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Unveiling Strategies and Difficulties: Investigating Secondary School Students' Approaches to Area Measurement Problems

Year 2024, Issue: 61, 2607 - 2631, 27.09.2024
https://doi.org/10.53444/deubefd.1502725

Abstract

This study aims to explore the strategies that secondary school students employ and the difficulties they encounter when solving area measurement problems. The participants consist of 75 seventh and eighth-grade students from southeast Turkey. Data were obtained through a form comprising six open-ended problems, designed to uncover the “nature of justifications”. Analysis of the students' responses revealed 11 distinct strategies and 11 difficulties. The most frequently employed strategies for solving area problems were reasoning through drawing shapes and applying the area formula (axb). Students struggled the most with distinguishing changes in the area from changes in the perimeter. It was observed that the root of the difficulties experienced by the students was challenges in measuring length. Notably, when presented with contextual problems, students focused on the context and justified their solutions based on cultural factors. As such, it is recommended that the process should be designed while considering cultural factors (both facilitators and inhibitors) in teaching subjects such as area measurement, which are closely related to real life.

References

  • Adıgüzel Doğan, F. (2021). Dokuzuncu sınıf öğrencilerinin geometri bağlamında cebirsel muhakemelerinin incelenmesi: üçgenler alt öğrenme alanında bir uygulama [Yayınlanmamış doktoratezi]. Anadolu Üniversitesi.
  • Asil-Güzel, A. (2018). Ortaokul öğrencilerinin uzunluk ölçme ve karşılaştırmaya dair kavrayışlarının incelenmesi. (Yayımlanmamış yüksek lisans tezi) Gaziantep Üniversitesi Eğitim Bilimleri Enstitüsü.
  • Aydurmuş, L. (2013). 8. Sınıf öğrencilerinin problem çözme sürecinde kullandığı üstbiliş becerilerin incelenmesi. Yayınlanmamış yüksek lisanstezi. Karadeniz Teknik Üniversitesi, EğitimBilimleriEnstitüsü, Trabzon.
  • Balacheff, N. (1988). Une étude des processus de preuveen mathématique chez des élèves de collège (Doctoral dissertation, Institut National Polytechnique de Grenoble-INPG; Université Joseph-Fourier-Grenoble I).
  • Barrett, J. E., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., & Klanderman, D. (2012). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14(1), 28-54. https://doi.org/10.1080/10986065.2012.625075
  • Battista, M. (1982). Understanding area and area formulas. The Mathematics Teacher, 75(5), 362–368.
  • 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., & Özmantar, M. F. (2015). Matematiksel zorluklar ve çözüm önerileri. Matematiksel kavram yanılgıları: sebepleri ve çözüm arayışları, 1-30.
  • Bishop, A. J. (1988). Mathematics education in its cultural context. Educational studies in mathematics, 19(2), 179-191. https://doi.org/10.1007/BF00751231
  • Brousseau, G. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Springer Science & Business Media.
  • Buckley, J., Seery, N., & Canty, D. (2019). Investigating the use of spatial reasoning strategies in geometric problem-solving. International Journal of Technology and Design Education, 29(2), 341-362. https://doi.org/10.1007/s10798-018-9446-3
  • Bülbül, B. Ö., Elçi, A. N., Güler, M., & Güven, B. (2021). Matematik Öğretmeni Adaylarının Bilgisayar Destekli Ortamda Geometri Problem Çözme Stratejilerinin Belirlenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (51), 403-432. https://doi.org/10.53444/deubefd.936523
  • Burns, B. A., & Brade, G. A. (2003). Using the geoboard to enhance measurement instruction in the secondary school mathematics. Learning and teaching measurement, 256-270.
  • Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: an exploratory study. International journal of mathematical education in science and technology, 34(5), 719-737. https://doi.org/10.1080/00207390310001595401
  • Çavuş Erdem, Z. (2018). Matematiksel modelleme etkinliklerine dayalı öğrenim sürecinin alan ölçme konusu bağlamında incelenmesi yayınlanmamış doktora tezi. Adıyaman Üniversitesi.
  • Chua, B. L. (2017). A framework for classifying mathematical justification tasks. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (pp. 115–122). https://hal.science/hal-01873071.
  • Clements, D. H., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. D. H. Clements, & J. Samara (Eds.), Engaging Young Children in Mathematics. Standards for Early Childhood Mathematics Education (pp. 299–317). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
  • Crosby, A. W. (1997). The measure of reality: Quantification and western society, 1250–1600. Cambridge, UK: Cambridge University Press.
  • D’Ambrosio, U. (1995). Multiculturalism and mathematics education. International Journal of Mathematics Education in Science and Techology, 26(3), 337-346. https://doi.org/10.1080/0020739950260304
