Developmental perspectives of numerical thinking for the interpretation of physical quantities

This research reveals the perspectives in the teaching of numerical thinking through a documentary review. The representation of physical elements such as functions, vectors and operators, and their subsequent interpretation through numerical thinking gives meaning to the physical quantities that su...

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Autores:
Rincón Leal, Olga Lucy
Salazar-Torres, Juan-Pablo
Valbuena-Prada, Oscar
Tipo de recurso:
Article of journal
Fecha de publicación:
2020
Institución:
Universidad Francisco de Paula Santander
Repositorio:
Repositorio Digital UFPS
Idioma:
eng
OAI Identifier:
oai:repositorio.ufps.edu.co:ufps/1127
Acceso en línea:
http://repositorio.ufps.edu.co/handle/ufps/1127
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Atribución 4.0 Internacional (CC BY 4.0)
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dc.title.eng.fl_str_mv Developmental perspectives of numerical thinking for the interpretation of physical quantities
title Developmental perspectives of numerical thinking for the interpretation of physical quantities
spellingShingle Developmental perspectives of numerical thinking for the interpretation of physical quantities
title_short Developmental perspectives of numerical thinking for the interpretation of physical quantities
title_full Developmental perspectives of numerical thinking for the interpretation of physical quantities
title_fullStr Developmental perspectives of numerical thinking for the interpretation of physical quantities
title_full_unstemmed Developmental perspectives of numerical thinking for the interpretation of physical quantities
title_sort Developmental perspectives of numerical thinking for the interpretation of physical quantities
dc.creator.fl_str_mv Rincón Leal, Olga Lucy
Salazar-Torres, Juan-Pablo
Valbuena-Prada, Oscar
dc.contributor.author.none.fl_str_mv Rincón Leal, Olga Lucy
Salazar-Torres, Juan-Pablo
Valbuena-Prada, Oscar
description This research reveals the perspectives in the teaching of numerical thinking through a documentary review. The representation of physical elements such as functions, vectors and operators, and their subsequent interpretation through numerical thinking gives meaning to the physical quantities that such elements represent. A documentary sample integrated for 40 sources on numerical thinking such as articles published in indexed journals, postgraduate dissertations, and books is considered. A qualitative content analysis method is used. First, an encoding procedure is applied for tagging the extracted information from the source documents. Then, a split and merge procedure is considered in order to establish from the tags the dimensions and categories that allow determining the conceptual relationships that support the developmental perspectives of numerical thinking. The method reveals that the numerical thinking can be developed in the global context from four perspectives, namely, historical, theoretical, curricular, and social perspectives. From these results, an incorporation of the such perspectives can be institutionalized for promoting curricular, didactic and evaluative new proposals for numerical thinking teaching.
publishDate 2020
dc.date.issued.none.fl_str_mv 2020-11-04
dc.date.accessioned.none.fl_str_mv 2021-11-19T13:46:20Z
dc.date.available.none.fl_str_mv 2021-11-19T13:46:20Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.doi.none.fl_str_mv 10.1088/1742-6596/1672/1/012014
url http://repositorio.ufps.edu.co/handle/ufps/1127
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dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartof.none.fl_str_mv Journal of Physics: Conference Series
dc.relation.citationedition.spa.fl_str_mv Vol.1672 No.1.(2020)
dc.relation.citationendpage.spa.fl_str_mv 8
dc.relation.citationissue.spa.fl_str_mv 1 (2020)
dc.relation.citationstartpage.spa.fl_str_mv 1
dc.relation.citationvolume.spa.fl_str_mv 1672
dc.relation.cites.none.fl_str_mv Valbuena, O., Salazar-Torres, J., Diaz, J. A., Rincón-Leal, O., & Bravo, A. (2020, October). Developmental perspectives of numerical thinking for the interpretation of physical quantities. In Journal of Physics: Conference Series (Vol. 1672, No. 1, p. 012014). IOP Publishing.
