Categories to assess the understanding of university students about a mathematical concept
One of the problems in mathematics education is students’ little understanding of mathematics both at the basic and higher educational levels, which is why we consider essential the design of adequate instruments and methods that can measure understanding about specific concepts. Objective: To asses...
- Autores:
-
Rodríguez-Vásquez, Flor Monserrat
Arenas Peñaloza, Jhonatan
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2020
- Institución:
- Corporación Universidad de la Costa
- Repositorio:
- REDICUC - Repositorio CUC
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.cuc.edu.co:11323/8085
- Acceso en línea:
- https://hdl.handle.net/11323/8085
https://doi.org/10.17648/acta.scientiae.5892
https://repositorio.cuc.edu.co/
- Palabra clave:
- Understanding
Evaluation categories
Actual function
Mathematics education
Comprensión
Categorías de evaluación
Función real
Educación matemática
- Rights
- openAccess
- License
- CC0 1.0 Universal
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Categories to assess the understanding of university students about a mathematical concept |
| dc.title.translated.spa.fl_str_mv |
Categorías para evaluar la comprensión de estudiantes universitarios sobre un concepto matemático |
| title |
Categories to assess the understanding of university students about a mathematical concept |
| spellingShingle |
Categories to assess the understanding of university students about a mathematical concept Understanding Evaluation categories Actual function Mathematics education Comprensión Categorías de evaluación Función real Educación matemática |
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Categories to assess the understanding of university students about a mathematical concept |
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Categories to assess the understanding of university students about a mathematical concept |
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Categories to assess the understanding of university students about a mathematical concept |
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Categories to assess the understanding of university students about a mathematical concept |
| title_sort |
Categories to assess the understanding of university students about a mathematical concept |
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Rodríguez-Vásquez, Flor Monserrat Arenas Peñaloza, Jhonatan |
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Rodríguez-Vásquez, Flor Monserrat Arenas Peñaloza, Jhonatan |
| dc.subject.spa.fl_str_mv |
Understanding Evaluation categories Actual function Mathematics education Comprensión Categorías de evaluación Función real Educación matemática |
| topic |
Understanding Evaluation categories Actual function Mathematics education Comprensión Categorías de evaluación Función real Educación matemática |
| description |
One of the problems in mathematics education is students’ little understanding of mathematics both at the basic and higher educational levels, which is why we consider essential the design of adequate instruments and methods that can measure understanding about specific concepts. Objective: To assess the understanding of university students of the concept of a real function. Design: The research is qualitative as the attributes of a cognitive construct were analysed and interpreted. Setting and participants: There were 36 students of a degree in mathematics (18-20 years old) whose productions were analysed. All the students had taken the Calculus I course. Data collection and analysis: A test of six items related to tasks that involved the concept of function was applied, the data analysis was carried out from the evaluation categories proposed by Albert and Kim, who consider three categories to assess understanding, those being: the ability to justify, to understand why a particular mathematical statement is true, and to understand where a mathematical rule comes from. Results: The evaluation of the understanding of the concept of function has shown that, in order to achieve a high understanding, not only skills must be developed for the recognition of aspects of the function such as its definition, its discrimination or its application, but the ability to be able to justify such aspects must be considered too. Conclusion: The categories of understanding considered help to strengthen conceptual and procedural understanding, indicating comprehensive understanding. |
