Are 9th grade students ready to engage in the theoretical discursive process in geometry?

• Karpuz, Yavuz ^[2] ; Güven, Bülent ^[1]
  1. [1] Karadeniz Technical University

     Karadeniz Technical University

     Turquía

     
  2. [2] Recep Tayyip Erdogan University
• Localización: REDIMAT, ISSN-e 2014-3621, Vol. 11, Nº. 1, 2022 (Ejemplar dedicado a: REDIMAT), págs. 86-112
• Idioma: inglés
• DOI: 10.17583/redimat.3667
• Títulos paralelos:
  • ¿Están listos los estudiantes de noveno grado para participar en el proceso de discurso teórico en geometría?
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Este estudio se realizó para examinar si los estudiantes de noveno grado recién matriculados estaban listos para participar directamente en el proceso discursivo teórico desde la perspectiva del modelo cognitivo de Duval. La muestra del estudio estuvo compuesta por 51 estudiantes de noveno grado recién matriculados entre las edades de 14 y 15 años, que no habían recibido ninguna instrucción previa en geometría. Muchos de los estudiantes no pudieron mostrar los comportamientos necesarios para el proceso discursivo teórico. Los estudiantes en su mayoría no lograron convertir información discursiva en información perceptiva, escribir información discursiva basada en información perceptiva y hacer inferencias basadas en información discursiva. Estos hallazgos indican que los recién graduados de la escuela secundaria no están lo suficientemente preparados para participar directamente en el proceso discursivo teórico y, por lo tanto, podrían experimentar dificultades en habilidades de orden tan alto como proporcionar pruebas que requieren el proceso discursivo teórico.

  • English

    This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval’s Cognitive Model. The sample of the study was comprised of 51 newly-enrolled 9thgrade students between the ages of 14 and 15, who had not received any prior geometry instruction. These 51 students were posed two open-ended questions that would enable them to make a transition between perceptual and discursive apprehension. The qualitative data obtained from the open-ended questions were classified into three categories, and clinical interviews were held with three students from each category. According to the findings obtained from the study, many of the students could not display the necessary behaviors for theoretical discursive process. Students were mostly unsuccessful in converting discursive information into perceptual information, in writing discursive information based on perceptual information, and making inferences based on discursive information. These findings indicate that recent graduates of secondary school are not ready enough to directly engage in theoretical discursive process and, thus, they could experience difficulties in such high order skills as providing proof requiring the theoretical discursive process. 

• Referencias bibliográficas
  • Coşkun, F. (2009). Ortaöğretim öğrencilerinin Van Hiele geometri anlama seviyeleri ile ispat yazma becerilerinin ilişkisi [Correlation between...
  • Cuoco, A., Goldenberg, E. P. & Mark, J. (1996). Habits of mind: An organizing principle for mathematics curricula. The Journal of Mathematical...
  • Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In R. Sutherland & J. Mason (Ed.), Exploiting...
  • Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Ed.), Perspectives on the teaching of geometry...
  • Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. Retrieved...
  • Fischbein, E. (1993). The theory of figural concepts. Educational studies in mathematics, 24(2), 139-162.
  • Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38, 11–50
  • Fischbein, E. & Nachlieli, T. (1998). Concepts and figures in geometrical reasoning. International Journal of Science Education, 20(10),...
  • Fischbein, E., & Kedem, I. (1982). Proof and certitude in the development of mathematics thinking. In A. Vermandel (Ed.), Proceedings...
  • Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele Model of Thinking in Geometry among Adolescents. Journal for Research in Mathematics...
  • Goldin, G., A. (1997). Chapter 4: Observing Mathematical Problem Solving through Task-Based Interviews. Journal for Research in Mathematics...
  • Güven, B. (2006). Öğretmen adaylarının küresel geometri anlama düzeylerinin karakterize edilmesi. [Characterizing student mathematics teachers’...
  • Güven, B., Karataş, İ. (2009). The effect of dynamic geometry software (cabri) on pre-service elementary mathematics teachers' achievement...
  • Harel, G. & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. Research in collegiate mathematics education...
  • Healy, L. & Hoyles, C. (1998). Justifying and proving in school mathematics: Technical report on the nationwide survey. London, United...
  • Jones, K. (1998). Theoretical frameworks for the learning of geometrical reasoning. In Proceedings of the british society for research into...
  • Jones, K. (2000). Providing a foundation for deductive reasoning: Students' interpretations when using dynamic geometry software and their...
  • Llinares, S. & Clemente, F. (2014) Characteristics of Pre- Service Primary School Teachers’ Configural Reasoning, Mathematical Thinking...
  • Mason, M. M. (1998): The van Hiele levels of geometric understanding. In: The Professional Handbook for Teachers Geometry: Boston: McDougal-Littell/Houghton-Mifflin,...
  • McCrone, S. M., & Martin, T. S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Math, Science...
  • Meyer, M. (2010). Abduction—A logical view for investigating and initiating processes of discovering mathematical coherences. Educational...
  • Michael, P. (2013). Geometrical figure apprehension: cognitive processes and structure (Unpublished doctoral dissertation). The University...
  • Michael, P., Gagatsis, A., Avgerinos, E., & Kuzniak, A. (2011). Middle and High school students’ operative apprehension of geometrical...
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Özlem, D. (1994). Mantık [Logic]. İstanbul, Turkey: Ara Yayıncılık.
  • Ramatlapana K. and Berger M. (2018). Prospective mathematics teachers’ perceptual and discursive apprehensions when making geometric connections....
  • Senk, S. (1989). Van Hiele levels and achievement in writing geometry Proofs. Journal for Research in Mathematics Education, 20(3), 309-321.
  • Senk, S. L. (1985). How well do students write geometry proofs? Mathematics Teacher, 78, 448-456.
  • Sriraman, B. (2004). Gifted ninth graders' notions of proof: Investigating parallels in approaches of mathematically gifted students and...
  • Stylianides, G. J. & Stylianides, A. J. (2008). Proof in school mathematics: Insights from psychological research into students' ability...
  • Torregrosa, G. & Quesada, H. (2008). The coordination of cognitive processes in solving geometric problems requiring proof. In Proceedings...
  • Türkiye Cumhuriyeti Milli Eğitim Bakanlığı [MoNE]. (2013a). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı [Republic...
  • Türkiye Cumhuriyeti Milli Eğitim Bakanlığı [MoNE]. (2013b). Ortaokul Matematik Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı [Republic of...
  • Ubuz, B. (1999). 10. ve 11. sınıf öğrencilerinin temel geometri konularındaki hataları ve kavram yanılgıları [10th and 11th grade students’...