Öz
Dinamik geometri yazılımları (DGY), bir geometrik özelliğin keşfedilmesi, genellenmesi ve ispatlanması için önemli bir potansiyele sahiptir. Araştırmalar, DGY’nin bu bağlamda etkin kullanımının doğal bir süreç olmadığının altını çizmekte ve öğretmenin rolünün önemine dikkat çekmektedirler. Bu çalışmada, üçgenin yardımcı elemanlarının uzunluklarının DGY ortamında karşılaştırılmasına yönelik tasarlanan bir öğretimde öğretmenin keşif, varsayım ve ispat süreçlerindeki rolünü incelemek amaçlanmıştır. Durum çalışması yönteminin benimsendiği çalışmada beş yıldan fazla mesleki tecrübeye sahip ve dinamik geometri yazılımlarını derslerinde kullanmaya çalışan bir matematik öğretmeninin hazırlamış olduğu öğretim planına ve öğretim seansına odaklanılmıştır. Çalışmanın verileri, öğretmenin hazırladığı detaylı öğretim planından, öğretim seansının video kaydından ve öğretmenin uygulama sonrası raporundan oluşmaktadır. Veriler, öğretmenin öğretim sürecini planlarken başvurduğu Didaktik Durumlar Teorisinin aşamalarına göre betimsel olarak analiz edilmiştir. Verilerin analizi öğretmenin ölçme aracından elde edilen bilgileri ön plana çıkardığını ve ölçme aracı kullanılarak elde edilen ampirik doğrulamadan matematiksel doğrulamaya geçişi sağlamakta yetersiz kaldığını ortaya koymaktadır.
Anahtar Kelimeler
Dinamik geometri sürükleme ölçme üçgenin yardımcı elemanları Didaktik durumlar teorisi Ortaokul 7. sınıf
Teşekkür
bildiri olarak sunulmuştur
Kaynakça
- Ainsworth, S. (2008). How should we evaluate multimedia learning environments?. In Understanding multimedia documents (pp. 249-265). Springer US.
- Arzarello, F., Olivero, F., Paola, D. et Robutti O. (2002) A cognitive analysis of dragging practises in Cabri environments. Zentralblatt für Didaktik der Mathematik 34, 66–72
- Baccaglini-Frank, A., & Mariotti, M.A. (2010) Generating Conjectures in Dynamic Geometry: the Maintaining Dragging Model. International Journal of Computers for Mathematical Learning, 15(3), 225-253.
- Balacheff N. (1988) A study of students' proving processes at the junior high school level. In: Second UCSMP international conference on mathematics education. Chicago: NCTM.
- Bintaş, J., Ceylan, B., & Dönmez, O. (2006). Dinamik geometri yazılımları aracılığıyla ispat yoluyla öğrenme, Eğitimde Çağdaş Yönelimler–3 Yapılandırmacılık ve Eğitime Yansımaları Çalıştayı (29 Nisan 2006). İzmir: Tevfik Fikret Okulları.
- Brousseau, G. (1997). Theory of Didactical Situations in Mathematics : Didactique des mathématiques, 1970-1990. Kluwer Academic Publishers (Springer).
- Chazan, D. (1993) High school geometry students' justification for their views of empirical evidence and mathematical proof. Educ Stud Math 24, 359–387
- Christou , C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through Exploration in dynamic geometry environments. International Journal of Science and Mathematics Education (2004) 2: 339–352.
- Christou , C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through Exploration in dynamic geometry environments. International Journal of Science and Mathematics Education (2004) 2: 339–352.
- Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Montana Mathematics Enthusiast (TMME), 2(2), 125-143.
- De Villiers, M. (2003) Rethinking Proof with Sketchpad 4. Emeryville, CA: Key CurriculumPress,
- Edwards, L. (1997) Exploring the territory before proof: Students' generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2, pp. 187-215.
- Erdoğan, A. (2016). Didaktik durumlar teorisi. E. Bingölbali, S. Arslan, ve İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler içinde (s. 413-430). Ankara: Pegem.
- Güven, B., & Karataş, İ. (2003). Dinamik geometri yazılımı cabri ile geometri öğrenme: Öğrenci görüşleri. The Turkish Online Journal of Educational Technology – TOJET , 2 (2).
- Healy, L. & Hoyles, C. (2001). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6, 235–256.