  • Drake, M. (2014). Learning to measure length: The problem with the school ruler. Australian Primary Mathematics Classroom, 19(3), 27-32. https://search.informit.org/doi/10.3316/informit.662654173461232
  • Driscoll, M. J., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Portsmouth, NH: Heinemann.
  • Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century: An ICMI study (pp. 37–52). Dordrecht, The Netherlands: Kluwer.
  • Elçi, A. N. (2022). 4MAT Öğrenme Stillerine Uygun Olarak Seçilen Öğrenme Yöntemlerinin Matematik Öğretmen Adaylarının Açık Uçlu Problem Çözmedeki Başarısına Etkisi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (53), 725-741. https://doi.org/10.53444/deubefd.1119801
  • Ersoy, Y. (2006). İlköğretim matematik öğretim programındaki yenilikler-I: Amaç, içerik ve kazanımlar. İlköğretim online, 5(1), 30-44.
  • Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, Monograph, 3, 1-195. http://dx.doi.org/10.2307/749957
  • Gür, H. & Hangül, T. (2015). Ortaokul öğrencilerinin problem çözme stratejileri üzerine bir çalışma. Pegem Eğitim ve Öğretim Dergisi, 5(1), 95-112, http://dx.doi.org/10.14527/pegegog.2015.005
  • Gürefe, N. (2018). Ortaokulöğrencilerininalanölçümproblemlerindekullandıklarıstratejilerinbelirlenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 33(2), 417-438. http://dx.doi.org/10.16986/HUJE.2017032703
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning, 2, 805-842.
  • Huang, H. M. E., & Witz, K. G. (2011). Developing children's conceptual understanding of area measurement: A curriculum and teaching experiment. Learning and instruction, 21(1), 1-13. https://doi.org/10.1016/j.learninstruc.2009.09.002
  • 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
  • Jack, J. P., & Thompson, P. W. (2017). 4 Quantitative Reasoning and the Development of Algebraic Reasoning. In Algebra in the early grades (pp. 95-132). Routledge.
  • Jirotková, D., Vighi, P., & Zemanová, R. (2019, August). Misconceptions about the relationship between perimeter and area. In International Symposium Elementary Mathematics Teaching (pp. 221-231).
  • Jupri, A., Gozali, S. M., &Usdiyana, D. (2020). An analysis of a geometry learning process: The case of proving area formulas. Prima: Jurnal Pendidikan Matematika, 4(2), 154-163. http://dx.doi.org/10.31000/prima.v4i2.2619
  • Kidman, G., & Cooper, T. J. (1997). Area integration rules for grades 4, 6 and 8 students. In E. Pehkonen (Ed.), Proceedings of the 21st International Conference for the Psychology of Mathematics Education (pp. 136–143). Lahti, Finland.
  • Kospentaris, G., Spyrou, P., & Lappas, D. (2011). Exploring students’ strategies in area conservation geometry tasks. Educational Studies in Mathematics, 77, 105–127. https://doi.org/10.1007/s10649-011-9303-8
  • Lin, P.-J., & Tsai, W.-H. (2003). Fourth graders’ achievement of mathematics in TIMSS 2003 field test. (In Chinese) Science Education Monthly, 258, 2-20.
  • Machaba, F. M. (2016). The concepts of area and perimeter: Insights and misconceptions of Grade 10 learners. Pythagoras, 37(1), 1-11. https://doi.org/10.4102/pythagoras.v37i1.304
  • MEB Talim ve Terbiye Kurulu Başkanlığı. (2018). Matematik Dersi Öğretim Programı. Ankara.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. sage.
  • Milli Eğitim Bakanlığı (2023). Millî Eğitim Bakanlığı Yazılı ve Uygulamalı Sınavlar Yönergesi https://odsgm.meb.gov.tr/meb_iys_dosyalar/2023_10/12115933_MEB_yazili_ve_uygulamali_sinavlar_yonergesi.pdf
  • Moore, K. C., Carlson, M. P. &Oehrtman, M. (2009). The role of quantitative reasoning in solving applied precalculus problems. Paper presented at the Twelfth Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Educati¬on (SIGMAA on RUME) Conference, Raleigh, NC: North Carolina State University.
  • Moyer, P. S. (2001). Using representations to explore perimeter and area. Teaching Children Mathematics, 8(1), 52–57. https://doi.org/10.5951/TCM.8.1.0052
  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM. https://www.nctm.org/standards/.
  • Nitabach, E., & Lehrer, R. (1996). Developing spatial sense through area measurement. Teaching Children Mathematics, 2(8), 473–476. https://doi.org/10.5951/TCM.2.8.0473
  • Olkun, S.,Şahin, Ö., Akkurt, Z., Dikkartın, F.T. &Gülbağcı, H. (2009). Modellemeyoluyla problem çözmevegenelleme: ilköğretimöğrencileriylebirçalışma. EğitimveBilim, 34, 65-73
  • Outhred, L. & Mitchelmore, M. (1996). Children’s intuitive understanding of area measurement. Proceedings of the 20th International Conference for the Psychology of Mathematics Education (pp. 91–98).
  • 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
  • Owens, K., &Outhred, L. (2006). The complexity of learning geometry and measurement. In Handbook of research on the psychology of mathematics education (pp. 83-115). Brill. https://doi.org/10.1163/9789087901127_005
