The Effect of Problem-Solving Strategies Education on Developing Mathematical Literacy

Year 2022, , 275 - 303, 31.12.2022

Hasan Temel , Murat Altun

https://doi.org/10.17522/balikesirnef.1164584

Cited By: 1

Abstract

Today, how to increase the success and level of students' mathematical literacy is one of the most important areas of mathematics education. In this context, the study aimed to examine the effect of problem-solving strategies education on mathematical literacy. 42 students in the eighth grade of the secondary school participated in the study, in which the experimental design was preferred in quantitative research methods. Five-week problem-solving strategies education was carried out with 21 students in the experimental group. The data of the study were obtained with the mathematical literacy test, which was developed to determine the mathematical literacy achievement and levels of the experimental and control groups before and after the education. As a result of the findings, it was determined that problem-solving strategies education had a significant effect on students' mathematical literacy achievement. Concordantly, suggestions have been made regarding the need to use problem-solving strategies to improve mathematical literacy.

Keywords

mathematical literacy, mathematics education, PISA, problem-solving, problem-solving strategies

Matematik Okuryazarlığını Geliştirmede Problem Çözme Stratejileri Eğitiminin Etkisi

Abstract

Günümüzde matematik eğitiminin en önemli uğraşı alanlarının başında öğrencilerin matematik okuryazarlık başarı ve düzeyinin nasıl arttırılacağı gelmektedir. Bu bağlamda gerçekleştirilen çalışmada problem çözme strateji eğitiminin matematik okuryazarlığına etkisinin incelenmesi amaçlanmıştır. Araştırmaya ortaokul sekizinci sınıfta öğrenim gören 42 öğrenci katılmış ve nicel araştırma yöntemlerinden deneysel desen tercih edilmiştir. Deney grubunda bulunan 21 öğrenci ile beş haftalık problem çözme stratejileri eğitimi gerçekleştirilmiştir. Çalışmanın verileri, eğitim öncesi ve sonrasında deney ve kontrol grubunun matematik okuryazarlık başarı ve düzeylerini belirlemek amacıyla geliştirilen matematik okuryazarlık testi (MOT) ile elde edilmiştir. Elde edilen bulgular sonucunda, problem çözme stratejileri eğitiminin öğrencilerin matematik okuryazarlık başarı düzeylerine anlamlı bir etkisinin olduğu belirlenmiştir. Bu bağlamda matematik okuryazarlığını geliştirmede problem çözme stratejilerinden faydalanılması gerektiğine yönelik önerilerde bulunulmuştur. 

Keywords

matematik okuryazarlığı, matematik eğitimi, PISA, problem çözme, problem çözme stratejileri