dc.relation.ispartofjournal.spa.fl_str_mv Journal of Physics: Conference Series
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eu_rights_str_mv openAccess
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dc.publisher.spa.fl_str_mv Journal of Physics: Conference Series
dc.publisher.place.spa.fl_str_mv Madrid , España
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institution Universidad Francisco de Paula Santander
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spelling Rincón Leal, Olga Lucy937ec9a93090444fc664edf246861d5e600Salazar-Torres, Juan-Pablod3d10aa98acd1a12c2fc03292880d954600Valbuena-Prada, Oscar a3be9e9e1768410fd7f2770f0dc4230c6002021-11-19T13:46:20Z2021-11-19T13:46:20Z2020-11-04http://repositorio.ufps.edu.co/handle/ufps/112710.1088/1742-6596/1672/1/012014This research reveals the perspectives in the teaching of numerical thinking through a documentary review. The representation of physical elements such as functions, vectors and operators, and their subsequent interpretation through numerical thinking gives meaning to the physical quantities that such elements represent. A documentary sample integrated for 40 sources on numerical thinking such as articles published in indexed journals, postgraduate dissertations, and books is considered. A qualitative content analysis method is used. First, an encoding procedure is applied for tagging the extracted information from the source documents. Then, a split and merge procedure is considered in order to establish from the tags the dimensions and categories that allow determining the conceptual relationships that support the developmental perspectives of numerical thinking. The method reveals that the numerical thinking can be developed in the global context from four perspectives, namely, historical, theoretical, curricular, and social perspectives. From these results, an incorporation of the such perspectives can be institutionalized for promoting curricular, didactic and evaluative new proposals for numerical thinking teaching.application/pdfengJournal of Physics: Conference SeriesMadrid , EspañaJournal of Physics: Conference SeriesVol.1672 No.1.(2020)81 (2020)11672Valbuena, O., Salazar-Torres, J., Diaz, J. A., Rincón-Leal, O., & Bravo, A. (2020, October). Developmental perspectives of numerical thinking for the interpretation of physical quantities. In Journal of Physics: Conference Series (Vol. 1672, No. 1, p. 012014). IOP Publishing.Journal of Physics: Conference SeriesContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltdinfo:eu-repo/semantics/openAccessAtribución 4.0 Internacional (CC BY 4.0)http://purl.org/coar/access_right/c_abf2https://iopscience.iop.org/article/10.1088/1742-6596/1672/1/012014/metaDevelopmental perspectives of numerical thinking for the interpretation of physical quantitiesArtículo 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_970fb48d4fbd8a85Holton D 2001 The Teaching and Learning of Mathematics at University Level (Boston: Springer)Biza I, Giraldo V, Hochmuth R, Khakbaz A and Rasmussen C 2016 Research on Teaching and Learning Mathematics at the Tertiary Level: State-of-the-art and Looking Ahead (Switzerland: Springer International Publishing)Gravemeijer K, Stephan M, Julie C, Lin F L and Ohtani M 2017 International Journal of Science and Mathematics Education volume 14 105Geary D, Berch D, Ochsendorf R and Koepke K 2017 Acquisition of Complex Arithmetic Skills and Higher-order Mathematics Concepts (San Diego: Academic Press)Ernest P 1999 Educational Studies in Mathematics 38 67Cuoco A, Paul Goldenberg E and Mark J 1996 The Journal of Mathematical Behavior 15 375-402Mason J, Burton L and Stacey K 2011 Thinking Mathematically (London: Addison Wesley)Johnston-Wilder S and Lee C 2008 Proceedings for the British Society for Research into Learning Mathematics 28 54Burton L 1984 Journal for Research in Mathematics Education 15 35Verschaffel L, Greer B and De Corte E 2010 International Encyclopedia of Education (Oxford: Elsevier)Wu B 2011 Consumption