Provocation by Challenges: Optimizing Experience of Addressing Mathematical Tasks With High Cognitive Demand
DOI:
https://doi.org/10.15359/ree.24-3.9Keywords:
Cognitive demand, challenge, scaffolding, Mathematics education, homeworkAbstract
High cognitive demand mathematical tasks involve exercising skills to analyze, infer, relate and reflect on arithmetic, geometric and statistical information. In its development, student engagement is crucial to overcome increasingly complex situations in the learning process of the Peruvian school system. These variables are of vital importance because students need to avoid negative influences that cause academic failure or dropout, so it is valuable to live experiences of motivational improvement of their mathematical behavior to achieve permanent success in this area. In this proposal, the objective was to check whether the effects of a challenge provocation experience, based on Flow’s theory, optimized the approach to mathematical tasks with a certain cognitive demand. The design was of a pre-experimental quantitative type. A sample of 76 students was included. The instrument was the test of arithmetic problems with multiple cognitive demand. The results allowed concluding that the program stimulated the solution of memory tasks and problems with non-connective information, but its effect was less and slower in addressing tasks with high cognitive demand. The study contributed to verifying the benefits of scaffolding based on flow strategies, according to the challenges that stimulate the cognitive independence of the student who learns to tackle cognitive tasks, in accordance with the expertise and commitment obtained through interaction with the teacher or mediator.
References
Aguirre-Leguizamo, E. (2016). Flexibilidad cognitiva y atención en aprendices SENA según su desempeño académico [Tesis de maestría]. Universidad Internacional de la Rioja, Colombia. https://reunir.unir.net/handle/123456789/4876
Aubrey, S. (2016). Inter-cultural contact and flow in a task-based Japanese EFL classroom. Language Teaching Research, 21(6), 717-734. https://doi.org/10.1177/1362168816683563
Ayllón, M. F., Gómez, I. A. y Ballesta-Claver, J. (2016). Pensamiento matemático y creatividad a través de la invención y resolución de problemas matemáticos. Propósitos y representaciones, 4(1), 169-218. https://doi.org/10.20511/pyr2016.v4n1.89
Balbuena, H. C. (2017, febrero). ¿Cómo elaborar situaciones desafiantes para lograr aprendizajes en nuestros estudiantes? [Archivo en un blog]. http://hugocarlos.com/blog/44-como-elaborar-situaciones-desafiantes-para-lograr-aprendizajes-en-nuestros-estudiante
Baroody, A. J. (2000). El pensamiento matemático de los niños. Un marco evolutivo para maestros de preescolar, ciclo inicial y educación especial. Visor.
Barriteau Phaire, C. (2013). Managing mathematics: How does classroom management affect the maintenance of high cognitive demand tasks during lessons with standards-based instructional materials? (Publicación No. 3567225) [Tesis doctoral, New York University, United States]. ProQuest Dissertations Publishing LLC. https://search.proquest.com/docview/1417776134
Benedicto, C., Jaime, A., Gutiérrez, Á. (2015). Análisis de la demanda cognitiva de problemas de patrones geométricos. En C. Fernández Verdú, M. Molina González y N. Planas Raig (Eds.), Investigación en educación matemática XIX (pp. 153-162). Universidad de Alicante. http://rua.ua.es/dspace/handle/10045/51591
Bettencourt, K. (2017). Adolescent risk behavior and experiences with Flow [Tesis de doctorado]. William James College, United States.
Bologna, E. y Urrutia, A. (2011). Comparación entre dos grupos. En E. Bologna (Autor). Estadística para la psicología y educación (pp. 371-400). Brujas. https://www.academia.edu/27629330/Estadistica_Para_Psicologia_y_Educacion_1ed_Bologna
Budiarto, M. T., Khabibah, S. y Setianingsih, R. (2017). Construction of high school students’ abstraction levels in understanding the concept of quadrilaterals. International Education Studies, 10(2), 148-155. https://doi.org/10.5539/ies.v10n2p148
Butto Zarzar, C. M. y Delgado, J. (2020). Programa de talento matemático con estudiantes de educación básica: Un estudio con los procesos de generalización. Zona Próxima, 32, 1-13. http://rcientificas.uninorte.edu.co/index.php/zona/article/viewArticle/12079
Burgos, M., Giacomone, B., Beltrán-Pelliecer, P. y Godino, J. D. (2017). Reconocimiento de niveles de algebrización en una tarea de proporcionalidad por futuros profesores de matemáticas de secundaria. En J. M. Muñoz Escolano, A. ArnalBailera, P. Beltrán Pellicer, M. L. Callejo de la Vega y J. Carrillo Yáñez (Eds.), Investigación en educación matemática XXI (pp. 177-186). SEIEM. https://dialnet.unirioja.es/servlet/libro?codigo=705555
Campbell, D.T. y Stanley, J.C. (2011). Diseños experimentales y cuasiexperimentales en la investigación social. Amorrortu.