  • Oxford University Press. (2024). Oxford English Dictionary. Oxford University Press, available online at https://www.oed.com/search/dictionary/?scope=Entries&q=difficulty (accessed 13 February 2024)
  • Özdemir, B. G., Koçak, M., & Soylu, Y. (2018). Ortaokul matematik öğretmeni adaylarının sözel problemleri değişkensiz çözmede kullandıkları stratejiler ve yöntemler. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 8(3), 449-467. https://doi.org/10.24315/trkefd.327712
  • Pamungkas, M. D., Juniati, D., &Masriyah, M. (2018, July). Mathematical Justification Ability: Students’ Divergent and Convergent Process in Justifying Quadrilateral. In Mathematics, Informatics, Science, and Education
  • International Conference (MISEIC 2018) (pp. 38-41). Atlantis Press. https://doi.org/10.2991/miseic-18.2018.10 Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri (ÇevEdt: Bütün, M. ve Demir, S. B). Ankara: Pegem Akademi Yayınları.
  • Piaget, J., Inhelder, B. &Szeminska, A. (1960). The child's conception of geometry. Oxford, Enand: Basic Books.
  • Polya, G. (1973). How to solve it: a new aspect of mathematical thinking. Princeton, New Jersey: Princeton University Press.
  • Presmeg, N. (2014). Contemplating visualization as an epistemological learning tool in mathematics. ZDM, 46, 151-157. https://doi.org/10.1007/s11858-013-0561-z
  • Pressley, M., & Hilden, K. (2006). Cognitive strategies. Handbook of child psychology, 2, 511-556.
  • Probosiwi, W. I., Suyitno, H., &Dwidayati, N. K. (2021). Mathematical Creative Thinking Ability Based on Intellectual Intelligence and Cognitive Style in SSCS Learning with Open-Ended Problems. Unnes Journal of Mathematics Education Research, 10(A).
  • Ramnarain, U. (2014). Empowering educationally disadvantaged mathematics students through a strategies-based problem solving approach. The Australian Educational Researcher, 41(1), 43-57 https://doi.org/10.1007/s13384-013-0098-8
  • Sarama, J., & Clements, D. H. (2009). Early Childhood Mathematics Education Research. Routledge. New York
  • Schoenfeld, A. H. (1999). Looking toward the 21st century: Challenges of educational theory and practice. Educational researcher, 28(7), 4-14. https://doi.org/10.3102/0013189X028007004
  • Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3-31. https://doi.org/10.1016/S0732-3123(96)90036-X
  • Smith, J. P. & Barrett, J. E. (2017). The learning and teaching of measurement: Coordinating quantity and number. J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 355–385). Reston, VA: National Council of Teachers of Mathematics.
  • Smith, J. P., Males, L. M., Dietiker, L. C., Lee, K., & Mosier, A. (2013). Curricular treatments of length measurement in the United States: Do they address known learning challenges? Cognition & Instruction, 31, 388–433. doi:10.1080/ 07370008.2013.828728
  • Staples, M., Bartlo, J., & Staples, M. (2010). Justification as a learning practice: Its purposes in middle grades mathematics classroom. CRME Publications, 3(1), 1–9. https://opencommons.uconn.edu/merg_docs/3
  • Sulistiowati, D. L., Herman, T., &Jupri, A. (2019, February). Student difficulties in solving geometry problem based on Van Hiele thinking level. In Journal of Physics: Conference Series (Vol. 1157, No. 4, p. 042118). IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042118
  • Tan Sisman, 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
  • Thompson, P. (1989). A cognitive model of quantity-based algebraic reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, USA.
  • Thompson, T. D., & Preston, R. V. (2004). Measurement in the middle grades: Insights from NAEP and TIMSS. Mathematics Teaching in the Middle School, 9, 514–519.
  • Tsamir, P. (2003). Using the intuitive rule more A-more B for predicting and analysing students' solutions in geometry. International Journal of Mathematical Education in Science and Technology, 34(5), 639-650. https://doi.org/10.1080/0020739031000148840
  • Vale, I., & Barbosa, A. (2018). Mathematical problems: the advantages of visual strategies. Journal of the European Teacher Education Network, 13, 23–33. http://hdl.handle.net/20.500.11960/3697
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics. Pearson.
  • Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., … & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://files.eric.ed.gov/fulltext/ED532215.pdf
  • Yazgan, Y., &Bintaş, Y. (2005). İlköğretim dördüncü ve beşinci sınıf öğrencilerinin problem çözme stratejilerini kullanabilme düzeyleri bir öğretim deneyi. Hacettepe Üniversitesi Egitim Fakültesi Dergisi, 28, 210-218
  • 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
  • Zembat, D. Ö (2014). Kavram yanılgısı nedir? In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri. Ankara: Pegem Akademi Yayıncılık.

