The process of solving skill-based problems about multipliers and multiples by advanced learners in math and gifted students

Year 2023, , 196 - 217, 11.07.2023

Müjdat Karadağ , Esra Altıntaş

https://doi.org/10.17478/jegys.1299832

Abstract

Globalization has also been reflected in mathematics education, and as a result, international exams, in which Turkey also participate, have become widespread since the 20th century. After participating in international exams in Turkey, it started to make changes in the questions in the exams it held throughout the country. The most striking of these changes is the preparation of skill-based questions that measure metacognitive skills in the High School Entrance System exam. In order to solve such questions effectively, as emphasized in the mathematics curriculum, the problem solving process must be managed well and correctly. In this research, it is aimed to examine the processes of solving skill-based questions about multipliers and multiples. The difficulties experienced by the students in the process of solving skill-based questions and the points they missed were determined. In this study, case study, one of the qualitative research methods, was used. The study group consists of 8 students, 4 of whom are highly successful in mathematics and 4 of whom are gifted, studying in the 8th grade. The Factors and Multiples Achievement Test consisting of 10 open-ended questions was developed in order to measure the students' skills on the subject of multipliers and multiples. While applying the Multipliers and Multiples Achievement Test, we conducted a clinical interview with each student and enabled the students to solve the questions by thinking aloud. We made the descriptive analysis of the obtained data according to the Polya’ problem solving steps. While presenting the findings, we made use of the tables and interpreted them according to each question and step. As a result of the research, we determined that the students who successfully realized the step of understanding the problem were able to perform the other steps and solve the questions correctly. We also found that students who are successful in mathematics try to apply Polya's problem solving steps more and are more successful than gifted students. According to these results, we recommend that students use Polya's problem-solving steps effectively while solving problems and that the research results should be investigated in more detail

Keywords

Advanced learners in math, Gifted student, Math education, Multipliers and multiples, Problem solving process, Skill-based problem