Canet-Juric, L., Introzzi, I., Andrés, M. L. y Stelzer, F. (2016). La contribución de las funciones ejecutivas a la autorregulación. Cuadernos de Neuropsicología, Panamerican Journal of Neuropsychology, 10(2), 106-128. http://www.cnps.cl/index.php/cnps/article/view/238/253
Caviedes-Barreda, S.; de Gamboa-Rojas, G. y Badillo-Jiménez, E. (2019). Conexiones matemáticas que establecen maestros en formación al resolver tareas de medida y comparación de áreas. Praxis, 15(1), 69-87. http://dx.doi.org/10.21676/23897856.2984
Challco, G. C., Andrade, F. R. H., Borges, S. S., Bittencourt, I. I. y Isotani, S. (2016). Toward a unified modeling of learner’s growth process and flow theory. Educational Technology & Society, 19(2), 215-227. https://drive.google.com/file/d/1B1nmLRKLKPrN3pLLuIvkwRwvLE6AwLS1/view
Cirino de Jesús, C. (2011). Análise crítica de tarefas matemáticas: um estudo com professores que ensinam matemática nos anos iniciais do ensino fundamental [Tesis de maestría]. Universidad Estatal de Londrina, Londrina, Brasil. http://www.educadores.diaadia.pr.gov.br/modules/mydownloads_01/visit.php?cid=4&lid=7101
Csikszentmihalyi, M. (2014). Learning, “flow,” and happiness. En Applications of Flow in Human Development and Education (pp. 153-172). https://doi.org/10.1007/978-94-017-9094-9_7
Csikszentmihalyi, M. (1998a). Creatividad. El fluir y la psicología del descubrimiento y la invención. Paidós.
Csikszentmihalyi, M. (1998b). Fluir (Flow). Una psicología de la felicidad. Editorial Kairós.
Csikszentmihalyi, M. y Csikszentmihalyi, I. S. (Eds.). (1998). Experiencia óptima. Estudios psicológicos del flujo en la conciencia. Desclée de Brouwer.
Dávila, K. y Trujillo, E. (2016). Rendimiento de los estudiantes de 6° grado de primaria en la prueba FAB de resolución de tareas de alta y baja demanda cognitiva referencias a fracciones [Tesis de maestría]. Pontificia Universidad Católica del Perú, Lima, Perú.
Defaz, G. J. (2017). El desarrollo de habilidades cognitivas mediante la resolución de problemas matemáticos. Journal of Science and Research, 2(5), 14-17. https://doi.org/10.26910/issn.2528-8083vol2iss5.2017pp14-17
Doyle, W. (1983). Academic work. Review of Educational Research, 53(2), 159-199. https://doi.org/10.3102/00346543053002159
Doyle, W. (1988). Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologists, 23(2), 167-180. https://doi.org/10.1207/s15326985ep2302_6
Ersöz, G. y Eklund, R. C. (2017). Behavioral regulation and dispositional flow in exercise among American College Students relative to stages of change and gender. Journal of American College Health, 65(2), 94-102. https://doi.org/10.1080/07448481.2016.1239203
Garces-Bascal, R. M., Cohen, L. y Tan, L. S. (2011). Soul behind the skill, heart behind the technique: Experiences of flow among artistically talented students in Singapore. Gifted Child Quarterly, 55(3), 194-207. https://doi.org/10.1177/0016986211413574
Georgius, K. (2013). Planning and enacting mathematical tasks of high cognitive demand in the primary classroom (Publicación No. 3618592) [Tesis doctoral]. The University of Nebraska, Lincoln. ProQuest Dissertations Publishing LLC. https://search.proquest.com/docview/1530478491
Godino, J. D., Batanero, C., Font, V., Cid, E., Ruiz, F. y Roa, R. (2004). Didáctica de la matemática para maestros. GAMI. https://www.ugr.es/~jgodino/edumat-maestros/manual/9_didactica_maestros.pdf
González, A. (2013). ¿A resolver problemas se enseña? El problema como contenido a ser enseñado de 1º a 7º. Homo Sapiens.
