Errors and difficulties in solving algebraic procedures in secondary school students
The research presented was aimed at determining the errors and difficulties presented by secondary school students in a Colombian public educational institution when faced with the solution of algebraic procedures. A contribution is sought to contribute to studies that monitor the performance of the...
- Autores:
-
HERNANDEZ SUAREZ, CESAR AUGUSTO
Paz Montes, Luisa Stella
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2019
- Institución:
- Universidad Francisco de Paula Santander
- Repositorio:
- Repositorio Digital UFPS
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.ufps.edu.co:ufps/463
- Acceso en línea:
- http://repositorio.ufps.edu.co/handle/ufps/463
https://doi.org/10.1088/1742-6596/1408/1/012010
- Palabra clave:
- Rights
- openAccess
- License
- Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence
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Errors and difficulties in solving algebraic procedures in secondary school students |
| title |
Errors and difficulties in solving algebraic procedures in secondary school students |
| spellingShingle |
Errors and difficulties in solving algebraic procedures in secondary school students |
| title_short |
Errors and difficulties in solving algebraic procedures in secondary school students |
| title_full |
Errors and difficulties in solving algebraic procedures in secondary school students |
| title_fullStr |
Errors and difficulties in solving algebraic procedures in secondary school students |
| title_full_unstemmed |
Errors and difficulties in solving algebraic procedures in secondary school students |
| title_sort |
Errors and difficulties in solving algebraic procedures in secondary school students |
| dc.creator.fl_str_mv |
HERNANDEZ SUAREZ, CESAR AUGUSTO Paz Montes, Luisa Stella |
| dc.contributor.author.none.fl_str_mv |
HERNANDEZ SUAREZ, CESAR AUGUSTO Paz Montes, Luisa Stella |
| description |
The research presented was aimed at determining the errors and difficulties presented by secondary school students in a Colombian public educational institution when faced with the solution of algebraic procedures. A contribution is sought to contribute to studies that monitor the performance of the teaching and learning processes of students. The methodology was based on the quantitative paradigm with a descriptive design, for which two instruments were applied to detect errors and difficulties in students. The results allowed to detect that, of the 12 errors that were taken as dimensions, six are significantly replicated, the most significant being the simple calculation error, unfinished procedure and the errors when performing arithmetic-algebraic operations. Participants allege associated difficulties, mostly to teaching problems, which generated guidelines aimed at teachers in order to raise didactic situations related to error as a source of learning. |
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2019 |
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2019-11-26 |
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2021-10-29T00:37:26Z |
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2021-10-29T00:37:26Z |
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Artículo de revista |
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https://doi.org/10.1088/1742-6596/1408/1/012010 |
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Journal of Physics: Conference Series ISSN: 1742-6596, 2019 vol:1408 fasc: N/A págs: 1 - 7, DOI:10.1088/1742-6596 |
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Vol. 1408. No.(2019) |
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7 |
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(2019) |
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A Diaz et al 2019 J. Phys.: Conf. Ser. 1408 012010 |
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Journal of Physics: Conference Series |
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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence |
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openAccess |
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8 Páginas |
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Journal of Physics: Conference Series |
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https://iopscience.iop.org/article/10.1088/1742-6596/1408/1/012010 |
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Universidad Francisco de Paula Santander |
