Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity

Mehmet Fatih Öçal; Tugrul Kar; Gürsel Güler; Ali Sabri İpek

Ayuda

Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity

ÖÇAL, MEHMET FATIH ^[1] ; KAR, TUĞRUL ^[2] ; GÜLER, GÜRSEL ^[3] ; İPEK, ALI SABRI ^[2]
1. [1] Ağrı İbrahim Çeçen University
  
  Ağrı İbrahim Çeçen University
  
  Turquía
2. [2] Recep Tayyip Erdoğan University
  
  Recep Tayyip Erdoğan University
  
  Turquía
3. [3] Bozok Universitesi
  
  Bozok Universitesi
  
  Turquía
Mostrar afiliaciones +
Localización: REDIMAT, ISSN-e 2014-3621, Vol. 9, Nº. 3, 2020, págs. 243-272
Idioma: inglés
DOI: 10.17583/redimat.2020.3879
Títulos paralelos:
- Comparación de las habilidades para plantear problemas de los futuros maestros de matemáticas usando papel y lápiz en un entono de geometría dinámica en términos de creatividad
Enlaces
- Texto completo (pdf)
Resumen
- español
  Este estudio tiene como objetivo investigar las similitudes y diferencias entre las habilidades de pensamiento creativo de los futuros maestros de matemáticas usando lápiz y papel en un entorno apoyado por Geogebra en términos de planteamiento de problemas. Este estudio de caso utilizó un método de muestreo intencional para seleccionar a los participantes. Los resultados revelan que las actividades llevadas a cabo en el entorno de GeoGebra eran insuficientes para producir problemas creativos, y la principal utilidad de GeoGebra para los futuros maestros fue identificar sus errores relacionados con los conceptos matemáticos y las discrepancias entre los valores numéricos de los problemas planteados. Se discuten las razones del bajo rendimiento en plantear problemas: (i) falta de experiencia en la presentación de problemas, (ii) la estructura de la actividad de presentación de problemas y (iii) el conocimiento del contenido matemático de los futuros maestros.
- English
  This study aims to investigate the similarities and differences between prospective mathematics teachers’ creative thinking skills in paper-pencil test and on a Geogebra-supported environment in terms of problem-posing. This case study used purposive sampling method for determining the participants. Findings revealed that the activities carried out in the GeoGebra-supported environment were insufficient to produce creative problems, and GeoGebra’s main utility to prospective teachers was in identifying their mistakes related to mathematical concepts and discrepancies among numerical values of the problems posed. The reasons for the low achievement in posing problem were discussed: These were; (i) lack of problem-posing experience, (ii) the structure of problem-posing activity, and (iii) prospective teachers’ mathematical content knowledge.
Referencias bibliográficas
- Abramovich, S., & Cho, E. K. (2015). Technology as a medium for elementary preteachers' problem-posing experience in mathematics....
- Artigue, M. (2002). Learning mathematics in a cas environment: The genesis of a reflection about instrumentation and the dialectics between...
- Ayllon, M. F., Gomez, I. A., & Balleste-Claver, J. (2016). Mathematical thinking and creativity through mathematical problem posing and...
- Balka, D. S. (1974). Creative ability in mathematics. The Arithmetic Teacher, 21(7), 633-636.
- Beal, C. R., & Cohen, P. R. (2012). Each ourselves: Technology to support problem posing in the STEM classroom. Creative Education, 3(4),...
- Bonotto, C., & Santo, L. D. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school....
- Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect...
- Carter, J., & Ferrucci, B. (2009). Using Geogebra to enhance prospective elementary school teachers' understanding of geometry. Electronic...
- Chen, L. C., Dooren, W. V., & Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders’ problem-posing and problem-solving...
- Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment....
- Conteras, J. (2007). Unraveling the mystery of the origin of mathematical problems: Using a problem-posing framework with prospective mathematics...
- Cropley, A. J. (1999). Creativity and cognition: Producing effective novelty. Roeper Review, 21, 253–260.
- Cropley, A. (2006). In praise of convergent thinking. Creativity Research Journal, 18(3), 391-404. https://doi.org/10.1207/s15326934 crj1803_13
- Drijvers, P., & Gravemeijer, K. P. E. (2004). Computer algebra as an instrument: Examples of algebraic schemes. In D. Guin, K. Ruthven,...
- Drijvers, P., Kieran, C., & Mariotti M.A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles...
- Ellerton, N. F. (1986). Children’s made-up mathematics problems: A new perspective on talented mathematicians. Educational Studies in Mathematics,...
