Ortaokul Öğrencilerinin Alan Ölçme Bilgi ve Becerilerinin İncelenmesi

Year 2023, , 342 - 370, 20.10.2023

Zeynep Çavuş Erdem

https://doi.org/10.17522/balikesirnef.1348147

Abstract

Bu çalışmada, ortaokul öğrencilerinin alan ölçme bilgi ve becerilerinin incelenmesi amaçlanmıştır. Betimsel yöntemin kullanıldığı araştırmada veriler, yedinci sınıfta öğrenim gören 92 öğrenciden, 8 adet açık uçlu soru ile yazılı olarak toplanmıştır. Öğrencilerin cevapları açık uçlu soruları puanlama ölçeği ile analiz edilmiştir. Araştırmada, alan ölçme birimlerinin büyüklüğünü doğru bir şekilde tahmin eden öğrencilerin çoğunlukta olduğu, fakat standart alan ölçme birimlerinin dönüşümünde zorlandıklarını göstermektedir. Alanı, bir bölgeyi kaplayan birim karelerin sayısı olarak hesaplayabilen öğrenciler çoğunluktadır. Dikdörtgenin alanını ölçmede başarılı olan öğrencilerin, paralelkenar, üçgen ve yamuğun alanını ölçmedeki başarısı düşük olarak belirlenmiş ve öğrencilerin alan ölçerken çokgenin iki kenarını çarpmaya meyilli oldukları gözlenmiştir. Ayrıca bazı öğrencilerin alanı çevre ile karıştırdıkları belirlenmiştir.

Keywords

alan ölçme, alan ölçme becerisi, geometri öğretimi, ortaokul öğrencileri

Investigation of Secondary School Students' Area Measurement Knowledge and Skills

Abstract

In this study, it is aimed to examine the area measurement knowledge and skills of secondary school students. In the study, in which the descriptive method was used, the data were collected in written form with 8 open-ended questions from 92 seventh grade students. Students' answers to open-ended questions were analyzed with a scoring scale. The research shows that the majority of students who correctly estimate the size of the area measurement units are in the majority, but they have difficulty in transforming the standard area measurement units. Students who can calculate the area as the number of unit squares covering a region are in the majority. It was observed that the students who were successful in measuring the area of the rectangle had low success in measuring the area of the parallelogram, triangle and trapezoid, and it was observed that the students tended to multiply the two sides of the polygon while measuring the area. In addition, it was determined that some students confused the area with the environment.

Keywords

area measurement konowledge, area measurement skill, geometry teaching, secondary student