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2020 |
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2020-11-11 |
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2021-04-07T13:56:03Z |
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2021-04-07T13:56:03Z |
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Corporación Universidad de la Costa |
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eng |
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Albert, L. & Kim, R. (2015). Applying CCSSM Definition of Understanding to Assess Students Mathematical Learning. In: Assessment to Enhance Teaching and Learning (pp. 233-246). National Council of Teachers of Mathematics. Amaya, T. & Sgreccia, N. (2014). Dificultades de los estudiantes de once grado al hacer transformaciones de representaciones de una función. Épsilon: Revista de la Sociedad Andaluza de Educación Matemática “Thales”, 31(88), 21-38. https://thales.cica.es/epsilon/sites/thales.cica.es.epsilon/files/%5Bfield_volumen-formatted%5D/epsilon88_2.pdf Amaya, T., Pino-Fan, L. & Medina R. (2016). Evaluación del conocimiento de futuros profesores de matemáticas sobre las transformaciones de las representaciones de una función. Educación matemática, 28(3), 111-144. https://doi.org/10.24844/EM2803.05 Arizmendi, H., Carrillo, A. & Lara. M. Cálculo. Primer curso nivel superior. Addison-Wesley Iberoamericana. Arnon, I., Cottril, J., Dubinsky, E., Oktaç, A., Roa, S., Trigueros, M. & Weller, K. (2014). APOS Theory. A Framework for Research and Curriculum Development in Mathematics Education. Springer. Bardini, C., Pierce, R., Vincen, J. & King, D. (2014). Undergraduate mathematics students’ understanding of the concept of function. IndoMS-JME, 5(2), 85-107. https://files.eric.ed.gov/fulltext/EJ1079527.pdf Common Core State Standards for Mathematics (2010). National Governors Association Center for Best Practices. Council of Chief State School Officer. http://www.corestandards.org/wpcontent/uploads/Math_Standards.pdf Cuevas, C. & Pluvinage, F. (2017). Revisitando la noción de función real. El cálculo y su enseñanza, 8, 19-35. https://recacym.org/index.php/recacym/article/view/43/25 Delgado, M. L., Codes, M., Monterrubio, M. C. & González, M. T. (2014). El concepto de serie numérica. Un estudio a través del modelo de Pirie y Kieren centrado en el mecanismo “folding back”. Avances de Investigación en Educación Matemática, 6, 25-44. https://doi.org/10.35763/aiem.v1i6.85 Díaz, J. (2013). El concepto de función: ideas pedagógicas a partir de su historia e investigaciones. El Cálculo y su enseñanza, 4, 13-26. https://mattec.matedu.cinvestav.mx/el_calculo/data/docs/Diaz.a535a5 fbaf7a54a6250cf5a0bf132fda.pdf Crespo, C. & Ponteville, C. (2003). El concepto de función: su comprensión y análisis. Acta Latinoamericana de Matemática Educativa, 16(1), 235241. Díaz, M., Haye, E., Montenegro., F. & Córdoba, L. (2015). Dificultades de los estudiantes para articular representaciones gráficas y algebraicas de funciones lineales y cuadráticas. Unión: Revista Iberoamericana de Educación Matemática, 41, 20-38. http://www.fisem.org/www/union/revistas/2015/41/Artigo1.pdf Dreyfus, T. & Eisenberg, T. (1982). Intuitive Functional Concepts: A Baseline Study on Intuitions. Journal for Reseach in Mathematics Education, 13(5). 360-380. Farfán, R. & García, M. (2005). El concepto de Función: Un breve recorrido epistemológico. Acta Latinoamericana de Matemática Educativa, 18, 489-494. Figueiredo, C. & Contreras, L. (2013). A função quadrática: variação, transparência e duas tipologias de exemplos. Avances de Investigación en Educación Matemática, 3, 45-68. https://doi.org/10.35763/aiem.v0i3.62 Flores, J., Neira, V., Carrillo, F. & Peñaloza, T. (2019). Funciones reales de variable real: mediación de la calculadora científica. Acta Latinoamericana de Matemática Educativa, 32 (2), 684-692. https://www.clame.org.mx/documentos/alme32_2.pdf Hiebert, J. & Carpenter, T. P. (1992). Learning and Teaching with Understanding. In: Handbook of Research on Mathematics Teaching and Learning (pp. 65-97). Macmillan. Kastberg, S. E. (2002). Understanding Mathematical Concepts: The Case of the Logarithmic Function. The University of Georgia. Michener, E. R. (1978). Understanding understanding Mathematics. Cognitive Science, 2, 361-383. https://doi:10.1207/s15516709cog0204_3 National Governors Association Center for Best Practices and Council of Chief School Officers (NGA Center and CCSSO). (2010). Common Core State Standards for Mathematics. NGA Center and CCSSO. