor retención de esos conceptos a largo plazo. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Electronic Journal of Research in Educational Psychology is the property of Editorial of the University of Almeria (Spain) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 18 StartPage: 243 Subjects: – SubjectFull: Problem solving Type: general – SubjectFull: Collaborative learning Type: general – SubjectFull: Primary education Type: general – SubjectFull: Algebra problems & exercises Type: general – SubjectFull: Functional representation Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Introspection Type: general Titles: – TitleFull: Pensamiento numérico-algebraico avanzado: construyendo el concepto de covariación como preludio al concepto de función. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hitt, Fernando – PersonEntity: Name: NameFull: Morasse, Christian IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: 2009 Type: published Y: 2009 Identifiers: – Type: issn-print Value: 16962095 Numbering: – Type: volume Value: 7 – Type: issue Value: 1 Titles: – TitleFull: Electronic Journal of Research in Educational Psychology Type: main |
| ResultId | 1 |