References

• Baturo, A., & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268. https://doi.org/10.1007/BF00376322
• Bingölbali, E., & Coşkun, M. (2016). A proposed conceptual framework for enhancing the use of making connections skill in mathematics teaching. Eğitim ve Bilim, 41(183), 233-249. http://dx.doi.org/10.15390/EB.2016.4764
• Bingölbali, E., & Özmantar, M. F. (Eds). (2009). İlköğretimde karşılaşılan matematiksel zorluklar ve çözüm önerileri [Mathematical difficulties encountered in primary education and solution suggestions] (1st ed.). Pegem Akademi.
• Bragg, P., & Outhred, L. (2000, July, 23-27). Students' knowledge of length units: do they know more than rules about rulers? [Oral presented]. 24th Conference of the International Study Group for the Psychology of Mathematics Education, Hiroshima, Japan.
• Cavanagh, M. (2008). Area measurement in year 7. Reflections, 33(1), 55-58. https://researchers.mq.edu.au/en/publications/area-measurement-in-year-7/fingerprints/
• Chappell, M. F., & Thompson, D. R. (1999). Take time for action: perimeter or area? Which measure is it? Mathematics Teaching in the Middle School, 5(1), 20-23. https://doi.org/10.5951/MTMS.5.1.0020
• Clements, D. H. ve Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. D. H. Clements, J. Sarama & A.-M. DiBiase (Eds.). In Engaging young children in mathematics: Standards for early childhood mathematics education, (pp. 299-317), Routledge.
• Creswell, J. (2020). Qualitative inquiry & research design choosing among five approaches (Revised 5th ed.) (S.B., Demir & M., Bütün, trans.). Siyasal Kitabevi (Original work published 2013).
• Çağlayan, N., Dağıstan, A., & Korkmaz, B. (2021). Ortaokul ve imam hatip ortaokulu 6. sınıf matematik ders kitabı [Middle and imam hatip middle school 6th grade mathematics textbook]. MEB Yayınları.
• Çavuş Erdem, Z. (2013). Determination of students' mistakes and misconceptions about equations and teacher views on reasons and solutions of these mistakes and misconceptions [Unpublished master’s thesis], Adıyaman University.
• Çavuş Erdem, Z. (2018). Investigation of the learning process based on mathematical modeling activities in the context of area measurement [Unpublished doctoral dissertation], Adıyaman University.
• Çelik, S., (2023). Connection forms of sixth grade students regarding the conceptions of length, perimeter, area and volume. [Unpublished master’s thesis], Ankara University.
• Çetin, H. (2020). Alan ölçme ve öğretimi [Area measurement and teaching]. E., Ertekin ve M., Ünlü (Eds). Geometri ve ölçme öğretimi: Tanımlar, kavramlar ve etkinlikler [In Teaching geometry and measurement: Definitions, concepts and activities ] (pp. 645-676), Pegem Akademi.
• Doğan Coşkun, S. (2017). Investigation of primary school teachers' mathematical knowledge in teaching for length measurement and perimeter topics with the knowledge quartet model [Unpublished doctoral dissertation]. Gazi University.
• Dursun, Ş., & Dede, Y.(2004). The factors affecting students’ success in mathematics: mathematics teachers’ perspectives. Journal of Gazi Faculty of Education, 24(2), 217-230. https://dergipark.org.tr/tr/pub/gefad/issue/6759/90924
• Fauzan, A. (2002). Applying Realistic Mathematics Education (RME) in teaching geometry in Indonesian primary schools, [Published doctoral dissertation]. Twente University.
• Hansen, A. (2014). Children’s errors in mathematics (3rd ed.)Los Angeles: Learning Matters.
• Huang, H. M. E., & 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. http://dx.doi.org/10.5430/jct.v2n1p10
• Horzum, T. (2018). he investigation of preservice mathematics teachers’ knowledge about quadrilaterals through concept maps. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(1), 1-30. http:// doi/10.16949/turkbilmat.333678
• Gelici, Ö. (2022). Investigation of secondary school students' concept images and proof schemes about perimeter and area [Unpublished master’s thesis]. Anadolu University.
• Gürbüz, R., & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers & Education, 58(3), 931-941. https://doi:10.1016/j.compedu.2011.11.005
• Gürefe N. (2018). Determining strategies used in area measurement problems by middle school students. Hacettepe University Journal of Education, 33(2), 417-438. https://doi:10.16986/HUJE.2017032703
• Kamii, C., & Kysh, J. (2006). The difficulty of “length× width”: Is a square the unit of measurement? The Journal of Mathematical Behavior, 25(2), 105-115. https://doi.org/10.1016/j.jmathb.2006.02.001
• Kaya, D. (2019). Problem solving skills related to area measurement of 6th grade students. International Journal of Educational Studies in Mathematics, 6(4), 144-171. https://dergipark.org.tr/en/pub/ijesim/issue/50978/626133
• Kidman, G., & Cooper, T. J. (1997, July, 14-19 ). Area integration rules for grades 4, 6 and 8 students. [Oral presentation]. In Proceedings of the 21st international Conference for the Psychology of Mathematics Education, Lahti, Finland. https://www.igpme.org/publications/current-proceedings/
• Konold, T. R., & Canivez, G. L. (2010). Differential relationships between WISC-IV and WIAT-II scales: An evaluation of potentially moderating child demographics. Educational and Psychological Measurement, 70(4), 613-627. https://doi:10.1177/0013164409355686
• Lim C. S., & Ernest, P. (1999). Public Images of Mathematics. Philosophy of Mathematics Education Journal, 11, 43-55. https://education.exeter.ac.uk/research/centres/stem/publications/pmej/pome11/art6.htm
• Martin, W. G., & Strutchens, M. E. (2000). Geometry and measurement. In E. A. Silver & P. A. Kennedy (Eds.), Results from the seventh mathematics assessment of the national assessment of education progress (pp. 193-234), Reston, Va.
• Monaghan, F. (2000). What difference does it make? Children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2),179-196. https://doi.org/10.1023/A:1004175020394