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. NCTM. Nickerson, R. S. (1985). Understanding Understanding. American Journal of Education 93(2), 201-239. Ortega, T. & Pecharromán, C. (2014). Errores en el aprendizaje de las propiedades globales de las funciones. Revista de Investigación en Educación, 12(2), 209-221. http://reined.webs.uvigo.es/index.php/reined/article/view/258/305 Pino-Fan, L. R., Parra-Urrea, Y. E. & Castro-Gordillo, W. F. (2019). Significados de la función pretendidos por el currículo de matemáticas chileno. Revista Internacional de Investigación en Educación, 11(23), 201-220. https://doi.org/10.11144/Javeriana.m11- 23.sfpc Pirie, S. & Kieren, T. (1994). Growth in mathematical understading: how can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165-190. https://doi.org/10.1007/BF01273662 Prada, R., Hernández, C. & Ramírez, P. (2014). Comprensión del concepto de función en los primeros cursos de educación superior. El Cálculo y su Enseñanza, 6(6), 29-44. Schoenfeld, A. H. (2007). What is mathematical proficiency and how can it be assessed? In: Assessing Mathematical Proficiency (pp. 59-74). Cambridge University Press. Sfard, A. (1989). Transition from operational to structural conception: The notion of function revisited. In: Proceedings of the Thirteenth International Conference for the Psychology of Mathematics Education, 3, 151-158. G.R Didactique, CNRS. Sierpinska, A. (1990). Some Remarks on Understanding in Mathematics. For the Learning of Mathematics, 10(3), 24-36. Sierpinska, A. (1992). On understanding the notion of function. In: The concept of function: Aspects of epistemology and pedagogy. Mathematical Association of America. Skemp, R. (1976). Relational Understanding and Instrumental Understanding. Mathematics Teaching, 77, 20-26. Skemp, R. (1980). Psicología del aprendizaje de las Matemáticas. Ediciones Morata S.A. Secretaria de Educación Pública. (2011). Programa de estudio 2011. Guía para el Maestro. Educación Básica. Secundaria. Matemáticas. SEP. Serrano, W. (2007). Concepciones de los estudiantes sobre la inyectividad, sobreyectividad de la función cuadrática y sobre la gráfica de H: R{0}→R definida por h (x)= sen x/x. Sapiens: revista universitaria de investigación, 8(2), 169-186. https://www.redalyc.org/articulo.oa?id=41080211 Silva, L. & Kaiber, C. (2013). Reflexões sobre o ensino de funções sob a perspectiva do enfoque ontossemiótico. Educação matemática em revista, 14(2), 27-36. Vinner, S. (1983). Concept definition, concept image and the notion of function. The International Journal of Mathematical Education in Science and Technology, 14, 293-305. Vinner, S. & Dreyfus, T. (1989). Images and Definitions for the Concept of Function. Journal for Research in Mathematics Education, 20(4), 356-366. Watson, A. & Harel, G. (2013). The role of Teacher’s Knowledge of Functions in their teaching: a conceptual approach with illustrations from two cases. Canadian Journal of Science Mathematics and Technology Education, 13(2), pp. 154-158. http://dx.doi.org/10.1080/14926156.2013.784826 Wilkerson-Jerde, M. H. & Wilensky, U. J. (2011). How do mathematicians learn math?: resources and acts for constructing and understanding mathematic. Educational Studies in Mathematics, 78, 21-43. https://doi.org/10.1007/s10649-011-9306-5 |
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Rodríguez-Vásquez, Flor Monserrat37facdd61a70f2e9925645969c8aaf37Arenas Peñaloza, Jhonatanee629966765667d5d30ecb81f5acbff52021-04-07T13:56:03Z2021-04-07T13:56:03Z2020-11-111517-44922178-7727https://hdl.handle.net/11323/8085https://doi.org/10.17648/acta.scientiae.5892Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/One of the problems in mathematics education is students’ little understanding of mathematics both at the basic and higher educational levels, which is why we consider essential the design of adequate instruments and methods that can measure understanding about specific concepts. Objective: To assess the understanding of university students of the concept of a real function. Design: The research is qualitative as the attributes of a cognitive construct were analysed and interpreted. Setting and participants: There were 36 students of a degree in mathematics (18-20 years old) whose productions were analysed. All the students had taken the Calculus I