- Guilford, J. P. (1950). Creativity. American Psychologist, 5, 444–454.
- Harpen, V. X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students' mathematical...
- Haylock, D. (1997). Recognising mathemmatical creativity in Schoolchildren. Zentralblatt für Didaktik der Mathematik (ZDM), 29(3), 68-74....
- Hohenwarter, M., & Fuchs, K. (2004). Combination of dynamic geometry, algebra and calculus in the software system GeoGebra. In Computer...
- Işık, C., & Kar, T. (2012). The analysis of the problems posed by the preservice teachers about equations. Australian Journal of Teacher...
- Kerr, B. (2016). Creativity. In Encyclopædia Britannica. Retrieved from www.britannica.com/EBchecked/topic/142249/creativity
- Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics...
- Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2011). Indicators of creativity in mathematical PP: How indicative are they? In...
- Lavy, I. (2015). Problem posing activities in a dynamic geometry environment: When and How. In F. M. Singer, N.F. Ellerton & J. Cai (Ed)....
- Leikin, R., & Grossman, D. (2013). Teachers modify geometry problems: from proof to investigation. Educational Studies in Mathematics,...
- Leikin, R. (2015). Problem posing for and through investigations in a dynamic geometry environment. In F. M. Singer, N. Ellerton, & J....
- Leung, A. (2008). Dragging in dynamic geometry environment through the lens of variation, International Journal of Computers for Mathematical...
- Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralblatt für Didaktik der Mathematik (ZDM), 97(3), 81–85. https://doi.org/10.1007/s11858-997-0004-9
- Liang, H., & Sedig, K. (2010). Can interactive visualization tools engage and support pre-university students in exploring non-trivial...
- Luo, F. (2009). Evaluating the effectiveness and insights of pre-service elementary teachers’ abilities to construct word problems for fraction...
- Manuel, D., & Freiman, V. (2017). Differentiating instruction using a virtual environment: A study of mathematical PP among gifted and...
- Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics...
- National Council of Teachers of Mathematics [NCTM], (2000). Principles and standards for school mathematics. National Council of Teachers...
- Öçal, M. F. (2017). Geometri sorularındaki kavramsal hataları belirlemede GeoGebra’nın rolü [The role of GeoGebra in determining conceptual...
- Pehkonen, E. (1995). Introduction: Use of open-ended problems. International Reviews on Mathematical Education, 27(2), 55-57.
- Ranasinghe, A. I., & Leisher, D. (2009). The benefit of integrating technology into the classroom. International Mathematical Forum, 4(40)....
- Segal, R., Stupel, M., Sigler, A., & Jahangiril, J. (2018). The effectiveness of ‘what if not’ strategy coupled with dynamic geometry...
- Silber, S., & Cai, J. (2017). Pre-service teachers' free and structured mathematical problem posing, International Journal of Mathematical...
- Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
- Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt für Didaktik...
- Silver, E. A., & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
- Singer, F. M., & Voica, C. (2017). When mathematics meets real objects: How does creativity interact with expertise in problem solving...
- Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: new questions and directions. Educational...
- Singer, F. M., Pelczer, I., & Voica, C. (2011). Problem posing and modification as a criterion of mathematical creativity. In M. Pytlak,...
- Sriraman, B. (2005). Are giftedness and creativity synonyms in mathematics? An analysis of constructs within the professional and school realms....
- Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical PP. Unpublished PhD dissertation. University of...
- Stoyanova, E. (1997). Extending and exploring students' problem solving via problem posing: A study of Years 8 and 9 students involved...
- Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in mathematics...
- Thompson, P. W., Byerley, C., & Hatfield, N. (2013). A conceptual approach to calculus made possible by technology. Computers in the Schools,...
- Torrance, E. P. (1988). The nature of creativity as manifest in its testing. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary...
- Treffinger, D. J., Young, G. C., Selby, E. C., & Shepardson, C. (2002). Assessing creativity: A guide for educators (RM02170). University...
- Verillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity....
- Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers:...
- Yuan, X., & Sriraman, B. (2010). An exploratory study of relationships between students’ creativity and mathematical problem-posing abilities....