7. Sınıf Öğrencilerinin Dörtgenlerin Alan Formüllerini Oluşturma Süreçleri: RBC+C Modeli

Duygu Altaylı Özgül; Abdullah Kaplan

doi:10.30703/cije.1052000

EN TR

Examination of the Processes of Grade 7 Students to Constructing The Area Formula of Quadrilateral: RBC+C Model

Abstract

In this study, it is aimed to analyze the formation processes of 7th grade students in constructing area formulas in quadrilaterals according to the RBC+C model. In this study, case study, one of the qualitative research methods, was used. The study group of the research consists of 7th grade students in a public secondary school in the Central Anatolia region. While one of the two randomly selected classes was educated according to the teaching activities prepared according to the epistemic actions of the RBC+C model, the other class was taught according to the mathematics curriculum of the Ministry of National Education. Then, a total of 6 students, one from each with low, medium and high achievement levels, were selected from these two classes according to the maximum diversity sampling method. Semi-structured interviews were conducted with these students. As a data collection tool, two questions developed by the researcher to construction the area formula of the trapezoid and rhombus were used. The data obtained as a result of individual interviews with the students were analyzed using the RBC+C model. As a result of the study, the students in the classroom taught with the activities prepared according to the epistemic actions of the RBC+C model; It has been seen that the quadrilaterals pass to the level of creation by using the existing information structures in the process of constructing the area formula. It has also been observed that students with low achievement levels exhibit a self-confident attitude and try to explain their ideas using mathematical language. In line with these results, it is considered necessary and recommended to organize teaching activities that will allow students to learn meaningfully.

Keywords

7. Sınıf Öğrencilerinin Dörtgenlerin Alan Formüllerini Oluşturma Süreçleri: RBC+C Modeli

Öz

Bu çalışmada, 7. Sınıf öğrencilerinin dörtgenlerde alan formülü oluşturma konusundaki oluşturma süreçlerinin RBC+C modeline göre analiz edilmesi amaçlanmıştır. Bu araştırmada nitel araştırma yöntemlerinden durum çalışmasından yararlanılmıştır. Araştırmanın çalışma grubunu İç Anadolu bölgesindeki bir devlet ortaokulundaki 7. sınıf öğrencileri oluşturmaktadır. Rastgele seçilen iki sınıftan birine RBC+C modelinin epistemik eylemlerine göre hazırlanan öğretim faaliyetlerine göre eğitim yapılırken diğer sınıfa Milli Eğitim Bakanlığı matematik ders öğretim programına göre öğretim yapılmıştır. Daha sonra bu iki sınıftan maksimum çeşitlilik örnekleme yöntemine göre düşük, orta ve yüksek başarı düzeyine sahip birer öğrenci olmak üzere toplam 6 öğrenci seçilmiştir. Bu öğrencilerle yarı yapılandırılmış görüşme yapılmıştır. Veri toplama aracı olarak araştırmacı tarafından, yamuk ve eşkenar dörtgenin alan formülünü oluşturmalarına yönelik geliştirilen iki soru kullanılmıştır. Öğrencilerle yapılan bireysel görüşmeler sonucunda elde edilen veriler RBC+C modelinden yararlanılarak analiz edilmiştir. Çalışmanın sonucunda RBC+C modelinin epistemik eylemlerine göre hazırlanan etkinliklerle öğretim yapılan sınıftaki öğrencilerin; dörtgenlerin alan formülünü oluşturma süreçlerinde var olan bilgi yapılarını kullanarak oluşturma düzeyine geçtikleri görülmüştür. Ayrıca düşük başarı düzeyine sahip öğrencilerin özgüvenli bir tavır sergilediği ve matematiksel dil kullanarak fikirlerini açıklamaya çalıştığı da gözlemlenmiştir. Bu sonuçlar doğrultusunda öğrencilerin anlamlı öğrenmelerine fırsat verecek öğretim etkinliklerinin düzenlenmesi gerekli görülmekte ve önerilmektedir