References

• Ahmetoglu, S. (2021). Yedinci sınıf öğrencilerinin yaşam temelli soruların çözüm sürecinin incelenmesi (investigation seventh grade students’ process of solving life-based questions). Master Thesis, Bursa Uludağ University, Institute of Education Sciences, Bursa. http://hdl.handle.net/11452/21360
• Alpaslan, D. N. (2011). Mühendislik tarihi ve felsefesi üzerine bir araştırma (a research on the history and philopsophy of engineering). The Journal of Marmara Social Research, 1, 1-10. https://dergipark.org.tr/tr/pub/marusad/issue/391/2749
• Altıntas, E. (2009). Purdue modeline dayalı matematik etkinliği ile öğretimin üstün yetenekli öğrencilerin başarılarına ve eleştirel düşünme becerilerine etkisi (the effect of teaching with the mathematics activity based on purdue model on the achievement and critical thinking skills of gifted students). Master Thesis, Marmara University, Institute of Education Sciences, İstanbul. https://acikbilim.yok.gov.tr/handle/20.500.12812/476923
• Altıntas, E., Ilgun, S. & Angay, M. (2022). İlköğretim matematik öğretmenlerinin problem çözme ile ilgili görüşleri (opinions of primary school mathematics teachers on problem solving). Inonu University Journal of the Faculty of Education, 23(2), 1223- 1244. https://doi.org/10.17679/inuefd.1132779
• Altıntas, E., Ilgün, S. & Karadag, M. (2022). Ortaokul öğrencilerinin matematik okuryazarlık öz-yeterlik algılarının çeşitli değişkenler açısından incelenmesi (examination of secondary school students' perceptions of mathematics literacy self-efficacy in terms of various variables), Iğdır University Journal of Social Sciences, 31, 255-267. https://doi.org/10.54600/igdirsosbilder.1128169
• Angay, M. (2022). Mantıksal akıl yürütme yöntemleri ile işlenen matematik dersinin öğrencilerin beceri temelli sorulardaki başarısına etkisi ve öğretime dair öğrenci görüşleri (the effect of the mathematics course taught with logical reasoning methods on the success of students in skill-based questions and student opinions on teaching). Master Thesis, Kafkas University, Graduate School of Applied and Natural Sciences, Kars.
• Aydemir, H. & Kubanc, Y. (2014). Problem çözme sürecinde üstbilişsel davranışların incelenmesi (investigation of the cognitive behavioral problem solving process). Journal of Turkish Studies, 9(2), 203-219. http://dx.doi.org/10.7827/TurkishStudies.6555
• Bal, A. P. & Doganay, A. (2010). İlköğretim beşinci sınıf matematik öğretiminde ölçme-değerlendirme sürecinde yaşanan sorunların analizi an analysis of problems encountered in the process of measurement and evaluation in teaching mathematics at primary school 5th grade). Educational Administration: Theory and Practice, 3(3), 373-398. https://dergipark.org.tr/tr/pub/kuey/issue/10331/126631
• Buyukozturk, S. (2020). Sosyal bilimler için veri analizi el kitabı istatistik, araştırma deseni spss uygulamaları ve yorum (data analysis handbook for social sciences statistics, research design spss applications and ınterpretation) (28. Edition). Pegem Academy Publishing, Ankara.
• Buyukozturk, S., Kilic Cakmak, E., Akgun, O. E., Karadeniz, S. & Demirel, F. (2018). Eğitimde bilimsel araştırma yöntemleri (scientific research methods in education) (25. Edition). Pegem Academy Publishing, Ankara.
• Calik, M. & Ayas, A. (2003). Çözeltilerde kavram başarı testi hazırlama ve uygulama (preparation and application of a concept success test in solutions). Pamukkale University Faculty of Education Journal, 14(14), 1-17. https://dergipark.org.tr/tr/pub/pauefd/issue/11129/133088
• Cepni, S. (2020). Eğitimde “bir adım ötesi” tartışmalarının kavramsal çerçevesini anlamak: dijitalleşme ve insanileşme (etik ve değerler) kavramlarında denge kurma arayışları (understanding the conceptual framework of the “one step ahead” discussions in education: seekıng a balance in the concepts of digitalization and humanization (ethics and values)). Journal of Science, Mathematics, Entrepreneurship and Technology Education, 3(2), 65-79. https://dergipark.org.tr/tr/pub/fmgted/issue/56406/741427
• Demir, E. (2010). Uluslararası Öğrenci Değerlendirme Programı (PISA) bilişsel alan testlerinde yer alan soru tiplerine göre türkiye’de öğrenci başarıları (the students achievement in turkey, according to the question types used in Program for International Student Assessment (PISA) Cognitive Domain Tests). Master Thesis, Hacettepe University, Social Sciences Institute, Ankara.
• Demir, G. (2019). 8. sınıf öğrencilerinin kullandıkları problem çözme stratejileri ve problem çözme sürecinde karşılaştıkları hatalar. (problem-solving strategies utilized by 8th grade students and errors they face during the problem-solving process). Master Thesis, University of Uşak Graduate School of Natural and Applied Sciences, Uşak.
• Erden, B. (2020). Türkçe, matematik ve fen bilimleri dersi beceri temelli sorularına ilişkin öğretmen görüşleri (teachers' views related to skill-based questions in turkish, mathematics and science lessons). Academia Journal of Educational Research, 5(2), 270-292. https://dergipark.org.tr/tr/pub/egitim/issue/54643/742630
• Firat, T. & Kocak, D. (2019). Başarılı okuyucular ile öğrenme güçlüğü olan öğrencilerin metni anlamak için kullandıkları bilişsel ve üstbilişsel stratejiler (cognitive and metacognitive strategies used by good readers and students with learning disabilities to understand a text). Kastamonu Journal of Education, 27(2), 669-681. https://doi.org/10.24106/kefdergi.2672