Hernández Sampieri, R., Fernández Collado, C. y Baptista Lucio, P. (2014). Metodología de la investigación (6ª Ed.). McGraw-Hill.
Holguin-Alvarez, J. A. Villa-Morocho, C., Montalvo-Callirgos, M., Villena-Guerrero, M., Carrasco-Núñez, Y. y Espinola-
Ayala, L. (2019). Significado del aprendizaje-enseñanza de la matemática en contextos lingüísticos del quechua y citadinos, Investigación Valdizana, 13(3), 143-155. https://doi.org/10.33554/riv.13.3.343
Hong, F.-Y. (2017). Antecedent and consequence of school academic optimism and teachers’ academic optimism model. Educational Studies, 43(2), 165-185. https://doi.org/10.1080/03055698.2016.1248902
León, J. y Youn, M.-J. (2016). El efecto de los procesos escolares en el rendimiento en matemática y las brechas de rendimiento debido a diferencias socioeconómicas de los estudiantes peruanos. Revista Peruana de Investigación Educativa, 8, 149-180. http://revistas.siep.org.pe/index.php/RPIE/article/view/72/138
Makvandi, A., Naderi, F., Makvandi, B., Pasha, R. y Ehteshamzadeh, P. (2018). Academic optimism and organizational citizenship behaviour amongst secondary school teachers. International Journal of Emotional Education, 10(1), 164-166. https://www.um.edu.mt/ijee
Mateus Nieves, E. (2015). Configuraciones epistémicas previas para dar significado global al objeto matemático “método de integración por partes”. En P. Lestón (Ed.), Acta Latinoamericana de Matemática Educativa, 28, 145-153). Comité Latinaomericano de Matemática Educativa. http://funes.uniandes.edu.co/10718/
McCormick, M. (2016). Exploring the cognitive demand and features of problem solving tasks in primary mathematics classrooms. En B. White, M. Chinnappan y S. Trenholm (Eds.), Opening up mathematics education research (Actas de la 39th conferencia anual del Mathematics Education Research Group of Australasia). MERGBA. https://eric.ed.gov/?q=+tasks+of+high+cognitive+demand&pg=2&id=ED572329
Mesurado, B. (2008). Validez factorial y fiabilidad del cuestionario de experiencia óptima (Flow) para niños y adolescentes. Revista Iberoamericana de Diagnóstico y Evaluación - e Avaliação Psicológica, 1(25), 159-178. http://www.redalyc.org/articulo.oa?id=459645445009
Ministerio de Educación, Perú. (2016a). Programa curricular de educación primaria. http://www.minedu.gob.pe/curriculo/
Ministerio de Educación, Perú. (2016b). Resultados de la evaluación censal de estudiantes ECE 2016. http://umc.minedu.gob.pe/resultadosece2016/
Mwadzaangati, L. (2019). Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom. Pythagoras, 40(1), 1-14. https://doi.org/10.4102/pythagoras.v40i1.458
Nakamura, J. (1998). Experiencia óptima y las aplicaciones del talento. En M. Csikszentmihalyi e I. S. Csikszentmihalyi (Eds.), Experiencia óptima. Estudios psicológicos del flujo en la conciencia (pp. 71-90). Desclée de Brouwer.