Anahtar Kelimeler

Kaynakça

Altaylı Özgül, D. (2018). Ortaokul öğrencilerinin çokgenler konusundaki soyutlama süreçlerinin incelenmesi: RBC+C modeli. (Doktora Tezi). Atatürk Üniversitesi
Altun, M., ve Yılmaz, A. (2010). Lise öğrencilerinin parçalı fonksiyon bilgisini oluşturma ve pekiştirme süreci. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 311-337. http://dergipark.ulakbim.gov.tr/uefad/article/viewFile/5000152459/5000138271 adresinden edinilmiştir.
Battista, M. (1982). Understanding area and area formulas. Mathematics Teacher, 75(5), 362–368. Retrieved from http://www.jstor.org/stable/27962957
Baturo, A., and Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235–268. doi:10.1007/BF00376322
Dooley, T. (2007). Construction of knowledge by primary pupils: The role of whole-class interaction. CERME-5,1658-1668. Retrieved from https://www.researchgate.net/profile/Therese_Dooley/publication/265929686.pdf
Dreyfus, T. (2007). Processes of abstraction in context the nested epistemic actions model. Retrieved from http://medicina.iztacala.unam.mx/medicina/dreyfus.pdf
Dreyfus, T., and Tsamir, P. (2004). Ben’s consolidaiton of knowledge structures about infinite sets. Journal of Mathematical Behavior, 23(3), 271-300. doi:10.1016/j.jmathb.2004.06.002
Dreyfus, T., Hadas, N., Hershkowitz, R., and Schwarz, B. B. (2006). Mechanisms for consolidating knowledge construct. J. Novotna, H. Moraova, M. Kratha & N. Stehlikova (Eds.), Proceedings of the 30th Conference of International Group for the Psychology of Mathematics Education, Prague, Czech Repuclic: Charles University Faculty of Education, 2, 465-472.