and Management (Oxford: Chandos Publishing)2005 Estándares Básicos de Competencias Matemáticas (Colombia: Ministerio de Educación Nacional) Ministerio de Educación NacionalKlose O M 1966 The Number Systems and Operations of Arithmetic (Oxford: Pergamon)Patton M Q 1990 Qualitative Evaluation and Research Methods (London: SAGE Publications)Baena G 1986 Manual para Elaborar Trabajos de Investigación Documental (Mexico: Editores Mexicanos Unidos)Corbin J and Strauss A 2007 Basics of Qualitative Research: Techniques and Procedures for Developing Grounded Theory (Thousand Oaks: SAGE Pulications)Miguélez M M 2007 Ciencia y Arte en la Metodologia Cualitativa (Mexico: Trillas)Freudenthal H 1968 Educational Studies in Mathematics 1 3Boaler J 1993 For the Learning of Mathematics 13 12Loase J F 1987 Mathematical Modelling 8 175Buldt B, Löwe B and Müller T 2008 Erkenntnis (1975-) 68 309Robinson A 1975 Proceedings of the Logic Colloquium 80 41Segal J 1999 The Journal of Mathematical Behavior 18 191Posada M E 2005 Interpretación e Implementación de los Estándares Básicos de Matemáticas (Medellìn: Gobernación de Antioquia)Villarroel J 2009 Electronic Journal of Research in Educational Psychology 7 555Bashirov A 2014 Mathematical Analysis Fundamentals (Boston: Elsevier)Pitta-Pantazi D 2014 Encyclopedia of Mathematics Education (Dordrecht: Springer Netherlands)Verschaffel L, Depaepe F and De Corte E 2015 International Encyclopedia of the Social & Behavioral Sciences (Oxford: Elsevier)Nowakowska M 1980 International Journal of Man-Machine Studies 13 223Leibovich T, Katzin N, Harel M and Henik A 2017 Behavioral and Brain Sciences 40 el64Micheli J and Ernst C 1997 Journal of Mathematical Psychology 41 345Malet A 2006 Historia Mathematica 33 63Sfard A 1991 Educational Studies in Mathematics 2 1Céspedes E 2018 Cinta de Moebio 63 323Chesney M and Hazari B 1998 Journal of Mathematical Economics 29 1Cooney J B 1991 Learning and Individual Differences 3 83Cantlon J F 2015 Evolutionary Origins and Early Development of Number Processing (London: Elsevier)DeWolf M, Bassok M and Holyoak K J 2017 Acquisition of Complex Arithmetic Skills and Higher-rder Mathematics Concepts (San Diego: Academic Press)Yanuschik O V, Batbold M and Ustyuzhanina A K 2015 Procedia - Social and Behavioral Sciences 215 202Marwiang M, Junpeng P and Nakorn N N 2014 Procedia - Social and Behavioral Sciences 143 764Hadar L L 2017 Studies in Educational Evaluation 55 153de Abreu G 1998 Learning and Instruction 8 567Xolocotzin Eligio U 2017 Understanding Emotions in Mathematical Thinking and Learning (San Diego: Academic Press)Trouche L, Gitirana V, Miyakawa T, Pepin B and Wang C 2019 International Journal of Educational Research 93 53Cárdenas-Soler R, Piamonte-Contreras S and Gordillo-Catellanos P 2017 Pensamiento y Acción 23 31Nunes T 1993 Significant Influences on Children’s Learning of Mathematics (Paris: UNESCO)Rodrìguez M E 2016 Revista Eleuthera 15 34Cobb P 1994 Learning Mathematics. 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texttext/plain23679https://repositorio.ufps.edu.co/bitstream/ufps/1127/3/Developmental%20perspectives%20of%20numerical%20thinking%20for%20the%20interpretation%20of%20physical%20quantities.pdf.txt3e6af136e0477236f97dd675557e70acMD53open accessTHUMBNAILDevelopmental perspectives of numerical thinking for the interpretation of physical quantities.pdf.jpgDevelopmental perspectives of numerical thinking for the interpretation of physical quantities.pdf.jpgGenerated Thumbnailimage/jpeg9145https://repositorio.ufps.edu.co/bitstream/ufps/1127/4/Developmental%20perspectives%20of%20numerical%20thinking%20for%20the%20interpretation%20of%20physical%20quantities.pdf.jpg266b72fdb3337ef4adda752653b10f0eMD54open accessufps/1127oai:repositorio.ufps.edu.co:ufps/11272022-05-23 10:53:31.445open accessRepositorio Universidad Francisco de Paula 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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.


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