Strateji ve Zorlukları Ortaya Çıkarma: Ortaokul Öğrencilerinin Alan Ölçme Problemlerine Yaklaşımlarının İncelenmesi

Year 2024, Issue: 61, 2607 - 2631, 27.09.2024
https://doi.org/10.53444/deubefd.1502725

Abstract

Bu araştırma ortaokul öğrencilerinin alan problemleri çözümlerine yansıyan stratejileri ve karşılaştıkları zorlukları ortaya koymak amacı ile gerçekleştirilmiştir. Çalışmaya Türkiye’nin güney doğusundaki bir büyük şehirden 7 ve 8. sınıflar öğrencilerinden oluşan 75 kişi katılmıştır. Farklı gerekçelendirme türleri dikkate alınarak oluşturulan 6 açık uçlu sorudan 3 bağlam içerisinde sorulmuştur. Öğrencilerin çözümleri incelendiğinde 11 farklı strateji ve 11 farklı zorlukla karşılaşıldığı tespit edilmiştir. Öğrencilerin alan problemi çözümünde en sık kullandıkları stratejinin şekil çizerek muhakeme etmek ve alan formülü (axb) kullanmak olduğu görülmüştür. Yapılan incelemeler ışığında en sık yaşanan zorluk ise öğrencilerin alandaki değişim ile çevrede gerçekleşen değişimi ayırt etmek olduğu tespit edilmiştir. Ayrıca öğrencilerin yaşadıkları zorlukların temelinde uzunluğu hesaplama ve tespit etmeye dair zorluklar olduğu görülmüştür. Son olarak bağlam içinde sorulan problemlerde öğrencilerin bağlama odaklandıkları ve kültürel faktörler ışığında çözüm gerekçeleri sundukları tespit edilmiştir. Bu bağlamda günlük hayata teması çok olan alan ölçme /hesaplama gibi konuların öğretiminde kültürel faktörler (kolaylaştırıcı ve engelleyici) dikkate alınarak sürecin tasarlanması önerilmektedir.