course. Data collection and analysis: A test of six items related to tasks that involved the concept of function was applied, the data analysis was carried out from the evaluation categories proposed by Albert and Kim, who consider three categories to assess understanding, those being: the ability to justify, to understand why a particular mathematical statement is true, and to understand where a mathematical rule comes from. Results: The evaluation of the understanding of the concept of function has shown that, in order to achieve a high understanding, not only skills must be developed for the recognition of aspects of the function such as its definition, its discrimination or its application, but the ability to be able to justify such aspects must be considered too. Conclusion: The categories of understanding considered help to strengthen conceptual and procedural understanding, indicating comprehensive understanding.Contexto: Una de las problemáticas en educación matemática, es la endeble comprensión en matemáticas que tienen los estudiantes, tanto en el nivel educativo básico como en el superior, por lo que consideramos fundamental el diseño de instrumentos y métodos adecuados que puedan medir la comprensión sobre conceptos específicos. Objetivo: Evaluar la comprensión de estudiantes universitarios sobre el concepto de función real. Diseño: La investigación es cualitativa, debido a que se analizaron e interpretaron los atributos sobre un constructo cognitivo. Escenario y participantes: Fueron 36 estudiantes de una licenciatura en matemáticas (18-20 años) de quienes se analizaron sus producciones, todos habían llevado el primer curso de cálculo. Colección y análisis de datos: Se aplicó un test de seis ítems relativos a tareas que involucraron el concepto de función, el análisis de datos se realizó desde las categorías de evaluación propuestas por Albert y Kim, quienes consideran tres categorías para evaluar la comprensión, a saber, la habilidad para justificar, entender por qué una afirmación matemática particular es verdadera y, entender de dónde viene una regla matemática. Resultados: La evaluación sobre la comprensión del concepto función, ha evidenciado que, para alcanzar una comprensión alta se deben desarrollar no solo habilidades para el reconocimiento de aspectos de la función como su definición, su discriminación o su aplicación, sino además considerar la habilidad para poder justificar tales aspectos. Conclusión: Las categorías de comprensión consideradas, ayudan en el fortalecimiento del entendimiento conceptual y procedimental indicando una comprensión integral.application/pdfengCorporación Universidad de la CostaCC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Acta Scientiaehttp://www.periodicos.ulbra.br/index.php/acta/article/view/5892UnderstandingEvaluation categoriesActual functionMathematics educationComprensiónCategorías de evaluaciónFunción realEducación matemáticaCategories to assess the understanding of university students about a mathematical conceptCategorías para evaluar la comprensión de estudiantes universitarios sobre un concepto matemáticoArtículo 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/acceptedVersionAlbert, L. & Kim, R. (2015). Applying CCSSM Definition of Understanding to Assess Students Mathematical Learning. In: Assessment to Enhance Teaching and Learning (pp. 233-246). National Council of Teachers of Mathematics.Amaya, T. & Sgreccia, N. (2014). Dificultades de los estudiantes de once grado al hacer transformaciones de representaciones de una función. Épsilon: Revista de la Sociedad Andaluza de Educación Matemática “Thales”, 31(88), 21-38. https://thales.cica.es/epsilon/sites/thales.cica.es.epsilon/files/%5Bfield_volumen-formatted%5D/epsilon88_2.pdfAmaya, T., Pino-Fan, L. & Medina R. (2016). Evaluación del conocimiento de futuros profesores de matemáticas sobre las transformaciones de las representaciones de una función. Educación matemática, 28(3), 111-144. https://doi.org/10.24844/EM2803.05Arizmendi, H., Carrillo, A. & Lara. M. Cálculo. Primer curso nivel superior. Addison-Wesley Iberoamericana.Arnon, I., Cottril, J., Dubinsky, E., Oktaç, A., Roa, S., Trigueros, M. & Weller, K. (2014). APOS Theory. A Framework for Research and Curriculum Development in Mathematics Education. Springer.Bardini, C., Pierce, R., Vincen, J. & King, D. (2014). Undergraduate mathematics students’ understanding of the concept of function. IndoMS-JME, 5(2), 