Ni, Y., Zhou, D., Li, X. y Li, Q. (2014). Relations of instructional tasks to teacher-student discourse in mathematics classrooms of chinese primary schools. Cognition and Instruction, 32(1), 2-43. https://doi.org/10.1080/07370008.2013.857319
Ni, Y., Zhou, D.-H. R., Cai, J., Li, X., Li, Q. y Sun, I. X. (2018). Improving cognitive and affective learning outcomes of students through mathematics instructional tasks of high cognitive demand. Journal of Educational Research, 111(6), 704-719. https://doi.org/10.1080/00220671.2017.1402748
Organización para la Cooperación y el Desarrollo Económico. (2015). PISA 2015: Primeros resultados. http://umc.minedu.gob.pe/resultados-de-evaluacion-pisa-2015/
Ponce, L., Preiss, D. y Núñez, M. (2010). Demanda cognitiva en la clase de matemáticas chilena. https://docplayer.es/40897836-Demanda-cognitiva-en-la-clase-de-matematicas-chilena.html
Rosillo Juárez, J. (2018). Desarrollo cognitivo y demanda cognitiva [Diapositivas en PowerPoint]. https://danielalmeyda.files.wordpress.com/2018/04/ppt-demanda-cognitiva.pdf
Sanz, P. (2015). El tránsito de la escuela pública a la escuela privada en el sector emergente de Lima Metropolitana: ¿Buscando mejor calidad? Revista Peruana de Investigación Educativa, 7, 95-125. http://revistas.siep.org.pe/index.php/RPIE/article/view/51
Scattarética Muñoz, F. (2017). Caracterización de tareas multiplicativas a partir de la invención de problemas matemáticos [Tesis de licenciatura]. Universidad Catolica del Norte, Antofagasta, Chile. http://funes.uniandes.edu.co/9296/
Sedigh Srouni, A., Jenaabadi, H. y Pourghaz, A. (2016). The relationship of mental pressure with optimism and academic achievement motivation among second grade male high school students. International Education Studies, 9(8), 127-133. https://doi.org/10.5539/ies.v9n8p127
Sosa Moguel, L. E., Aparicio Landa, E. y Cabañas-Sánchez, G. (2020). Fases del razonamiento inductivo que presentan profesores de matemáticas al resolver un problema de generalización, PNA, 14(2), 118-140. http://hdl.handle.net/10481/60196
Stein, M. K., Smith, M. S., Henningsen, M. y Silver, E. (2009). Implementing standards-based mathematics instruction: A Casebook for Professional Development (2da ed.). National Academy Press.
Suh, J. y Seshaiyer, P. (2015). Examining teachers’ understanding of the mathematical learning progression through vertical articulation during lesson study. Journal of Mathematics Teacher Education, 18(3) 207-229. http://dx.doi.org/10.1007/s10857-014-9282-7
Wu, J. H. y Lin, C. Y. (2017). A multilevel analysis of teacher and school academic optimism in Taiwan elementarys. Asia Pacific Education Review, 19(1), 53-62. https://doi.org/10.1007/s12564-017-9514-5
Yeh, Y.-C y Lin, C. S. (2018). Achievement goals influence mastery experience via two paths in digital creativity games among elementary school students. Journal of Computer Assisted Learning, 34(3), 223-232. https://doi.org/10.1111/jcal.12234
Downloads
Published
How to Cite
Issue
Section
License
1. In case the submitted paper is accepted for publication, the author(s) FREELY, COSTLESS, EXCLUSIVELY AND FOR AN INDEFINITE TERM transfer copyrights and patrimonial rights to Universidad Nacional (UNA, Costa Rica). For more details check the Originality Statement and Copyright Transfer Agreement
2. REUTILIZATION RIGHTS: UNA authorizes authors to use, for any purpose (among them selfarchiving or autoarchiving) and to publish in the Internet in any electronic site, the paper´'s final version, both approved and published (post print), as long as it is done with a non commercial purpose, does not generate derivates without previous consentment and recognizes both publisher's name and authorship.
3. The submission and possible publication of the paper in the Educare Electronic Journal is ruled by the Journal’s editorial policies, the institutional rules of Universidad Nacional and the laws of the Republic of Costa Rica. Additionally, any possible difference of opinion or future dispute shall be settled in accordance with the mechanisms of Alternative Dispute Resolution and the Costa Rican Jurisdiction.
4. In all cases, it is understood that the opinions issued are those of the authors and do not necessarily reflect the position and opinion of Educare, CIDE or Universidad Nacional, Costa Rica. It is also understood that, in the exercise of academic freedom, the authors have carried out a rogorous scientific-academic process of research, reflection and argumentation thar lays within the thematic scope of interest of the Journal.
5. The papers published by Educare Electronic Journal use a Creative Commons License:
The articles published by Educare Electronic Journal can be shared with a Creative Commons License: 