Dreyfus, T., Hershkowitz, R., and Schwarz, B. (2001a). Abstraction in context: The case of peer interaction. Cognitive Science Quartely, 1(3), 307-368. Retrieved from https://www.researchgate.net/publication/273134154
Dreyfus, T., Hershkowitz, R., and Schwarz, B. (2001b). The construction of abstract knowledge in interaction. M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of International Group for the Psychology of Mathematics Education. (pp.377-384). Utrecht: The Netherlands.
Furinghetti, F., and Paola, D. (1999). Explorıng students’ımages and defınıtıons of area. In O. Zaslavsky (Ed.), In Proceedings of the Conference of the International Group for the Psychology of Mathematics Education, Israel, 2, 345-352. Retrieved from https://files.eric.ed.gov/fulltext/ED436403.pdf#page=775
Gürefe, N. (2017). Ortaokul öğrencilerinin alan ölçüm problemlerinde kullandıkları stratejilerin belirlenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 1-22. doi:10.16986/HUJE.2017032703
Hershkowitz, R., Hadas, N., and Dreyfus, T. (2006). Diversty in the construction of a group’s shared knowledge. J. Novatha, H. Moraova, M. Kratka & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 297-304. Prague : PME.
Hershkowitz, R., Hadas, N., Dreyfus, T., and Schwarz, B. (2007). Abstracting processes, from individuals’ constructing of knowledge to a group’s shared knowledge. Mathematics Education Research, 19(2), 41-68. Retrieved from https://link.springer.com/content/pdf/10.1007%2FBF03217455.pdf
Hershkowitz, R., Schwarz, B. B., and Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 195-222. http://dx.doi.org/10.2307/749673
Hershkowitz, R., Tabach, M., and Dreyfus, T. (2017). Creative reasoning and shifts of knowledge in the mathematics classroom, ZDM Mathematics Education, 49, 25-36. doi: 10.1007/s11858-016-0816-6
Hershkowitz, R., Tabach, M., Rasmussen, C., and Dreyfus, T. (2014). Knowledge shifts in a probability classroom: A case study coordinating two methodologies. ZDM Mathematics Education, 46, 363-387. https://doi.org/10.1007/s11858-014-0576-0
Huang, H. M. E. (2017). Curriculum interventions for area measurement instruction to enhance children’s conceptual understanding. International Journal of Science and Mathematics Education, 15(7), 1323-1341. doi:10.1007/s10763-016-9745-7
Huang, H. M. E., and Witz, K. G. (2011). Developing children's conceptual understanding of area measurement: A curriculum and teaching experiment. Learning and Instruction, 21(1), 1-13. doi:10.1016/j.learninstruc.2009.09.002
Huang, H. M. E., and Witz, K. G. (2013). Children’s conceptions of area measurement and their strategies for solving area measurement problems. Journal of Curriculum and Teaching, 2(1), 10-26. doi:10.5430/jct.v2n1p10.
Kabapınar, F. (2003). Kavram yanılgılarının ölçülmesinde kullanılabilecek bir ölçeğin bilgi-kavrama düzeyini ölçmeyi amaçlayan ölçekten farklılıkları. Kuram ve Uygulamada Eğitim Yönetimi, 35, 398-417. http://dergipark.gov.tr/download/article-file/108430 adresinden edinilmiştir.
Kamii, C., and Kysh, J. (2006). The difficulty of “length×width”: Is a square the unit of measurement? Journal of Mathematical Behavior, 25, 105–115. doi:10.1016/j.jmathb.2006.02.001
Katrancı, Y. (2010). Olasılığın temel kuralları bilgisinin yapılandırmacı kurama göre oluşturulması sürecinin incelenmesi (Yükseklisans tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi'nden edinilmiştir. (Tez No. 311069)
Katrancı, Y., ve Altun, M. (2013). İlköğretim ikinci kademe öğrencilerinin olasılık bilgisini oluşturma ve pekiştirme süreci. Kalem Eğitim ve İnsan Bilimleri Dergisi, 3(2), 11-58.
Kidman, G., and Cooper, T. (1997). Area integration rules for grades 4, 6 and 8 students. In E. Pehkonen (Ed.), Proceedings of the 21st conference of the international group for the psychology of the mathematics education (PME21) (pp. 136-143). Lahti Finland.
Kidron, I., and Dreyfus, T. (2008). Abstraction in context, combining constructions, justification and enlightenment. In M. Goos, R. Brown & K. Makar (Eds.), Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, Australia, 303-309.
Kidron, I., Lenfant, A., Bikner-Ahsbahs, A., Artigue, M., and Dreyfus, T. (2008). Toward networking three theoretical approaches: the case of social interactions. ZDM Mathematics Education, 40(2), 247-264. doi: 10.1007/s11858-008-0079-y
Koçak, M., and Soylu, Y. (2017). Analysis of pre-service mathematics teachers' teaching strategy knowledge of geometric formulas. Universal Journal of Educational Research, 5(3), 297-315. doi: 10.13189/ujer.2017.050302
Kordaki, M., and Potari, D. (1998). Children's approaches to area measurement through different contexts. The Journal of Mathematical Behavior, 17(3), 303-316. Retrieved from https://www.researchgate.net/profile/Maria_Kordaki/publication/222306293
