Articles
Año 9 No.26 Mayo - Agosto 2023
Problem posing in the mathematical teaching praxis
Facultad de Ciencias Físico Matemáticas. Benemérita Universidad Autónoma de Puebla
Bio
Facultad de Ciencias Físico Matemáticas. Benemérita Universidad Autónoma de Puebla
Bio
Facultad de Ciencias Físico Matemáticas. Benemérita Universidad Autónoma de Puebla
Bio
Abstract
Problem solving has been, for many years, the focus of attention when teaching mathematics. To achieve this, dissimilar
mathematical problems present in the literature and various didactic strategies are used that seek to bring
the resolution of these problems to a successful conclusion. The development of educational theories has evolved
towards student-centered teaching, where representing and responding to their realities plays a fundamental role.
From this perspective, the existing problems, for the most part, ceased to be pertinent, since the specific realities of
each group of students could not usually be represented by them. With this premise, the problems posing began
to be the center of the scientific production of several researchers, who not only demonstrated its relevance for the
teacher, but also found a close relationship between it and problem solving, the understanding of mathematical
concepts, creativity and mathematical ability, among others, which pointed to a need for students to also learn to
problems posing. In the Mexican curriculum, the problems posing is present as a disciplinary competence. Despite
this, its use in educational institutions is not widespread and there is little understanding of its importance. This article
aims to raise awareness about the advantages that its application entails and it is proposed to encourage it from
different spaces that enable a deeper understanding of this skill in the teaching community.
References
Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers‟ problem solving performance. Journal of Science and Mathematics Education, 56–69.
Akay, H., & Boz, N. (2008). The effect of problem posing oriented calculus-II instruction on academic success. ResearchGate. https://www.researchgate.net/publication/263627772_The_Effect_of_Problem_Posing_Oriented_Calculus-II_Instruction_on_Academic_Success
Akay, H., & Boz, N. (2010). The effect of problem posing oriented analysis-II course on the attitudes toward mathematics and mathematics self-efficacy. Australian Journal of Teacher Education, 35, 59–75.
Brown, S. I., & Walter, M. I. (1993). Problem posing: Reflection and applications. Hillsdale.
Cai, J., Koichu, B., Rott, B., Zazkis, R., & Jiang, C. (2022). Mathematical Problem Posing: Task Variables, Processes and Products. Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, 119–145.
Campistrous, L., & Rizo, C. (1996). Aprende a resolver problemas aritméticos. Editorial Pueblo y Educación.
Cankoy, O., & Darbaz, S. (2010). Effect of problem posing based problem solving instruction on understanding problem. Journal of Education, 38, 11–24.
Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT: International Journal on Math, Science and Technology Education, 3(1), 19–36. https://doi.org/https://doi.org/10.31129/lumat.v3i1.1049
D’Amore, B. (2011). Didáctica de las Matemáticas (2nd ed.). Cooperativa Editorial Magisterio.
Demir, B. B. (2005). The effect of instruction with problem posing on tenth grade students‟ probability achievement and attitudes toward probability. Middle East Technical University, Turkey.
English, L. D. (1997). The development of fifth-grade children‟s problem posing abilities. Educational Studies in Mathematics, 34, 183–217. https://doi.org/http://dx.doi.org/10.1023/A:1002963618035
English, L. D. (1998). Children‟s problem posing writing formal and informal contexts. Journal for Research in Mathematics Education, 29, 83–106.
Fetterly, J. (2010). An exploratory study of the use of a problem-posing of preservice elementary education teachers‟ mathematical creativity, beliefs, and anxiety. Florida State University, Tallahassee, FL.
Guvercin, S., Cilavdaroglu, A. K., & Savas, A. C. (2014). The effect of problem posing instruction on 9 th grade students‟ mathematics academic achievement and retention. Anthropologist, 17(1), 129–136.
Guvercin, S., & Verbovskiy, V. (2014). The effect of problem posing tasks used in mathematics instruction to mathematics academic achievement and attitudes toward mathematics. International Online Journal of Primary Education, 59–65.