• Moreira, C. Q. and Contente, M. D. R. (1997, July, 14-19). The role of writing to foster pupil’s learning about area. [Oral presentation]. In Proceedings of the 21st PME International Conference, Lahti, Finland. https://www.igpme.org/publications/current-proceedings/
• Ministry of National Education (MoNE), (2018). Ortaokul matematik dersi (1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) öğretim programı [Middle school mathematics lesson (1, 2, 3, 4, 5, 6, 7 and 8th grades) curriculum ]. MoNE.
• Ministry of National Education (MoNE), (2022). Matematik seferberliği başladı [Mathematics campaign has begun]. Retrieved April 2, 2023 from https://www.meb.gov.tr/matematik-seferberligi-basladi/haber/26241/tr
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (3rd ed.). Sage.
• Olkun, S., Çelebi, Ö., Fidan, E., Engin, Ö., & Gökgün, C. (2014). The meaning of unit square and area formula for Turkish students. Hacettepe University Journal of Education, 29(29-1), 180-195. http://www.efdergi.hacettepe.edu.tr/shw_artcl-111.html
• Olkun, S., & Toluk-Uçar, Z. (2009). İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics teaching in primary education](6th ed.) Anı Yayıncılık.
• 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 self-efficacy beliefs and basic procedural and conceptual knowledge of area and perimeter [Unpublished master's thesis], Orta Doğu Teknik University.
• Outhred, L. N., & Mitchelmore, M. C. (2000). Young children's intuitive understanding of rectangular area measurement. Journal For Research In Mathematics Education, 31(2), 144-167. https://doi.org/10.2307/749749
• Önal, H., & Aydın, O. (2018). Misconceptions and error patterns mathematics lesson in primary school. Journal of Education, Theory and Practical Research, 4(2), 1-9. https://dergipark.org.tr/en/pub/ekuad/issue/38280/442698
• Öztürk, F. N., & Gürefe, N. (2021, October, 28-30). Ortaokul öğrencilerinin kesri belirlemede geometrik alan ölçme bilgisini kullanması [Middle school students' use of Their geometric area measurement knowledge in determining the fraction], [Oral presented], 5th Turkish Computer & Mathematics Education Symposium, Antalya, Turkey. https://bilmat.org/turkbilmat2021/?dil=tr
• Savaş, E., Taş, S., & Duru, A. (2010). Factors affecting students’ achievement in mathematics. Mathematics Learning, 11(1), 113-132. http://hdl.handle.net/11616/4342
• Schifter, D., & Szymaszek, J. (2003). Structuring a rectangle: Teachers write to learn about their students’ thinking. H.D., Clements, and G. Bright (Eds). Learning and teaching measurement, NCTM, Reston.
• Simon, M. A., & Blume, G. W. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472-494. https://doi.org/10.5951/jresematheduc.25.5.0472
• Smith III, J. P., Males, L. M., & Gonulates, F. (2016). Conceptual limitations in curricular presentations of area measurement: One nation’s challenges. Mathematical Thinking and Learning, 18(4), 239-270. https://doi.org/10.1080/10986065.2016.1219930
• Stafslien, C. (2001), Gender differences in achievement in mathematics. Retrieved July 2, 2022 from http://www.math.wisc.edu/~weinberg/MathEd/Gender_Term_Paper.doc
• Şahin, B. (2013). Öğretmen adaylarının “matematik öğretmeni”, “matematik” ve “matematik dersi” kavramlarına ilişkin sahip oldukları metaforik algılar. Mersin University Journal of the Faculty of Education, 9(1), 313-321. https://dergipark.org.tr/en/pub/mersinefd/issue/17382/181617
• Tan Şişman, G., & Aksu, M. (2009). Seventh grade students' success on the topics of area and perimeter. Elementary Education Online, 8(1), 243-253. https://ilkogretim-online.org/index.php?mno=121376
• Tan Şişman, G., & 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, 1293-1319. https://doi.org/10.1007/s10763-015-9642-5
• Thomson, S., Lokan, J., Stephen, L., & Ainley, J. (2003). Lessons from the third international mathematics and science study. Retrieved October, 5, 2022 from https://research.acer.edu.au/timss_monographs/9
• Şenol, A., Dündar, S., Kaya, İ., Gündüz, N., & Temel, H. (2015). Investigation of secondary school mathematics teachers’ opinions on mathematics fear. Journal of Theory & Practice in Education (JTPE), 11(2), 653-672. https://dergipark.org.tr/en/pub/eku/issue/5465/74216
• Van De Walle, J. A., Karp, K. S. ve Bay-Williams, J. M. (2014). İlkokul ve ortaokul matematiği gelişimsel yaklaşımla öğretim [Elementary & middle school mathematics: teaching developmentally] (S., Durmuş, Trans.), Nobel Akademik Yayıncılık.
• Yaman, F., & Yaman, B. (2020). Metaphoric perceptions of secondary school students on mathematics concept. Eurasian Journal of Researches in Social and Economics (EJRSE), 7(6), 250-265. https://dergipark.org.tr/en/pub/asead/issue/55211/737640
• Yenilmez, K., & Yaşa, E., (2008). Primary school students’ misconceptions about geometry. Journal of Uludag University Faculty of Education, 21(2), 461-483. https://dergipark.org.tr/en/pub/uefad/issue/16688/173427
• Yenilmez, K., & Pargan, A. Ş. (2008). Primary school 2nd grade students’ perceptions towards standard unit of length measurement Ahi Evran University Journal of Kırşehir Education Faculty, 9(2), 59-67. https://dergipark.org.tr/en/pub/kefad/issue/59525/856031
• Yin, R.K. (2009). Case study methods: design and methods (4th Ed.). Sage. Yorulmaz, A., & Önal, H. (2017). Examination of the views of class teachers regarding the errors primary school students make in four operations. Universal Journal of Educational Research, 5(11), 1885-1895 https://doi.org/10.13189/ujer.2017.051105
• Zacharos, K. (2006). Prevailing educational practices for area measurement and students’ failure in measuring areas. The Journal of Mathematical Behavior, 25(3), 224-239. https://doi.org/10.1016/j.jmathb.2006.09.003