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## entrDetermination of the Relative Positions of Three Planes: Action ResearchÜç Düzlemin Birbirine Göre Konumunun Belirlenmesi: Eylem Araştırması

#### Tuba Ada [1] , Aytaç Kurtuluş [2]

The purpose of this study was to explore how a more effective lesson plan and teaching environment can be achieved so as to improve elementary mathematics teacher candidates achievement in analytical examination of planes in space. In order to improve achievement in expressing the relative positions of three planes not only algebraically but also visually the study used an action research approach as planned by the researchers. In Implementation 1, the teacher candidates were given the equations of three planes and they were asked to determine the relative positions of the planes so that their prior knowledge could be identified. In this stage, the candidate teachers tried to determine the relative positions of the planes in one direction by examining the plane equations in pairs. In Implementation 2, the candidate teachers were asked to find the solution set of the linear equation system consisting of three equations with three unknowns and to come up with geometric interpretation of this solution. In this stage, some of the candidate teachers were able to solve the equation, but they couldnt interpret it geometrically. In Implementation 3, Maple, a computer algebra system, was used so that the candidate teachers could visualize and observe the relative positions of the three planes by using the plane equations. In this stage, the candidate teachers associated the set of solutions of the plane equations with the three-dimensional images obtained with Maple. The results of the implementation showed that the proposed plan improved the mathematics teacher candidates’ visualization of the relative positions of the three planes.

Keywords: planes in space, analytic geometry, Maple, action research

Üç Düzlemin Birbirine Göre Konumunun Belirlenmesi: Eylem Araştırması

Öz

Anahtar kelimeler: Uzayda düzlemler, analitik geometri, Maple, eylem araştırması

Anahtar kelimeler: Uzayda düzlemler, analitik geometri, Maple, eylem araştırması

Determination of the Relative Positions of Three Planes:  Action Research

Abstract

The purpose of this study was to explore how a more effective lesson plan and teaching environment can be achieved so as to improve elementary mathematics teacher candidates achievement in analytical examination of planes in space. In order to improve achievement in expressing the relative positions of three planes not only algebraically but also visually the study used an action research approach as planned by the researchers. In Implementation 1, the teacher candidates were given the equations of three planes and they were asked to determine the relative positions of the planes so that their prior knowledge could be identified. In this stage, the candidate teachers tried to determine the relative positions of the planes in one direction by examining the plane equations in pairs. In Implementation 2, the candidate teachers were asked to find the solution set of the linear equation system consisting of three equations with three unknowns and to come up with geometric interpretation of this solution. In this stage, some of the candidate teachers were able to solve the equation, but they couldnt interpret it geometrically. In Implementation 3, Maple, a computer algebra system, was used so that the candidate teachers could visualize and observe the relative positions of the three planes by using the plane equations. In this stage, the candidate teachers associated the set of solutions of the plane equations with the three-dimensional images obtained with Maple. The results of the implementation showed that the proposed plan improved the mathematics teacher candidates’ visualization of the relative positions of the three planes.

Keywords: planes in space, analytic geometry, Maple, action research

Uzayda düzlemler, analitik geometri, Maple, eylem araştırması
• Baki, A., Kösa, T.& Karakuş, F. (2008). Uzay geometri öğretiminde 3D dinamik geometri
• yazılımı kullanımı: Öğretmen Görüşleri. 8th International Education Technology
• Baki, A., Erkan, İ., Demir, E.(2012). Ders planı etkililiğinin lesson study ile geliştirilmesi: bir
• aksiyon araştırması, X.Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Erişim
• Tarihi: 25.08.2015
• Bako, M. (2003). Different projecting methods in teaching spatial geometry.
• http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG7/TG7_Bako_cerme3.pdf
• Erişim tarihi: 25.08.2015
• Çepni S., Araştırma ve Proje Çalışmalarına Giriş (2010), KTÜ, Fatih Eğitim Fakültesi
• Yayınları.
• Kösa, T., Karakuş, F. ve Çakıroğlu, Ü. (2008). Uzay geometri öğretimi için üç boyutlu dinamik
• geometri yazılımı kullanarak çalışma yapraklarının geliştirilmesi, International
• Educational Technology Conference, Anadolu University, Eskişehir.
• Schumann, H. (2003). Computer aided treatment of 3d- problems in analytic geometry.
• Zentralblatt für Didaktik der Mathematik (ZDM), 35 (1), 7-13.
Bölüm Makaleler Yazar: Tuba Ada Yazar: Aytaç Kurtuluş Yayımlanma Tarihi : 31 Temmuz 2016
 Bibtex @ { tojqi256268, journal = {Turkish Online Journal of Qualitative Inquiry}, issn = {}, eissn = {1309-6591}, address = {}, publisher = {Abdullah KUZU}, year = {2016}, volume = {7}, pages = {165 - 198}, doi = {10.17569/tojqi.69714}, title = {Determination of the Relative Positions of Three Planes: Action Research}, key = {cite}, author = {Ada, Tuba and Kurtuluş, Aytaç} } APA Ada, T , Kurtuluş, A . (2016). Determination of the Relative Positions of Three Planes: Action Research. Turkish Online Journal of Qualitative Inquiry , 7 (3) , 165-198 . DOI: 10.17569/tojqi.69714 MLA Ada, T , Kurtuluş, A . "Determination of the Relative Positions of Three Planes: Action Research". Turkish Online Journal of Qualitative Inquiry 7 (2016 ): 165-198 Chicago Ada, T , Kurtuluş, A . "Determination of the Relative Positions of Three Planes: Action Research". Turkish Online Journal of Qualitative Inquiry 7 (2016 ): 165-198 RIS TY - JOUR T1 - Determination of the Relative Positions of Three Planes: Action Research AU - Tuba Ada , Aytaç Kurtuluş Y1 - 2016 PY - 2016 N1 - doi: 10.17569/tojqi.69714 DO - 10.17569/tojqi.69714 T2 - Turkish Online Journal of Qualitative Inquiry JF - Journal JO - JOR SP - 165 EP - 198 VL - 7 IS - 3 SN - -1309-6591 M3 - doi: 10.17569/tojqi.69714 UR - https://doi.org/10.17569/tojqi.69714 Y2 - 2020 ER - EndNote %0 Turkish Online Journal of Qualitative Inquiry Determination of the Relative Positions of Three Planes: Action Research %A Tuba Ada , Aytaç Kurtuluş %T Determination of the Relative Positions of Three Planes: Action Research %D 2016 %J Turkish Online Journal of Qualitative Inquiry %P -1309-6591 %V 7 %N 3 %R doi: 10.17569/tojqi.69714 %U 10.17569/tojqi.69714 ISNAD Ada, Tuba , Kurtuluş, Aytaç . "Determination of the Relative Positions of Three Planes: Action Research". Turkish Online Journal of Qualitative Inquiry 7 / 3 (Temmuz 2016): 165-198 . https://doi.org/10.17569/tojqi.69714 AMA Ada T , Kurtuluş A . Determination of the Relative Positions of Three Planes: Action Research. TOJQI. 2016; 7(3): 165-198. Vancouver Ada T , Kurtuluş A . Determination of the Relative Positions of Three Planes: Action Research. Turkish Online Journal of Qualitative Inquiry. 2016; 7(3): 198-165.

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