References

• Alibali, M. W., Phillips, K. M., & Fischer, A. D. (2009). Learning new problem-solving strategies leads to changes in problem representation. Cognitive Development, 24(2), 89-101. https://doi.org/10.1016/j.cogdev.2008.12.005
• Altun M., & Memnun D. S. (2008). Mathematics teacher trainees’ skills and opinions on solving non-routine mathematical problems. Journal of Theory and Practice in Education, 4(2), 213-238.
• Altun, M. (2014). Ortaokullarda (5, 6, 7 ve 8. sınıflarda) matematik öğretimi [Teaching mathematics in secondary schools (5th, 6th, 7th and 8th grades)]. (10th ed.). Alfa Aktüel.
• Altun, M., & Akkaya, R. (2014). Mathematics teachers’ comments on PISA math questions and our country’s students’ low achievement levels. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Hacettepe University Journal of Education], 29(1), 19-34.
• Altun, M., & Arslan, Ç. (2006). İlköğretim öğrencilerinin problem çözme stratejilerini öğrenmeleri üzerine bir çalışma [A study on elementary school students' learning problem solving strategies]. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 19(1), 1-21.
• Altun, M., & Bozkurt, I. (2017). A new classification proposal for mathematical literacy problems. Education and Science, 42(190), 171-188. http://dx.doi.org/10.15390/EB.2017.6916
• Altun, M., Memnun, D. S., & Yazgan, Y. (2007). Primary school teacher trainees’ skills and opinions on solving non-routine mathematical problems. Elementary Education Online, 6(1), 127-143.
• Anderson, J. (2009). Mathematics curriculum development and the role of problem solving. The Australian Curriculum Studies Association's 2009 Biennial Conference (ACSA Conference). Retrieved from http://www.acsa.edu.au/pages/images/-Judy%20Anderson%20-%20Mathematics%20Curriculum%20Development.pdf
• Anıl, D., Özkan, Y. Ö., & Demir, E. (2015). PISA 2012 araştırması ulusal nihai rapor [PISA 2012 survey national final report]. Retrieved from https://drive.google.com/file/d/0B2wxMX5xMcnhaGtnV2x6YWsyY2c/view?resourcekey=0-eKJtL9If8HV5aaL2vclhMg
• Artut, P. D., & Tarım, K. (2006). İlköğretim öğrencilerinin rutin olmayan sözel problemleri çözme düzeylerinin çözüm stratejilerinin ve hata türlerinin incelenmesi [Investigation of the elemantary school students’ problem solving levels, problem solving strategies and error types in the nonroutine word problems]. Çukurova Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 15(2), 39-50.
• Baki, A. T., & Özpınar, İ. T. (2007). Logo destekli geometri öğretimi materyalinin öğrencilerin akademik başarılarına etkileri ve öğrencilerin uygulama ile ilgili görüşleri. Çukurova Üniversitesi Eğitim Fakültesi Dergisi, 3(34), 153.
• Bautier, E., & Rayou, P. (2007). What PISA really evaluates: literacy or students’ universes of reference?. Journal of Educational Change, 8(4), 359-364. https://doi.org/10.1007/s10833-007-9043-9
• Bolstad, O. H. (2021). Lower secondary students’ encounters with mathematical literacy. Mathematics Education Research Journal, 1-17. https://doi.org/10.1007/s13394-021-00386-7
• Breakspear, S. (2012).The Policy Impact of PISA: An Exploration of the Normative Effects of International Benchmarking in School System Performance. OECD Education Working Papers, No. 71, OECD Publishing, Paris, https://doi.org/10.1787/5k9fdfqffr28-en.
• Breen, S., Cleary, J., & O'Shea, A. (2009). An investigation of the mathematical literacy of first year third-level students in the Republic of Ireland. International Journal of Mathematical Education in Science and Technology, 40(2), 229-246. https://doi.org/10.1080/00207390802566915
• Büyüköztürk, Ş. (2013). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences]. PegemA Yayıncılık.
• Can, A. (2014). SPSS ile bilimsel araştırma sürecinde nicel veri analizi [Quantitative data analysis in the scientific research process with SPSS] (3rd ed.). Pegem Akademi.
• Carvalho, L. M., Costa, E., & Gonçalves, C. (2017). Fifteen years looking at the mirror: On the presence of PISA in education policy processes (Portugal, 2000‐2016). European Journal of Education, 52(2), 154-166. https://doi.org/10.1111/ejed.12210
• Cohen, L., Manion, L. ve Morrison, K. (2005). Research methods in education (5th ed.). Routledge Falmer.
• Colwell, J., & Enderson, M. C. (2016). “When I hear literacy”: Using pre-service teachers' perceptions of mathematical literacy to inform program changes in teacher education. Teaching and Teacher Education, 53, 63-74. https://doi.org/10.1016/j.tate.2015.11.001
• Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.
• Çelebioğlu, B., & Yazgan, Y. (2009). İlköğretim öğrencilerinin bağıntı bulma ve sistematik liste yapma stratejilerini kullanma düzeyleri. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 22(1), 15-28.
• Delice, A., & Sevimli, E. (2010). Geometri problemlerinin çözüm süreçlerinde görselleme becerilerinin incelenmesi: ek çizimler [Investigation of visualization ability in geometry problem solving process: auxiliary drawings]. M.Ü. Atatürk Eğitim Fakültesi Eğitim Bilimleri Dergisi, 31, 83-102.
• Dinçer, B., Akarsu, E., & Yılmaz, S. (2016). İlköğretim matematik öğretmeni adaylarının matematik okuryazarlığı özyeterlik algıları ile matematik öğretimi yeterlik inanç düzeylerinin incelenmesi [The investigation of perceptions of math literacy self-efficacy and mathematics teaching efficacy belief levels of preservice primary mathematics teachers]. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(1), 207-228. https://doi.org/10.16949/turcomat.99884
• Dossey, J., McCrone, S., Turner, R., & Lindquist, M. (2008). PISA 2003 mathematical literacy and learning in the Americas. Canadian Journal of Science, Mathematics and Technology Education, 8(2), 140-152. https://doi.org/10.1080/14926150802169289