• Kablan, Z. & Bozkus, F. (2021). Liselere giriş sınavı matematik problemlerine ilişkin öğretmen ve öğrenci görüşleri (mathematics teachers’ and students’ opinions on mathematics problems of the high schools entrance exam). Journal of Mersin University Faculty of Education, 17(1), 211-231. https://doi.org/10.17860/mersinefd.800738
• Karatas, I. & Guven, B. (2003). Problem çözme davranışlarının değerlendirilmesinde kullanılan yöntemler: klinik mülakatın potansiyeli (methods used to evaluate problem-solving behaviors: the potential of the clinical ınterview). Elementary Education Online, 2(2).
• Karataş, I., & Guven, B. (2004). 8. sınıf öğrencilerinin problem çözme becerilerinin belirlenmesi: bir özel durum çalışması (determining 8th grade students' problem solving skills: a case study). Journal of National Education, 163, 132-143.
• Karatas, Z. (2015). Sosyal bilimlerde nitel araştırma yöntemleri (qualitative research methods in the social sciences). Journal of Spiritual Based Social Work Research, 1(1), 62-80.
• Kaya, M. O. (2019). PISA ve TEOG sınavları matematik sorularının öğretim ilkeleri bağlamında değerlendirilmesi (evaluation of mathematics questions in PISA and TEOG exams in the context of teaching principles). Master Thesis, Marmara University, Institute of Educational Sciences, İstanbul.
• Kertil, M., Gülbagci Dede, H. & Ulusoy, E. G. (2021). Skill-based mathematics questions: what do middle school mathematics teachers think about and how do they ımplement them? Turkish Journal of Computer and Mathematics Education, 12(1), 151-186.
• Koç Koca, A. (2022). Özel yetenekli öğrencilerin matematiksel problem çözme süreçleri ve kullandıkları stratejiler (the mathematical problem solving processes of gifted students and the strategies they used). Master Thesis, Adiyaman University, Graduate Education Instıtute, Adıyaman.
• MoNET (Ministry of National Education of Turkiye), (2018). 2023 Eğitim Vizyonu (2023 Education Vision). Ankara. https://www.gmka.gov.tr/dokumanlar/yayinlar/2023_Eğitim%20Vizyonu.pdf
• Ozkubat, U. & Ozmen, E. R. (2018). Öğrenme güçlüğü olan öğrencilerin matematik problemi çözme süreçlerinin incelenmesi: sesli düşünme protokolü uygulaması (analysis of mathematical problem solving process of students with learning disability: ımplementation of think aloud protocol). Ankara University Faculty of Educational Sciences Journal of Special Education, 19(1), 155-180. https://doi.org/10.21565/ozelegitimdergisi.299494
• Ozturk, A. Y. & Sahin, C. (2013). Süreç odaklı ölçme-değerlendirme yöntemlerinin uygulanmasında yaşanacak güçlüklere ilişkin sınıf öğretmeni adaylarının görüşleri (pre-service teachers' views on difficulties on ımplementation of process-oriented assessment and evaluation methods). Buca Faculty of Education Journal, 36, 109-129.
• Polya, G. (1957). How to solve it, a new aspect of mathematical method, Princeton Universty Press, New Jersey. Salvucci, S., Walter, E., Conley, V., Fink, S. & Saba, M. (1997). Measurement error studies at The National Center for Education Statistics (NCES). Washington D. C.: U. S. Department of Education.
• Sipahi, Y. (2021). Problem-solvıng processes of mathematically gifted and non-gifted students. Master Thesis, The Graduate School Of Natural And Applıed Scıences Of Mıddle East Technıcal University, Ankara.
• Tan, S. (2009). Misuses of KR-20 and Cronbach’s Alpha reliability coefficients. Education and Science, 34(152), 101-112.
• Treagust, D. F. (1988). Development and use of diagnostic tests to evaluate students’ misconceptions in science. International Journal of Science Education, 10(2), 159-169.
• Umay, A., Akkus, O. & Duatepe-Paksu, A. (2006). Matematik dersi 1.-5. sınıf öğretim programının NCTM prensip ve standartlarına göre incelenmesi (mathematics lesson 1.-5. examining the classroom curriculum according to NCTM principles and standards). Journal of Hacettepe University Faculty of Education, 31, 198-211. https://hdl.handle.net/11499/41104
• Umurbek, M. (2020). Ortaokul 7. sınıf öğrencilerinin cebirsel sözel problemleri çözme sürecinin incelenmesi (the investigation of the solution process of algebraic verbal problems in seventh grades). Master Thesis, Aydın Adnan Menderes University, Graduate School of Applied and Natural Sciences, Aydın.
• Uzun, H. (2021). Yeni nesil matematik sorularına ilişkin ortaokul matematik öğretmenlerinin yaklaşımlarının incelenmesi (investigation of secondary school mathematics teachers' approaches to new generation mathematics questions). Master Thesis, Gaziantep University, Institute of Education Sciences, Gaziantep.
• Yesilova, O. (2013). İlköğretim 7. sınıf öğrencilerinin problem çözme sürecindeki davranışları ve problem çözme başarı düzeyleri (behaviors and problem solving success levels of primary 7th grade students in the problem solving process). Master Thesis, Marmara University, Institute of Education Sciences, İstanbul.
• Yildirim, A. & Simsek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri(qualitative research methods in the social sciences). Seçkin Publishing, Ankara.
• Yilmaz, K. (2021). Öğretmen adaylarının problem çözme süreçlerinin incelenmesi (examination of pre-service teachers' problem solving processes). Master Thesis, Erzincan Binali Yıldırım University, Graduate School of Applied and Natural Sciences, Erzincan.