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HERNANDEZ SUAREZ, CESAR AUGUSTOe68aa9e1677f4d5e4b155d813077e750600Paz Montes, Luisa Stella0e3478b349a3546b22afc7ddef1720a26002021-10-29T00:37:26Z2021-10-29T00:37:26Z2019-11-26http://repositorio.ufps.edu.co/handle/ufps/463https://doi.org/10.1088/1742-6596/1408/1/012010The research presented was aimed at determining the errors and difficulties presented by secondary school students in a Colombian public educational institution when faced with the solution of algebraic procedures. A contribution is sought to contribute to studies that monitor the performance of the teaching and learning processes of students. The methodology was based on the quantitative paradigm with a descriptive design, for which two instruments were applied to detect errors and difficulties in students. The results allowed to detect that, of the 12 errors that were taken as dimensions, six are significantly replicated, the most significant being the simple calculation error, unfinished procedure and the errors when performing arithmetic-algebraic operations. Participants allege associated difficulties, mostly to teaching problems, which generated guidelines aimed at teachers in order to raise didactic situations related to error as a source of learning.8 PáginasengJournal of Physics: Conference SeriesJournal of Physics: Conference Series ISSN: 1742-6596, 2019 vol:1408 fasc: N/A págs: 1 - 7, DOI:10.1088/1742-6596Vol. 1408. No.(2019)7(2019)11408A Diaz et al 2019 J. Phys.: Conf. Ser. 1408 012010Journal of Physics: Conference SeriesContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licenceinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2https://iopscience.iop.org/article/10.1088/1742-6596/1408/1/012010Errors and difficulties in solving algebraic procedures in secondary school studentsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Castro E 2001 Didáctica de la matemática en la educación primaria (Madrid: Síntesis)Pozo J I, Scheuer N, Pérez M, Mateos M, Martín E, De la Cruz M 2006 Nuevas formas de pensar la enseñanza y el aprendizaje: las concepciones de profesores y alumnos (Madrid: Graó)Abrate R S, Pochulu M D, Vargas J M 2006 Errores y dificultades en matemática. análisis de causas y sugerencias de trabajo (Argentina: Universidad Nacional de Villa María)Ribas R, D ́Aquino A 2004 ¿Cómo corregir errores y no equivocarse en el intento? (Madrid: EDELSA)Astolfi J P 2001 Conceptos claves en la didáctica de las disciplinas: referencias, definiciones y bibliografias de didactica de las ciencias (Sevilla: Diada)Torijano J A 2004 Errores y aprendizaje, aprendizaje de los errores (Madrid: Arco Libros)Arrabal M A, Laporte E, Rivas S R 2006 Una reflexión sobre la importancia del error y su corrección en la clase de español como L2 (Brasil: III Simposio internacional José Carlos Lisboa de didáctica del español como lengua extranjera del Instituto Cervantes de Río de Janeiro)Brousseau G 1993 Fundamentos y métodos de la didáctica de la matemática (Cordoba, Argentina: Univerisdad Nacional de Córdoba)Gil M, Cortés F 1997 La epistemología genética y la ciencia contemporánea: Homanaje a Jean Piaget en su centenario (España: Gedisa) p 69Rico L, Sierra M 1997 Antecedentes del currículo de matemáticas bases teóricas delcurrículo de matemáticas en la educación secundaria ed Rico L (Madrid: Síntesis) p 17García J 2010 Análisis de errores y dificultades en la resolución de tareas algebraicas por alumnos de primer ingreso en nivel licenciatura (Granada: Universidad de Granada)Ruano R, Socas M, Palarea M 2008 Análisis y clasificación de errores cometidos por alumnos de secundaria en los procesos de sustitución formal,generalización y modelización en álgebra PNA 2 61Di Blasi M, Espro F, Lois A, Milevich L 2003 Dificultades y errores: Un estudio de caso (Buenos Aires: II Congreso Internacional de Matemática Aplicada a la Ingenieria y Enseñanza de la Matemática en ingeniería)Socas M 1997 Dificultades, obstáculos y errores en el aprendizaje de las matemáticas en la educación secundaria la educación matemática en la enseñanza eecundaria ed Rico L (Barcelona: Horsori- Universidad de Barcelona) p 125Suárez R 2002 La educación. Estrategias de enseñanza-aprendizaje, teorías educativas (Mexico: Trillas)Schunk D H 2012 Teorías del aprendizaje (México: Pearson Educación)Goleman D 1996 Inteligencia emocional (Barcelona: Kairos)Sánchez J, Segovia I, Miñán A 2011 Exploración de la ansiedad hacia las matemáticas en los futuros maestros de educación primaria Profesorado, Revista de Currículo y Formación del Profesorado 15 207Aragonés J I, Cuervo M A 2000 Psicología ambiental (España: Pirámide) p 23Damasio A 2001 El Error de descartes: La emoción, la razón y el cerebro humano (Barcelona: Critica)Alsina A 2007 El aprendizaje reflexivo en la formación permanente del profesorado: Un análisis desde la didáctica de las matemáticas Educación Matemática 19 99ORIGINALErrors and difficulties in solving algebraic procedures in secondary school students.pdfErrors and difficulties in solving algebraic procedures in secondary school 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
0000-0002-7974-5560e68aa9e1677f4d5e4b155d813077e7506000000-0002-8887-34410e3478b349a3546b22afc7ddef1720a2600 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