85-107. https://files.eric.ed.gov/fulltext/EJ1079527.pdfCommon Core State Standards for Mathematics (2010). National Governors Association Center for Best Practices. Council of Chief State School Officer. http://www.corestandards.org/wpcontent/uploads/Math_Standards.pdfCuevas, C. & Pluvinage, F. (2017). Revisitando la noción de función real. El cálculo y su enseñanza, 8, 19-35. https://recacym.org/index.php/recacym/article/view/43/25Delgado, M. L., Codes, M., Monterrubio, M. C. & González, M. T. (2014). El concepto de serie numérica. Un estudio a través del modelo de Pirie y Kieren centrado en el mecanismo “folding back”. Avances de Investigación en Educación Matemática, 6, 25-44. https://doi.org/10.35763/aiem.v1i6.85Díaz, J. (2013). El concepto de función: ideas pedagógicas a partir de su historia e investigaciones. El Cálculo y su enseñanza, 4, 13-26. https://mattec.matedu.cinvestav.mx/el_calculo/data/docs/Diaz.a535a5 fbaf7a54a6250cf5a0bf132fda.pdfCrespo, C. & Ponteville, C. (2003). El concepto de función: su comprensión y análisis. Acta Latinoamericana de Matemática Educativa, 16(1), 235241.Díaz, M., Haye, E., Montenegro., F. & Córdoba, L. (2015). Dificultades de los estudiantes para articular representaciones gráficas y algebraicas de funciones lineales y cuadráticas. Unión: Revista Iberoamericana de Educación Matemática, 41, 20-38. http://www.fisem.org/www/union/revistas/2015/41/Artigo1.pdfDreyfus, T. & Eisenberg, T. (1982). Intuitive Functional Concepts: A Baseline Study on Intuitions. Journal for Reseach in Mathematics Education, 13(5). 360-380.Farfán, R. & García, M. (2005). El concepto de Función: Un breve recorrido epistemológico. Acta Latinoamericana de Matemática Educativa, 18, 489-494.Figueiredo, C. & Contreras, L. (2013). A função quadrática: variação, transparência e duas tipologias de exemplos. Avances de Investigación en Educación Matemática, 3, 45-68. https://doi.org/10.35763/aiem.v0i3.62Flores, J., Neira, V., Carrillo, F. & Peñaloza, T. (2019). Funciones reales de variable real: mediación de la calculadora científica. Acta Latinoamericana de Matemática Educativa, 32 (2), 684-692. https://www.clame.org.mx/documentos/alme32_2.pdfHiebert, J. & Carpenter, T. P. (1992). Learning and Teaching with Understanding. In: Handbook of Research on Mathematics Teaching and Learning (pp. 65-97). Macmillan.Kastberg, S. E. (2002). Understanding Mathematical Concepts: The Case of the Logarithmic Function. The University of Georgia.Michener, E. R. (1978). Understanding understanding Mathematics. Cognitive Science, 2, 361-383. https://doi:10.1207/s15516709cog0204_3National Governors Association Center for Best Practices and Council of Chief School Officers (NGA Center and CCSSO). (2010). Common Core State Standards for Mathematics. NGA Center and CCSSO.National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. NCTM.Nickerson, R. S. (1985). Understanding Understanding. American Journal of Education 93(2), 201-239.Ortega, T. & Pecharromán, C. (2014). Errores en el aprendizaje de las propiedades globales de las funciones. Revista de Investigación en Educación, 12(2), 209-221. http://reined.webs.uvigo.es/index.php/reined/article/view/258/305Pino-Fan, L. R., Parra-Urrea, Y. E. & Castro-Gordillo, W. F. (2019). Significados de la función pretendidos por el currículo de matemáticas chileno. Revista Internacional de Investigación en Educación, 11(23), 201-220. https://doi.org/10.11144/Javeriana.m11- 23.sfpcPirie, S. & Kieren, T. (1994). Growth in mathematical understading: how can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165-190. https://doi.org/10.1007/BF01273662Prada, R., Hernández, C. & Ramírez, P. (2014). Comprensión del concepto de función en los primeros cursos de educación superior. El Cálculo y su Enseñanza, 6(6), 29-44.Schoenfeld, A. H. (2007). What is mathematical proficiency and how can it be assessed? In: Assessing Mathematical Proficiency (pp. 59-74). Cambridge University Press.Sfard, A. (1989). Transition from operational to structural conception: The notion of function revisited. In: Proceedings of the Thirteenth International Conference for the Psychology of Mathematics Education, 3, 151-158. G.R Didactique, CNRS.Sierpinska, A. (1990). Some Remarks on Understanding in Mathematics. For the Learning of Mathematics, 10(3), 24-36.Sierpinska, A. (1992). On understanding the notion of function. In: The concept of function: Aspects of epistemology and pedagogy. 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