Monaghan, J., and Özmantar, M. F. (2006). Abstraction and consolidation. Educational Studies in Mathematics, 62(3), 233-258. Retrieved from https://link.springer.com/content/pdf/10.1007%2Fs10649-006-8753-x.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Nitabach, E., and Lehrer, R. (1996). Research into practice: Developing spatial sense through area measurement. Teaching Children Mathematics, 2 (8), 473–476. Retrieved from http://www.jstor.org/stable/41198332
Olkun, S., Çelebi, Ö., Fidan. E., Engin., ve Gökgün, C. (2014). Birim kare ve alan formülünün Türk öğrenciler için anlamı. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 180-195. http://dergipark.gov.tr/download/article-file/87087 adresinden edinilmiştir.
Outhred, L. N., and Mitchelmore, M. C. (2000). Young children's intuitive understanding of rectangular area measurement. Journal for Research in Mathematics Education, 31(2), 144-167. doi: 10.2307/749749
Özçakır, B. (2013). The effects of mathematics instruction supported by dynamic geometry activities on seventh grade students achievement in area of quadrilaterals (Yükseklisans tezi). Yükseköğretim Kurulu Ulusal Tez Merkezi'nden edinilmiştir. (Tez No. 345124)
Özmantar, M. F. (2004). Scaffolding, abstraction, and emergent goals. In O. McNamara (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 24(2), 83-89. Retrieved from http://www.bsrlm.org.uk/IPs/ip24-2/BSRLM-IP-24-2-14.pdf
Özmantar, M. F., and Monaghan, J. (2005). Voices in scaffolding mathematical constructions. In M. Bosch (Ed.). Proceedings of CERME 4, Sant Feliu de Guixols, Spain, 1-10. Retrieved from http://www.mathematik.uni-dortmund.de/~erme/CERME4/CERME4_WG8.pdf#page=86
Özmantar, M. F., and Monaghan, J. (2006). Abstraction, scaffolding and emergent goals. In J. Novotna, M. Moraova, H. Kratha & N. Stehlikova (Eds.). Proceedings of the 30th International Conference for the Psychology of Mathematics Education, 2, 305-312. Retrieved from https://files.eric.ed.gov/fulltext/ED496934.pdf#page=313
Özmantar, M. F., and Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19(2), 89-112. Retrieved from https://link.springer.com/content/pdf/10.1007%2FBF03217457.pdf
Özmantar, M. F., and Roper, T. (2004). Mathematical Abstraction through Scaffolding. In M. J. Hoines & A. B. Fuglestad (Eds.). The 28th International Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway: PME, 3, 481-488. Retrieved from http://emis.ams.org/proceedings/PME28/RR/RR085_Ozmantar.pdf
Pesen, C. (2008). Yapılandırmacı öğrenme yaklaşıma göre matematik öğretimi. Ankara: Sempati Yayınları.
Prusak, N., Hershkowitz, R., and Schwarz, B. B. (2013). Conceptual learning in a principled design problem solving environment. Research in Mathematics Education, 15 (3), 266-285. doi: 10.1080/14794802.2013.836379
Özçakır Sümen, Ö. (2019). Primary school students' abstraction levels of whole-half-quarter concepts according to RBC theory. Journal on Mathematics Education, 10(2), 251-264.
Schofield, J. W. (1993). Increasing the generalizability of qualitative research. Open University Press.
Schwarz, B., Dreyfus, T., Hadas, N., and Hershkowitz, R. (2004). Teacher guidance of knowledge construction. M. J. Hoines & A. B. Fuglesad, (Eds.). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Norveç: Bergen University College, 169-176. Retrieved from http://emis.ams.org/proceedings/PME28/RR/RR175_Schwarz.pdf
Schwarz, B., Dreyfus, T., and Hershkowitz, R. (2009). The nested epistemic actions model for abstraction in context. In B. Schwarz, T. Dreyfus & R. Hershkowitz (Eds.), Transformation of knowledge through classroom interaction (pp. 11-41). Routledge: Taylor and Francis Group.
Schwarz, B., Hershkowitz, R., and Dreyfus, T. (2002). Emerging knowledge structures in and with algebra. In J. Novotna (Ed.). Proceedings of CERME 2, Czech Republic, 2, 81-91.
Sezgin Memnun D., ve Altun, M. (2012). İki altıncı sınıf öğrencisinin doğru denklemini oluşturma sürecinin incelenmesi. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 6(1), 171-200. http://dergipark.gov.tr/download/article-file/39848 adresinden edinilmiştir.
Sezgin Memnun, D., Aydın, B., Özbilen, Ö., and Erdoğan, G. (2017). The abstraction process of limit knowledge. Educational Sciences: Theory & Practice, 17, 345-371. http://dx.doi.org/10.12738/estp.2017.2.0404
Stake, E. R. (2010). Qualitative research: Studying how things work. New York: The Guilford Press.
Stehlikova, N. (2003). Building a Finite Arithmetic Structure: Interpretation in Terms of Abstraction in Context. In M. A. Mariotti (Ed.). Proceedings of CERME 3, Bellaria, Italy, 1-10.
Stephan, M., and Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. In D. H. Clements and G. Bright (Eds.), Learning and teaching measurement, 65th Yearbook (pp. 3–16). Reston, VA: National Council of Teachers of Mathematics.
Strutchens, M. E., Harris, K. A., and Martin, W. G. (2001). Assessing geometric and measurement understanding using manipulatives. Mathematics Teaching in Middle School, 6 (7), 402-405. Retrieved from http://www.jstor.org/stable/41180984