- Healy, L., Hoyles, C. (2002) Software Tools for Geometrical Problem Solving: Potentials and Pitfalls. International Journal of Computers for Mathematical Learning 6, 235–256
- Işıksal, M., & Aşkar, P. (2003). Elektronik tablolama ve dinamik geometri yazılımını kullanarak çalışma yapraklarının geliştirilmesi. İlköğretim Online, 2(2).
- Jones, K. (2000). Providing a foundation for a deductive reasoning: students’ interpretation when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1-2), 55–85.
- Jones, Keith (2000) Providing a foundation for deductive reasoning: students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44 (1-2), 55-85
- Köse, N. Y., & A. Özdaş (2009). İlköğretim 5. sınıf öğrencileri geometrik şekillerdeki simetri doğrularını cabri geometri yazılımı yardımıyla nasıl belirliyorlar? İlköğretim-Online, 8(1), 159-175.
- Laborde C. (2005) The Hidden Role of Diagrams in Students’ Construction of Meaning in Geometry. In: Kilpatrick J., Hoyles C., Skovsmose O., Valero P. (eds) Meaning in Mathematics Education. Mathematics Education Library, vol 37. Springer, New York, NY
- Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.
- Lagrange, J.-B., & Ozdemir Erdogan, E. (2009). Teachers’ emergent goals in spreadsheet-based lessons: analyzing the complexity of technology integration. Educational Studies in Mathematics, 71(1), 65–84
- Marrades, R., & Gutiérrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, pp. 87-125.
- Olivero, F., & Robutti, O. (2007). Measuring in dynamic geometry environments as a tool for conjecturing and proving. International Journal of Computers for Mathematical Learning, 12 (2), 135 - 156.
- Pandiscio, E. A. (2002). Alternative geometric constructions: Promoting mathematical reasoning. Mathematics Teacher, 95(1), 32–36.
- Soldano, C. & Arzarello, F. (2016). Learning with touchscreen devices: game strategies to improve geometric thinking. Mathematics Education Research Journal, 28, 9–30.
- Straesser, R. (2001). Cabri-geometre: Does Dynamic Geometry Software (DGS) change geometry and its teaching and learning?, International Journal of Computers for Mathematical Learning, Vol. 6, pp.319-333.
- Vadcard L. (1999) La validation en géométrie avec Cabri-géomètre : mesures exploratoires et mesures probatoires. Petit X 50, 5-21
- Yerushalmy, M. (2005). Challenging known transitions: Learning and teaching algebra with technology. For the learning of Mathematics, 25(3), 37-42.
Öz
The potential of Dynamic Geometry Software (DGS) in exploring, conjecturing and proving process has been revealed and the complexity of an effective use of DGS in this purpose has been underlined. The aim of this study is to examine this process in a teaching session which was designed to allow 7th grade students comparing the lengths of the auxiliary elements of a triangle. This case study focuses on that teaching session prepared by a mathematics teacher who has used DGS in her courses. The data of the study included the detailed plan of the teacher, the video and audio recording of the teaching session and the teacher’s report about the session. The data were descriptively analyzed according to the teaching design principles of the theory of didactical situations, which had also been used by the teacher in planning the teaching. The results showed that students exclusively used measuring tools and the teacher could not help students move from empirical verifications based on measurements to mathematical arguments as a first step pf proving.
Kaynakça
- Ainsworth, S. (2008). How should we evaluate multimedia learning environments?. In Understanding multimedia documents (pp. 249-265). Springer US.
- Arzarello, F., Olivero, F., Paola, D. et Robutti O. (2002) A cognitive analysis of dragging practises in Cabri environments. Zentralblatt für Didaktik der Mathematik 34, 66–72
- Baccaglini-Frank, A., & Mariotti, M.A. (2010) Generating Conjectures in Dynamic Geometry: the Maintaining Dragging Model. International Journal of Computers for Mathematical Learning, 15(3), 225-253.
- Balacheff N. (1988) A study of students' proving processes at the junior high school level. In: Second UCSMP international conference on mathematics education. Chicago: NCTM.
- Bintaş, J., Ceylan, B., & Dönmez, O. (2006). Dinamik geometri yazılımları aracılığıyla ispat yoluyla öğrenme, Eğitimde Çağdaş Yönelimler–3 Yapılandırmacılık ve Eğitime Yansımaları Çalıştayı (29 Nisan 2006). İzmir: Tevfik Fikret Okulları.