References

  • Adıgüzel Doğan, F. (2021). Dokuzuncu sınıf öğrencilerinin geometri bağlamında cebirsel muhakemelerinin incelenmesi: üçgenler alt öğrenme alanında bir uygulama [Yayınlanmamış doktoratezi]. Anadolu Üniversitesi.
  • Asil-Güzel, A. (2018). Ortaokul öğrencilerinin uzunluk ölçme ve karşılaştırmaya dair kavrayışlarının incelenmesi. (Yayımlanmamış yüksek lisans tezi) Gaziantep Üniversitesi Eğitim Bilimleri Enstitüsü.
  • Aydurmuş, L. (2013). 8. Sınıf öğrencilerinin problem çözme sürecinde kullandığı üstbiliş becerilerin incelenmesi. Yayınlanmamış yüksek lisanstezi. Karadeniz Teknik Üniversitesi, EğitimBilimleriEnstitüsü, Trabzon.
  • Balacheff, N. (1988). Une étude des processus de preuveen mathématique chez des élèves de collège (Doctoral dissertation, Institut National Polytechnique de Grenoble-INPG; Université Joseph-Fourier-Grenoble I).
  • Barrett, J. E., Sarama, J., Clements, D. H., Cullen, C., McCool, J., Witkowski-Rumsey, C., & Klanderman, D. (2012). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14(1), 28-54. https://doi.org/10.1080/10986065.2012.625075
  • Battista, M. (1982). Understanding area and area formulas. The Mathematics Teacher, 75(5), 362–368.
  • 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., & Özmantar, M. F. (2015). Matematiksel zorluklar ve çözüm önerileri. Matematiksel kavram yanılgıları: sebepleri ve çözüm arayışları, 1-30.
  • Bishop, A. J. (1988). Mathematics education in its cultural context. Educational studies in mathematics, 19(2), 179-191. https://doi.org/10.1007/BF00751231
  • Brousseau, G. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Springer Science & Business Media.
  • Buckley, J., Seery, N., & Canty, D. (2019). Investigating the use of spatial reasoning strategies in geometric problem-solving. International Journal of Technology and Design Education, 29(2), 341-362. https://doi.org/10.1007/s10798-018-9446-3
  • Bülbül, B. Ö., Elçi, A. N., Güler, M., & Güven, B. (2021). Matematik Öğretmeni Adaylarının Bilgisayar Destekli Ortamda Geometri Problem Çözme Stratejilerinin Belirlenmesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (51), 403-432. https://doi.org/10.53444/deubefd.936523
  • Burns, B. A., & Brade, G. A. (2003). Using the geoboard to enhance measurement instruction in the secondary school mathematics. Learning and teaching measurement, 256-270.
  • Cai, J. (2003). Singaporean students' mathematical thinking in problem solving and problem posing: an exploratory study. International journal of mathematical education in science and technology, 34(5), 719-737. https://doi.org/10.1080/00207390310001595401
  • Çavuş Erdem, Z. (2018). Matematiksel modelleme etkinliklerine dayalı öğrenim sürecinin alan ölçme konusu bağlamında incelenmesi yayınlanmamış doktora tezi. Adıyaman Üniversitesi.
  • Chua, B. L. (2017). A framework for classifying mathematical justification tasks. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (pp. 115–122). https://hal.science/hal-01873071.
  • Clements, D. H., & Stephan, M. (2004). Measurement in pre-K to grade 2 mathematics. D. H. Clements, & J. Samara (Eds.), Engaging Young Children in Mathematics. Standards for Early Childhood Mathematics Education (pp. 299–317). Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.
  • Crosby, A. W. (1997). The measure of reality: Quantification and western society, 1250–1600. Cambridge, UK: Cambridge University Press.
  • D’Ambrosio, U. (1995). Multiculturalism and mathematics education. International Journal of Mathematics Education in Science and Techology, 26(3), 337-346. https://doi.org/10.1080/0020739950260304