Haghverdi, M., & Gholami, M. (2015). A study of the effect of using “What if Not” strategy in posing geometry problems. https://www.researchgate.net/publication/283327008
Ishak, A. H. N., Osman, S., Wei, C. K., Kurniati, D., Ismail, N., & Nanna, A. W. I. (2021). Teaching Strategies for Mathematical Problem-Solving through the Lens of Secondary School Teachers. TEM Journal, 10(2), 743–750. http://10.0.71.245/TEM102-31
Kesan, C., Kaya, D., & Guvercin, S. (2010). The effect of problem posing approach to the gifted student´s mathematical abilities. International Online Journal of Educational Sciences, 2, 677–687.
Killpatrick, J. (1987). Problem formulating: Where do good problems come from? Cognitive Science and Mathematics Education, 123–147.
Kojima, K., Miwa, K., & Matsui, T. (2015). Experimental study of learning support through examples in mathematical problem posing. Research and Practice in Technology Enhanced Learning. Doi%0A10.1007/s41039-015-0001-5
Ling, C. Y., Osman, S., Daud, M. F., & Hussin, W. (2019). Application of Vee Diagram as a problem-solving strategy in developing students’ conceptual a nd procedural knowledge. International Journal of Innovative Technology and Exploring Engineering (IJITEE), 8(10), 2796–2800. https://doi.org/https://doi.org/10.35940/ijitee.J9591.0881019
Malaspina, U. (2013). Variaciones de un problema. El caso de un problema de R. Douady. UNION, Revista Iberoamericana de Educación Matemática, 34, 141–149.
Malaspina, U. (2016). Creación de problemas: sus potencialidades en la enseñanza y aprendizaje de las Matemáticas. Cuadernos de Investigación y Formación En Educación Matemática, 0(15), 321–331.
Malaspina, U., & Vallejo, E. (2014). Creación de problemas en la docencia y la investigación. Reflexiones y Propuestas En Educación Matemática, 7–54.
Medina, J. E. (2003). La formulación y reformulación de problemas o preguntas en el aprendizaje de las matemáticas en el nivel medio superior. EDUCACIÓN MATEMÁTICA, 15(2), 77–103. http://www.revista-educacion-matematica.org.mx/descargas/vol15/vol15-2/vol15-2-4.pdf
Nuño, A. (2017). Planes de estudio de referencia del marco curricular común de la educación media superior. Primera edición, Secretario de Educación Pública. http://www.sems.gob.mx/work/models/sems/Resource/12491/4/images/libro.pdf
Papadopoulos, Ioannis Patsiala, N., Baumanns, L., & Rott, B. (2022). Multiple approaches to problem posing: theoretical considerations regarding its definition, conceptualisation, and implementation. CEPS Journal, 12(1), 13–34. https://doi.org/https://doi.org/10.26529/cepsj.878
Polya, G. (1945). How to Solve it. In Princeton University Press. https://doi.org/10.1017/cbo9780511616747.007
Sánchez, B., & Torres, J. (2017). La responsabilidad del currículo de matemáticas en la formación de ciudadanos que cuestionen la estructura social de clases. Una mirada desde perspectivas sociopolíticas. Revista Colombiana de Educación, 73, 299–322.
Silver, E. A. (1994). On mathematical problem posting. For the Learning of Mathematics, 19–28.
Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem posing research in mathematics education: New questions and directions. Educational Studies in Mathematics: An International Journal., 82(3). https://doi.org/10.1007/s10649-013-9478-2
Stoyanova, E. (1999). Extending students‟ problem solving via problem posing. The Australian Mathematics Teacher., 55(3), 29–35.
Subsecretaría de Educación Media Superior. (2018). Documento Base Bachillerato General ( MEPEO ).
Tichá, M., & Hošpesová, A. (2009). Problem posing and development of pedagogical content knowledge in pre-service teacher training. Proceedings of CERME 6, 1941–1950. www.inrp.fr/editions/cerme6
Walsh, M. (2016). Pre-service primary teachers‟ understanding of mathematical problem posing and problem solving: Exploring the impact of a study intervention. University of Limerick.