- Brousseau, G. (1997). Theory of Didactical Situations in Mathematics : Didactique des mathématiques, 1970-1990. Kluwer Academic Publishers (Springer).
- Chazan, D. (1993) High school geometry students' justification for their views of empirical evidence and mathematical proof. Educ Stud Math 24, 359–387
- Christou , C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through Exploration in dynamic geometry environments. International Journal of Science and Mathematics Education (2004) 2: 339–352.
- Christou , C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2004). Proofs through Exploration in dynamic geometry environments. International Journal of Science and Mathematics Education (2004) 2: 339–352.
- Christou, C., Mousoulides, N., Pittalis, M., & Pitta-Pantazi, D. (2005). Problem solving and problem posing in a dynamic geometry environment. The Montana Mathematics Enthusiast (TMME), 2(2), 125-143.
- De Villiers, M. (2003) Rethinking Proof with Sketchpad 4. Emeryville, CA: Key CurriculumPress,
- Edwards, L. (1997) Exploring the territory before proof: Students' generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2, pp. 187-215.
- Erdoğan, A. (2016). Didaktik durumlar teorisi. E. Bingölbali, S. Arslan, ve İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler içinde (s. 413-430). Ankara: Pegem.
- Güven, B., & Karataş, İ. (2003). Dinamik geometri yazılımı cabri ile geometri öğrenme: Öğrenci görüşleri. The Turkish Online Journal of Educational Technology – TOJET , 2 (2).
- Healy, L. & Hoyles, C. (2001). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6, 235–256.
- Healy, L., Hoyles, C. (2002) Software Tools for Geometrical Problem Solving: Potentials and Pitfalls. International Journal of Computers for Mathematical Learning 6, 235–256
- Işıksal, M., & Aşkar, P. (2003). Elektronik tablolama ve dinamik geometri yazılımını kullanarak çalışma yapraklarının geliştirilmesi. İlköğretim Online, 2(2).
- Jones, K. (2000). Providing a foundation for a deductive reasoning: students’ interpretation when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44(1-2), 55–85.
- Jones, Keith (2000) Providing a foundation for deductive reasoning: students' interpretations when using dynamic geometry software and their evolving mathematical explanations. Educational Studies in Mathematics, 44 (1-2), 55-85
- Köse, N. Y., & A. Özdaş (2009). İlköğretim 5. sınıf öğrencileri geometrik şekillerdeki simetri doğrularını cabri geometri yazılımı yardımıyla nasıl belirliyorlar? İlköğretim-Online, 8(1), 159-175.
- Laborde C. (2005) The Hidden Role of Diagrams in Students’ Construction of Meaning in Geometry. In: Kilpatrick J., Hoyles C., Skovsmose O., Valero P. (eds) Meaning in Mathematics Education. Mathematics Education Library, vol 37. Springer, New York, NY
- Laborde, C. (2001). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.
- Lagrange, J.-B., & Ozdemir Erdogan, E. (2009). Teachers’ emergent goals in spreadsheet-based lessons: analyzing the complexity of technology integration. Educational Studies in Mathematics, 71(1), 65–84
- Marrades, R., & Gutiérrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, pp. 87-125.
- Olivero, F., & Robutti, O. (2007). Measuring in dynamic geometry environments as a tool for conjecturing and proving. International Journal of Computers for Mathematical Learning, 12 (2), 135 - 156.
- Pandiscio, E. A. (2002). Alternative geometric constructions: Promoting mathematical reasoning. Mathematics Teacher, 95(1), 32–36.
- Soldano, C. & Arzarello, F. (2016). Learning with touchscreen devices: game strategies to improve geometric thinking. Mathematics Education Research Journal, 28, 9–30.
- Straesser, R. (2001). Cabri-geometre: Does Dynamic Geometry Software (DGS) change geometry and its teaching and learning?, International Journal of Computers for Mathematical Learning, Vol. 6, pp.319-333.
- Vadcard L. (1999) La validation en géométrie avec Cabri-géomètre : mesures exploratoires et mesures probatoires. Petit X 50, 5-21
- Yerushalmy, M. (2005). Challenging known transitions: Learning and teaching algebra with technology. For the learning of Mathematics, 25(3), 37-42.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2020 |
| Gönderilme Tarihi | 17 Şubat 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 14 Sayı: 1 |