  • Drake, M. (2014). Learning to measure length: The problem with the school ruler. Australian Primary Mathematics Classroom, 19(3), 27-32. https://search.informit.org/doi/10.3316/informit.662654173461232
  • Driscoll, M. J., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Portsmouth, NH: Heinemann.
  • Duval, R. (1998). Geometry from a cognitive point of view. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century: An ICMI study (pp. 37–52). Dordrecht, The Netherlands: Kluwer.
  • Elçi, A. N. (2022). 4MAT Öğrenme Stillerine Uygun Olarak Seçilen Öğrenme Yöntemlerinin Matematik Öğretmen Adaylarının Açık Uçlu Problem Çözmedeki Başarısına Etkisi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (53), 725-741. https://doi.org/10.53444/deubefd.1119801
  • Ersoy, Y. (2006). İlköğretim matematik öğretim programındaki yenilikler-I: Amaç, içerik ve kazanımlar. İlköğretim online, 5(1), 30-44.
  • Fuys, D., Geddes, D., & Tischler, R. (1988). The van Hiele model of thinking in geometry among adolescents. Journal for Research in Mathematics Education, Monograph, 3, 1-195. http://dx.doi.org/10.2307/749957
  • Gür, H. & Hangül, T. (2015). Ortaokul öğrencilerinin problem çözme stratejileri üzerine bir çalışma. Pegem Eğitim ve Öğretim Dergisi, 5(1), 95-112, http://dx.doi.org/10.14527/pegegog.2015.005
  • Gürefe, N. (2018). Ortaokulöğrencilerininalanölçümproblemlerindekullandıklarıstratejilerinbelirlenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 33(2), 417-438. http://dx.doi.org/10.16986/HUJE.2017032703
  • Harel, G., & Sowder, L. (2007). Toward comprehensive perspectives on the learning and teaching of proof. Second handbook of research on mathematics teaching and learning, 2, 805-842.
  • Huang, H. M. E., & Witz, K. G. (2011). Developing children's conceptual understanding of area measurement: A curriculum and teaching experiment. Learning and instruction, 21(1), 1-13. https://doi.org/10.1016/j.learninstruc.2009.09.002
  • 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
  • Jack, J. P., & Thompson, P. W. (2017). 4 Quantitative Reasoning and the Development of Algebraic Reasoning. In Algebra in the early grades (pp. 95-132). Routledge.
  • Jirotková, D., Vighi, P., & Zemanová, R. (2019, August). Misconceptions about the relationship between perimeter and area. In International Symposium Elementary Mathematics Teaching (pp. 221-231).
  • Jupri, A., Gozali, S. M., &Usdiyana, D. (2020). An analysis of a geometry learning process: The case of proving area formulas. Prima: Jurnal Pendidikan Matematika, 4(2), 154-163. http://dx.doi.org/10.31000/prima.v4i2.2619
  • Kidman, G., & Cooper, T. J. (1997). Area integration rules for grades 4, 6 and 8 students. In E. Pehkonen (Ed.), Proceedings of the 21st International Conference for the Psychology of Mathematics Education (pp. 136–143). Lahti, Finland.
  • Kospentaris, G., Spyrou, P., & Lappas, D. (2011). Exploring students’ strategies in area conservation geometry tasks. Educational Studies in Mathematics, 77, 105–127. https://doi.org/10.1007/s10649-011-9303-8
  • Lin, P.-J., & Tsai, W.-H. (2003). Fourth graders’ achievement of mathematics in TIMSS 2003 field test. (In Chinese) Science Education Monthly, 258, 2-20.
  • Machaba, F. M. (2016). The concepts of area and perimeter: Insights and misconceptions of Grade 10 learners. Pythagoras, 37(1), 1-11. https://doi.org/10.4102/pythagoras.v37i1.304
  • MEB Talim ve Terbiye Kurulu Başkanlığı. (2018). Matematik Dersi Öğretim Programı. Ankara.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. sage.
