پیوندهای مفید
آمار
| تعداد نشریات | 25 |
| تعداد شمارهها | 499 |
| تعداد مقالات | 3,892 |
| تعداد مشاهده مقاله | 5,972,334 |
| تعداد دریافت فایل اصل مقاله | 2,860,273 |
بررسی انواع درکهای دانشآموزان دورة متوسطه در مواجهه با شکل هندسی | ||
| مطالعات آموزشی و آموزشگاهی | ||
| دوره 11، شماره 2 - شماره پیاپی 31، تیر 1401، صفحه 353-387 اصل مقاله (2.32 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| نویسندگان | ||
| سیما ربی1؛ نسیم اصغری* 2 | ||
| 1گروه ریاضی و آمار، واحد تهرانمرکزی، دانشگاه آزاد اسلامی، تهران، ایران | ||
| 2گروه ریاضی و آمار، دانشکدة علوم و فناوری های همگرا، واحد تهرانمرکزی، دانشگاه آزاد اسلامی، تهران، ایران | ||
| چکیده | ||
| بازنمایی، یکی از ابزارهای مناسب برای نمایش روابط بین اجزای یک مفهوم یا موقعیت است، اما هر بازنمایی نمیتواند یک مفهوم ریاضی را بهطور کامل شرح دهد، بلکه فقط اطلاعاتی راجع به جنبههایی از آن مفهوم را نشان میدهد. حل یک مسئلة هندسی، اغلب اوقات نیازمند تعامل بین این سه درک (اجمالی، عاملی و استدلالی) و تشخیص تمایز آنها از یکدیگر است. این مطالعه بر آن است که چگونگی درکهای اجمالی و عاملی دانشآموزان دورة متوسطه در مواجهه با شکل هندسی را هنگام انجام تکالیف هندسی بررسی کند، بدین منظور طی یک مطالعة موردی آزمونی براساس چارچوب دووال (1998) متشکل از دو فعالیت با شرکت 305 دانشآموز پایة نهم دهم و یازدهم برگزار شد. تجزیه و تحلیل پاسخهای دانشآموزان براساس چارچوب استدلال شناختی دووال انجام شد. نتایج نشان داد بسیاری از دانشآموزان برای پاسخ به سؤالات هندسی از درک اجمالی نسبت به درک عاملی بیشتر استفاده میکنند. همچنین، تدریس هندسه با توجه به درکهای اجمالی و عاملی میتواند به دانشآموزان کمک کند تا از مسیر درک طبیعی نگاهکردن به شکل هندسی به مسیر درک استدلالی ارتقا یابند. بنابراین، یافتههای این تحقیق میتواند افق تازهای برای آموزش ضمن خدمت معلمان بگشاید. | ||
| کلیدواژهها | ||
| آموزش هندسه؛ بازنمایی؛ درک اجمالی و عاملی؛ دورة متوسطه | ||
| عنوان مقاله [English] | ||
| Investigating of Different Apprehensions of Secondary school Students When Confronting Geometric Figures | ||
| نویسندگان [English] | ||
| Sima Rabbi1؛ Nasim Asghary2 | ||
| 1Department of Mathematics and Statistics, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| 2Department of Mathematics and Statistics, Faculty of Science and Congruent Technologies, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| چکیده [English] | ||
| Representation is one of the appropriate tools for displaying the relationship between the components of a concept or a situation. However, any representation cannot completely describe a mathematical concept and can only provide information regarding some aspects of that concept. Solving a geometrical task often requires interaction among these three types of apprehension (perceptual, operative, and discursive) and recognition of their differences. This study aims to investigate middle school students’ apprehensions about confronting geometrical figures when doing geometry homework. Thus, a case study was designed. To this end, a test based on Duval (1998) was given to 305 students of the ninth, tenth, and eleventh grades. Qualitative analysis of the answers based on Duval’s cognitive argument indicated that most of the students use perceptual apprehension more than operative apprehension to solve the problems. Further, teaching geometry regarding cognitive apprehensions can help students to promote from the natural path of looking at a geometrical figure to the mathematical one. Therefore, the findings of this study can shed light on the in-service training of teachers. | ||
| کلیدواژهها [English] | ||
| Geometry education, Operative apprehension, Perceptual apprehension, Representation, Secondary School | ||
| مراجع | ||
|
سازمان پژوهش و برنامهریزی آموزشی (1396). ریاضی پایۀ نهم دورۀ اول متوسطه. چاپ ششم تهران: شرکت چاپ و نشر کتابهای درسی ایران.
سازمان پژوهش و برنامهریزی آموزشی (1397). هندسۀ (1) پایۀ دهم دورۀ دوم متوسطه. چاپ پنجم، تهران: شرکت چاپ و نشر کتابهای درسی ایران.
ظهوری زنگنه، بیژن (1384). هندسة خط و صفحه در ریاضیات مدرسه ای. رشد آموزش ریاضی، 22(80)، 11-4.