Sun, X. (2009). Renew the Proving Experiences: An experiment for enhancement of a trapezoid area formula proof constructions of student teachers by "One problem multiple solutions". In: F.-L. Lin, F.-J. Hsieh, G. Hanna and M. de Villers (Eds.), Proceedings of the International Commission on Mathematical Instruction (ICMI), Study 19 conference: Proof and Proving in Mathematics Education, Taipei Taiwan, 2, 178–183.
Tabach, M., Hershkowitz, R., Rasmussen, C., and Dreyfus, T. (2014). Knowledge shifts in the classroom- a case study. Journal of Mathematical Behavior, 33, 192-208. doi:10.1016/j.jmathb.2013.12.001
Tabach, M., Hershkowitz, R., and Schwarz, B. (2006). Constructing and consolidating of algebraic knowledge within dyadic processes: A case study. Educational Studies in Mathematics, 63, 235-258. Retrieved from https://link.springer.com/content/pdf/10.1007%2Fs10649-005-9012-2.pdf
Tabach, M., Rasmussen, C., Dreyfus, T., and Apkarian, N. (2020). Towards an argumentative grammar for networking: a case of coordinating two approaches. Educational Studies in Mathematics, 103, 139-155. https://doi.org/10.1007/s10649-020-09934-7
Tan Şişman, G., ve Aksu, M. (2009). Yedinci sınıf öğrencilerinin alan ve çevre konularındaki başarıları. İlköğretim Online, 8(1), 243-253. http://ilkogretim-online.org.tr adresinden edinilmiştir.
Tan Şişman, G., and Aksu, M. (2016). A Study on Sixth Grade Students’ Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume. International Journal of Science and Mathematics Education, 14(7), 1293–1319. doi: 10.1007/s10763-015-9642-5
Tossavainen, T., Suomalainen H., and Mäkäläinen, T. (2017). Student teachers’ concept definitions of area and their understanding about two-dimensionality of area, International Journal of Mathematical Education in Science and Technology, 48(4), 520-532. doi: 10.1080/0020739X.2016.1254298
Tsamir, P., and Dreyfus, T. (2002). Comparing infinite sets-a process of abstraction: The case of Ben. The Journal of Mathematical Behavior, 21(1), 1-23. https://doi.org/10.1016/S0732-3123(02)00100-1
Tumova, V. (2017). What influences grade 6 to 9 pupils’ success in solving conceptual tasks on area and volume. In Dooley, T., and Gueudet, G. (Eds.), Proceedings of the10th Congress of the European Society for Research in Mathematics Education (CERME10), Dublin, Ireland, (pp. 669-676).
Ulaş, T. ve Yenilmez, K. (2017). Sekizinci sınıf öğrencilerinin özdeşlik kavramını oluşturma süreçlerinin incelenmesi. International e-Journal of Educational Studies (IEJES), 1 (2), 103-117. http://dergipark.gov.tr/download/article-file/393568 adresinden edinilmiştir.
Van de Walle, J. A., Karp, K. S., and Bay Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally. 7th Edition. Boston, MA: Allyn & Bacon.
Walton, C., and Randolph, T. (2017). Alternative Methods for Understanding Area Formulas. Illinois Mathematics Teacher, 64(1), 1-6. Retrieved from http://journal.ictm.org/index.php/imt/article/view/89/103
Wood, T., and McNeal, B. (2003). Complexity in Teaching and Children's Mathematical Thinking. In A. N. Pateman, B. J. Dougherty, and J. T. Zilliox (Eds.), Proceedings of the 27th International Group for the Psychology of Mathematics Education Conference, Honolulu, Hawai, 4, 435-441. Retrieved from https://files.eric.ed.gov/fulltext/ED501153.pdf
Wood, T., Williams, G., and McNeal, B. (2006). Children's mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222-255. Retrieved from https://www.jstor.org/stable/30035059
Yeşildere İmre, S., ve Türnüklü, E. (2016). RBC soyutlama teorisi. E. Bingölbali, S. Arslan & İ. Ö. Zembat (Eds.), Matematik Eğitiminde Teoriler içinde (1. Baskı, ss. 459-473). Ankara: Pegem Akademi.
Yew, W. T., Zamri, S. N. A. S., and Lian, L. H. (2010). Examining Preservice Teachers’ Knowledge of Area Formulae. Procedia-Social and Behavioral Sciences, 8, 198-206. doi:10.1016/j.sbspro.2010.12.027
Yin, R., K. (2003). Case study research, designs and methods (3rd Edition). California: Sage Publications.
Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. The Journal of Mathematical Behavior, 25(3), 224-239. doi:10.1016/j.jmathb.2006.09.003

Ayrıntılar

Birincil Dil

Türkçe

Konular

-

Bölüm

Araştırma Makalesi

Yazarlar

Duygu Altaylı Özgül ^*
0000-0003-2749-5050
Türkiye

Abdullah Kaplan
0000-0001-6743-6368
Türkiye

Yayımlanma Tarihi

30 Haziran 2022

Gönderilme Tarihi

31 Aralık 2021

Kabul Tarihi

24 Haziran 2022

Yayımlandığı Sayı

Yıl 2022 Cilt: 11 Sayı: 2

DOI

https://doi.org/10.30703/cije.1052000

IZ

https://izlik.org/JA94SY79RE

Kaynak Göster

RIS / Bibtex

APA

Altaylı Özgül, D., & Kaplan, A. (2022). 7. Sınıf Öğrencilerinin Dörtgenlerin Alan Formüllerini Oluşturma Süreçleri: RBC+C Modeli. Cumhuriyet Uluslararası Eğitim Dergisi, 11(2), 420-437. https://doi.org/10.30703/cije.1052000