  • Milli Eğitim Bakanlığı (2023). Millî Eğitim Bakanlığı Yazılı ve Uygulamalı Sınavlar Yönergesi https://odsgm.meb.gov.tr/meb_iys_dosyalar/2023_10/12115933_MEB_yazili_ve_uygulamali_sinavlar_yonergesi.pdf
  • Moore, K. C., Carlson, M. P. &Oehrtman, M. (2009). The role of quantitative reasoning in solving applied precalculus problems. Paper presented at the Twelfth Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Educati¬on (SIGMAA on RUME) Conference, Raleigh, NC: North Carolina State University.
  • Moyer, P. S. (2001). Using representations to explore perimeter and area. Teaching Children Mathematics, 8(1), 52–57. https://doi.org/10.5951/TCM.8.1.0052
  • NCTM (2000). Principles and standards for school mathematics. Reston, VA: NCTM. https://www.nctm.org/standards/.
  • Nitabach, E., & Lehrer, R. (1996). Developing spatial sense through area measurement. Teaching Children Mathematics, 2(8), 473–476. https://doi.org/10.5951/TCM.2.8.0473
  • Olkun, S.,Şahin, Ö., Akkurt, Z., Dikkartın, F.T. &Gülbağcı, H. (2009). Modellemeyoluyla problem çözmevegenelleme: ilköğretimöğrencileriylebirçalışma. EğitimveBilim, 34, 65-73
  • Outhred, L. & Mitchelmore, M. (1996). Children’s intuitive understanding of area measurement. Proceedings of the 20th International Conference for the Psychology of Mathematics Education (pp. 91–98).
  • 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
  • Owens, K., &Outhred, L. (2006). The complexity of learning geometry and measurement. In Handbook of research on the psychology of mathematics education (pp. 83-115). Brill. https://doi.org/10.1163/9789087901127_005
  • Oxford University Press. (2024). Oxford English Dictionary. Oxford University Press, available online at https://www.oed.com/search/dictionary/?scope=Entries&q=difficulty (accessed 13 February 2024)
  • Özdemir, B. G., Koçak, M., & Soylu, Y. (2018). Ortaokul matematik öğretmeni adaylarının sözel problemleri değişkensiz çözmede kullandıkları stratejiler ve yöntemler. Trakya Üniversitesi Eğitim Fakültesi Dergisi, 8(3), 449-467. https://doi.org/10.24315/trkefd.327712
  • Pamungkas, M. D., Juniati, D., &Masriyah, M. (2018, July). Mathematical Justification Ability: Students’ Divergent and Convergent Process in Justifying Quadrilateral. In Mathematics, Informatics, Science, and Education
  • International Conference (MISEIC 2018) (pp. 38-41). Atlantis Press. https://doi.org/10.2991/miseic-18.2018.10 Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri (ÇevEdt: Bütün, M. ve Demir, S. B). Ankara: Pegem Akademi Yayınları.
  • Piaget, J., Inhelder, B. &Szeminska, A. (1960). The child's conception of geometry. Oxford, Enand: Basic Books.
  • Polya, G. (1973). How to solve it: a new aspect of mathematical thinking. Princeton, New Jersey: Princeton University Press.
  • Presmeg, N. (2014). Contemplating visualization as an epistemological learning tool in mathematics. ZDM, 46, 151-157. https://doi.org/10.1007/s11858-013-0561-z
  • Pressley, M., & Hilden, K. (2006). Cognitive strategies. Handbook of child psychology, 2, 511-556.
  • Probosiwi, W. I., Suyitno, H., &Dwidayati, N. K. (2021). Mathematical Creative Thinking Ability Based on Intellectual Intelligence and Cognitive Style in SSCS Learning with Open-Ended Problems. Unnes Journal of Mathematics Education Research, 10(A).
  • Ramnarain, U. (2014). Empowering educationally disadvantaged mathematics students through a strategies-based problem solving approach. The Australian Educational Researcher, 41(1), 43-57 https://doi.org/10.1007/s13384-013-0098-8
