Examining The Efforts of Middle School 7th Grade Students To Draw Altitude In Parallelogram And Triangle

Abstract

The aim of this research is to examine the efforts of 7th grade students to draw altitude in parallelograms and triangles. Moreover, it is to reveal the difficulties students experience in drawing altitude. For this purpose, a case study from qualitative research methods was managed. Task-based interviews were conducted with ten 7th grade students and their efforts to draw altitude were examined. The task statuses offered to students consist of two parts: Altitudes for parallelograms tasks and altitudes for triangles tasks. The collected data were analysed with content analysis approach. As a result, it was seen that the students’ understanding of altitudes were low. In addition, some results of the difficulties experienced by the students are presented as themes.

Keywords

• Altitude
• parallelogram
• triangle

References

1. Akpınar, B. ve Akdoğan, S. (2010). Negatif bilgi kavramı: hata ve başarısızlıklardan öğrenme. Batı Anadolu Eğitim Bilimleri Dergisi (BAED), 1(1), 14-22.
2. Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics. Educational series 19. Brussels: International Academy of Education; Geneva: International Bureau of Education.
3. Baumard, P., ve Starbuck, Wi. H. (2005). Learning from failures: Why it may not happen, Long Range Planning, 38, 281–298.
4. Clements, D. H., Sarama, J. H., & Battista, M. (1998). Development of concepts of geometric figures in especially designed logo computer environment. Focus on Learning Problems in Mathematics, 20, 47-64.
5. Cutugno, P. & Spagnolo, F.Ç. (2002). Misconception about triangle in elementary school, http://www.math.unipa.it/grim/SiCutugnoSpa.PDF
6. Creswell, J. W. (2013). Research design: Qualitative, quantitative and mixed method approaches. Tousand Oaks Califormia: Sage Publications.
7. Duatepe, A.-Ersoy, Y. (2001). Teknoloji destekli matematik öğretimi-l: hesap makinesi ve okullarda geometri öğretimi. Matematik Etkinlikleri 2001 Sempozyumu, Ankara,110-119.
8. Fischbein, E. & T. Nachlieli, (1998). Concepts and figures in geometrical reasoning. International Journal of Science Education, 20, 1193-1211.

9. Grant, T., J. & Kline, K. (2003). Developing the building blocks of measurement with young children. Douglas, H. Clements ve George, W. Bright (Eds.), Learning and Teaching Measurement 2003 Yearbook (s.46-57). Reston,VA: NCTM.
10. Gutierrez, A. & Jaime, A. (1999). Pre-service primary teachers’ understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher of Education, 2(3), 253-275.
11. Gürefe, N., & Gültekin, S. H. (2016). Yükseklik kavramına dair öğrenci bilgilerinin incelenmesi. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi (KEFAD) Cilt 17, Sayı 2, Ağustos 2016, Sayfa 429-450.
12. Heinze, A. (2005). Mistake-handling activities in the mathematics classroom. In Chick, H. L. ve Vincent, J. L. (Eds.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, Melbourne 3, 105-112.
13. Hershkowitz, R. (1987). The acquisition of concepts and misconceptions in basic geometryor when “a little learning is a dangerous thing.” In J. Novak (Ed.), Proceedings of the 2nd International Seminar on Misconceptions and Educational Strategies in Science and Mathematics (Vol. III, pp. 238-251). Ithaca, NY: Cornell University.
14. Hızarcı, S., Ada, Ş. & Elmas, S. (2006) Geometrideki temel kavramların öğretilmesi ve öğrenilmesindeki hatalar. Kazım Karabekir Eğitim Fakültesi Dergisi, 13, 337-342.
15. Koichu, B., & Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathematics teachers. Educational Studies in Mathematics, 65(3), 349-365.
16. Krainer, K. (1993). Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction. Educational Studies in Mathematics, 24(1), 65–93.
17. Merriam, S. B. (2013). Nitel araştırma desen ve uygulama için bir rehber. (S. Turan, Çev. Ed.) Ankara: Nobel Yayıncılık
18. Miles, M. B., ve Huberman, A. M. (1994). Quality data analysis: An expanded sourcebook. Thousand Oaks: Sage Publications.
19. Ministry of National Education. (2018). Matematik dersi öğretim programı. https://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329, accessed at February 2021.
20. Minsky, M. (1994). Negative expertise. International Journal of Expert Systems, 7(1), 13–19.
21. Orhan, N., (2013). An Investigation of private middle school students' common errors in the domain of area and perimeter and the relationship between their geometry selfefficacy beliefs and basic procedural and conceptual knowledge of area and perimeter.[Unpublished master thesis]. Middle East Technical University.
22. Öksüz, C., & Başışık, H. (2019). 5. sınıf öğrencilerinin çokgenler ve dörtgenler konularında sahip oldukları kavram yanılgılarının belirlenmesi. Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi, (20), 413-430.
23. Polat, S., & Dede, Y. (2020). Matematik öğretmenlerinin matematiksel görev oluşturma durumlarının incelenmesi. Gazi Eğitim Bilimleri Dergisi, 6(2), 210-239.
24. Senger, E., (2019). The effect of socıomathematıcal norms and technology integrated instructıon on 6th grade students' understandıng of altıtude. (Publication No. 602907) Master thesis, Boğaziçi University.
25. Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80.
26. Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection. Mathematics Teaching in the Middle School, 3, 268-275.
27. Stephen , M. & Clements, D. H. (2003). Linear and area measurement in prekindergarten to grade 2. Douglas. H. Clements & George. W. Bright (Eds.), Learning and Teaching Measurement 2003 Yearbook (s. 3-16). Reston,VA: NCTM.
28. Sullivan, P., Clarke, D. M., Clarke, B. A., & O’Shea, H. (2009). Exploring the relationship between tasks, teacher actions, and student learning. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), In search of theories in mathematics education (Proceedings of the 33rd Conference of the International Group of Psychology of Mathematics Education, 5, 185-192.
29. Tomooğlu, Ö. (2017). 6. Sınıf öğrencilerine alan ölçme konusunun öğretimine yönelik bir eylem araştırması. (Publication No. 469672) Master thesis, Eskişehir Osmangazi Üniversitesi.
30. Vinner, S. & Hershkowitz, R. (1983). On concept formation in geometry. Zentralblatt fur didactic der mathematic, 15, 20-25.
31. Yıldırım, A. & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
32. Yin, R. K. (2015). Case study research: Design and methods. Thousand Oaks, California: Sage Publications.