Creswell, J. W. (2014). Research Design: Qualitative, Quantitative and Mixed Methods Approaches (4th Ed.). Thousand Oaks, CA: Sage. Cuoco, A. A., & Curcio, F. R. (Eds.). (2001). The roles of representation in school mathematics. Reston, VA: National Council of Teachers of Mathematics. Duval, R. (1995). Geometrical Pictures: Kinds of Representation and Specific Processings. In R. Sutherland and J. Mason (Eds.) Exploiting Mental Imagery with Computers in Mathematics Education: NATO ASI Series (Vol. 138, pp. 142-157). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-57771-0. Duval, R. (1998). Geometry from a cognitive point of view. Perspectives on the Teaching of Geometry for the 21st Century, 37-52. Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. In F. Hitt and M. Santos (Eds.), Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol 1, pp. 3-27). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131. Even, R. (1998). Factors involved in linking representations of functions. Mathematical Behavior, 17(1), 105-121. Fischbein, E. (1993). The theory of figural concepts. Educational studies in mathematics, 24(2), 139-162. Gagatsis, A., & Elia, I. (2004). The effects of different modes of representations on mathematical problem solving. In M. Johnsen Hoines & A. Berit Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol.2, pp.447-454). Bergen, Norway: Bergen University College. Gagatsis, A., Monoyiou, A., Deliyianni, E., Elia, I., Michael, P., Kalogirou, P., Panaoura, A., & Philippou, A. (2010). One way of assessing the understanding of a geometrical figure. Acta Didactica Universitaties Comenianae Matematics, 10, 33-50. Gal, H. (2019). When the use of cognitive conflict is ineffective-problematic learning situations in geometry. Educational Studies in Mathematics, 102(2), 239-256. Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe, P. Nesher, P. Cobb, G. A. Goldin, and B. Greer (Eds.), Theories of Mathematical Learning (pp. 397–430). Hillsdale, NJ: Erlbaum. Goldin, G. A., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics (pp. 1-23). Reston, VA: NCTM. Hershkowitz, R., Duval, R., Bartolini Bussi, M. G., Boero, P., Lehrer, R., Romberg, T., Berthelot, R., Salin, M. H. & Jones, K. (1998) Reasoning in Geometry. In C. Mammana and V. Villani (Eds.) Perspectives on the Teaching of Geometry for the 21st Century: New ICMI Study Series (Vol. 5, pp. 29-83) Dordrecht, Springer. Jones, K. (1998), Theoretical frameworks for the learning of geometrical reasoning. Proceedings of the British Society for Research into Learning Mathematics, 18(1&2), 29-34. Jones, K. (2002). Issues in the Teaching and Learning of Geometry. In Haggarty, L. (Ed.), Aspects of Teaching Secondary Mathematics: Perspectives on practice (pp. 121-139). London, UK: Routledge Falmer. Karpuz, Y., & Atasoy, E. (2019). Investigation of 9th-grade students’ geometrical figure apprehension. European Journal of Educational Research, 8(1), 285-300. Kastberg, S. E. (2002). Understanding mathematical concepts: the case of the logarithmic function. (Doctoral Dissertation). University of Georgia, Athens. Laborde, C. (2005). The hidden role of diagrams in students’ construction of meaning in geometry. In J. Kilpatrick, C. Hoyles, and O. Skovsmose (Eds.), Meaning in mathematics education (pp. 159–179). Berlin, Heidelberg: Springer. Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159-174. Mariotti M. A. (1995). Images and Concepts in Geometrical Reasoning. In R. Sutherland and J. Mason (Eds.) Exploiting Mental Imagery with Computers in Mathematics Education: NATO ASI Series (Vol. 138, pp. 97-116). Berlin, Heidelberg: Springer. Mesquita, A. L. (1998). On conceptual obstacles linked with external representation in geometry. The Journal of Mathematical Behavior, 17(2), 183-195. Michael– Chrysanthou, P., & Gagatsis, A. (2013). Geometrical figures in geometrical task solving: an obstacle or a heuristic tool. Acta Didactica Universitatis Comenianae–Mathematics, 13, 17-30. Michael– Chrysanthou, P., & Gagatsis, A., Avgerinos, E., & Kuzniak, A. (2011). Middle and High school students’ operative apprehension of geometrical figures. Acta Didactica Universitatis Comenianae–Mathematics, 11, 45-55. Michael, P. M. (2013). Geometrical figure apprehension: cognitive processes and structure doctoral Dissertation, University of Cyprus. Michael-Chrysanthou, P., & Gagatsis, A. (2014). Ambiguity in the way of looking at geometrical figures. Revista Latinoamericana de Investigación en Matemática Educativa, 17(4), 165-179. Miller, A. (1999). Einstein, Poincaré, and the testability of geometry. In J. Grey (Ed), The Symbolic Universe: Geometry and Physics 1890-1930 (pp. 47-57). Oxford University Press. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. reston. VA: NCTM. Selling, S. K. (2015). Learning to represent, representing to learn. Mathematical Behavior, 41, 191-209. Sharygin, I., & Protasov, V. (2004, July). Does the school of the 21st century need geometry? In V. Sadovnichii (Ed), The 10th International Congress on Mathematical Education: National Presentation: Russia (pp. 167-177). Moscow, Russia: Institute of New Technology. Van Hiele, P. M. (1985). The child's thought and geometry. In D. Fuys, D. Geddes, & R. Tischler (Eds), English translation of selected writings of Dina van Hiele-Geldof and Pierre M. van Hiele (pp. 243-252). Brooklyn, NY: Brooklyn College. | ||
|
آمار تعداد مشاهده مقاله: 689 تعداد دریافت فایل اصل مقاله: 528 |
||