  • Sarama, J., & Clements, D. H. (2009). Early Childhood Mathematics Education Research. Routledge. New York
  • Schoenfeld, A. H. (1999). Looking toward the 21st century: Challenges of educational theory and practice. Educational researcher, 28(7), 4-14. https://doi.org/10.3102/0013189X028007004
  • Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3-31. https://doi.org/10.1016/S0732-3123(96)90036-X
  • Smith, J. P. & Barrett, J. E. (2017). The learning and teaching of measurement: Coordinating quantity and number. J. Cai (Ed.), Compendium for Research in Mathematics Education (pp. 355–385). Reston, VA: National Council of Teachers of Mathematics.
  • Smith, J. P., Males, L. M., Dietiker, L. C., Lee, K., & Mosier, A. (2013). Curricular treatments of length measurement in the United States: Do they address known learning challenges? Cognition & Instruction, 31, 388–433. doi:10.1080/ 07370008.2013.828728
  • Staples, M., Bartlo, J., & Staples, M. (2010). Justification as a learning practice: Its purposes in middle grades mathematics classroom. CRME Publications, 3(1), 1–9. https://opencommons.uconn.edu/merg_docs/3
  • Sulistiowati, D. L., Herman, T., &Jupri, A. (2019, February). Student difficulties in solving geometry problem based on Van Hiele thinking level. In Journal of Physics: Conference Series (Vol. 1157, No. 4, p. 042118). IOP Publishing. https://doi.org/10.1088/1742-6596/1157/4/042118
  • Tan Sisman, 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
  • Thompson, P. (1989). A cognitive model of quantity-based algebraic reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, USA.
  • Thompson, T. D., & Preston, R. V. (2004). Measurement in the middle grades: Insights from NAEP and TIMSS. Mathematics Teaching in the Middle School, 9, 514–519.
  • Tsamir, P. (2003). Using the intuitive rule more A-more B for predicting and analysing students' solutions in geometry. International Journal of Mathematical Education in Science and Technology, 34(5), 639-650. https://doi.org/10.1080/0020739031000148840
  • Vale, I., & Barbosa, A. (2018). Mathematical problems: the advantages of visual strategies. Journal of the European Teacher Education Network, 13, 23–33. http://hdl.handle.net/20.500.11960/3697
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). Elementary and middle school mathematics. Pearson.
  • Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., … & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://files.eric.ed.gov/fulltext/ED532215.pdf
  • Yazgan, Y., &Bintaş, Y. (2005). İlköğretim dördüncü ve beşinci sınıf öğrencilerinin problem çözme stratejilerini kullanabilme düzeyleri bir öğretim deneyi. Hacettepe Üniversitesi Egitim Fakültesi Dergisi, 28, 210-218
  • 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
  • Zembat, D. Ö (2014). Kavram yanılgısı nedir? In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri. Ankara: Pegem Akademi Yayıncılık.
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Details

Primary Language English
Subjects Mathematics Education
Journal Section Articles
Authors

Ayşe Asil Güzel 0000-0002-2698-9852

Sibel Yeşildere İmre 0000-0003-3878-3859

Publication Date September 27, 2024
Submission Date June 19, 2024
Acceptance Date September 10, 2024
Published in Issue Year 2024 Issue: 61

Cite

APA Asil Güzel, A., & Yeşildere İmre, S. (2024). Unveiling Strategies and Difficulties: Investigating Secondary School Students’ Approaches to Area Measurement Problems. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi(61), 2607-2631. https://doi.org/10.53444/deubefd.1502725