• Eisenmann, P., Novotná, J., Přibyl, J., & Břehovský, J. (2015). The development of a culture of problem solving with secondary students through heuristic strategies. Mathematics Education Research Journal, 27(4), 535-562. https://doi.org/10.1007/s13394-015-0150-2
• Elia, I., Van Den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM, 41(5), 605. https://doi.org/10.1007/s11858-009-0184-6
• Evrekli, E., İnel, D., Deniş, H., & Balım, A. G. (2011). Fen eğitimi alanındaki lisansüstü tezlerdeki yöntemsel ve istatistiksel sorunlar [Methodological and statistical problems in graduate theses in the field of science education]. İlköğretim Online,10(1), 206-218.
• Fidan, Y., & Türnüklü, E. (2010). İlköğretim 5. sınıf öğrencilerinin geometrik düşünme düzeylerinin bazı değişkenler açısından incelenmesi [Examination of 5th grade students’ levels of geometric thinking in terms of some variables]. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 27(27), 185-197.
• Fraenkel, J. R. & Wallen, N. E. (2006). How to design and evaluate research in education. McGraw-Hill.
• Güler, H. K. (2013). Türk öğrencilerin PISA’da karşılaştıkları güçlüklerin analizi [Analysis of turkish students’ difficulties encountered in PISA]. Uludağ Üniversitesi Eğitim Fakültesi, 26(2), 501-522.
• Hopfenbeck, T. N., & Kjærnsli, M. (2016). Students’ test motivation in PISA: the case of Norway. The Curriculum Journal, 27(3), 406-422. https://doi.org/10.1080/09585176.2016.1156004
• Işık, C., & Kar, T. (2011). İlköğretim 6, 7 ve 8. sınıf öğrencilerinin sayı algılama ve rutin olmayan problem çözme becerilerinin incelenmesi [Investigating of the number perception and nonroutine problem solving skills of 6th, 7th and 8th grade students]. Ahi Evran Üniversitesi Eğitim Fakültesi Dergisi, 12(1), 57-72.
• İlbağı, E. A. (2012). PISA 2003 matematik okuryazarlığı soruları bağlamında 15 yaş grubu öğrencilerinin matematik okuryazarlığı ve tutumlarının incelenmesi [Examination of the mathematical literacy and attitudes of the students aged 15 in terms of PISA 2003 mathematical literacy items]. [Unpublished doctoral thesis]. Atatürk University, Erzurum.
• Jacobs, H. H. (1989). Interdisciplinary curriculum: Design and implementation. Association for Supervision and Curriculum Development.
• Johnson, B., & Christensen, L. (2014) Educational research: Quantitative, qualitative, and mixed approaches (5th ed.). SAGE Publications
• Karasar, N. (2008). Bilimsel araştırma yöntemi [Scientific research method]. Nobel Yayın Dağıtım.
• Kaur, B. & Yeap, B. H. (2009). Mathematical problem solving in Singaporeschools. In Kaur, B.,Yeap, B.H. & Kapur, M. (Eds.). Mathematical problem solving: Yearbook 2009 (pp. 3-13). Association of Mathematics Educationand World Scientific.
• Kılıç, S., Çene, E., & Demir, İ. (2012). Türkiye’deki matematik başarısının öğrenme stratejileri açısından 8 ülkeyle karşılaştırılması [Comparison of learning strategies for mathematics achievement in Turkey with eight countries]. Kuram ve Uygulamada Eğitim Bilimleri, 12(4), 2585-2598.
• Köse, M. (2012). PISA 2003, 2006 ve 2009 Türkiye Uygulaması matematik ortak maddelerindeki başarıların incelenmesi [Examining Academic Achivement in PISA 2003, 2006 and 2009 Turkey Implementation by Using Mathematic Common Items]. [Unpublished master thesis]. Hacettepe University, Ankara.
• Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.
• Lin, S. W., & Tai, W. C. (2015). Latent class analysis of students' mathematics learning strategies and the relationship between learning strategy and mathematical literacy. Universal Journal of Educational Research, 3(6), 390-395. Doi:10.13189/ujer.2015.030606
• Marczyk, G., DeMatteo, D. & Festinger, D. (2005). Essentials of research design and methodology. John Wiley & Sons.
• McMillan, J. H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7th ed.). Pearson
• Ministry of National Education [MoNE]. (2013). Ortaokul matematik dersi 5-8. sınıflar öğretim programı [Middle school math class 5th -8th classes curriculum]. Talim Terbiye Başkanlığı Yayınları.
• Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics lesson curriculum (Primary and secondary school grades 1, 2, 3, 4, 5, 6, 7 and 8)]. Retrieved from http://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
• Mudaly, R. (2011). Risking it: Entering uneven socio-scientific spaces in a life sciences classroom. African Journal of Research in Mathematics, Science and Technology Education, 15(3), 27-40. https://doi.org/10.1080/10288457.2011.10740716
• Muyo, M. (2015). Prizren Eğitim Fakültesi öğrencilerinin matematik okuryazarlığı problemlerini çözme becerilerinin geliştirilmesi [Improving mathematical literacy and problem solving abilities of students in Prizren faculty of education]. [Unpublished doctoral thesis]. Balıkesir University, Balıkesir.
• Nahornick, A. (2014). The effect of group dynamics on high-school students' creativity and problem-solving strategies with investigative open-ended non-routine problems. [Unpublished doctoral thesis]. Columbia University, Columbia.
• Novita, R., Zulkardi, Z., & Hartono, Y. (2012). Exploring primary student’s problem-solving ability by doing tasks like PISA's question. Journal on Mathematics Education, 3(2), 133-150. Retrieved from https://files.eric.ed.gov/fulltext/EJ1078578.pdf
• Organisation for Economic Co-operation and Development [OECD]. (2014). PISA 2012 Results: What Students Know and Can Do – Student Performance in Mathematics, Reading and Science (Volume I, Revised edition, February 2014). PISA, OECD Publishing. http://dx.doi.org/10.1787/9789264201118-en
• Organisation for Economic Co-operation and Development [OECD]. (2019), PISA 2018 assessment and analytical framework. PISA, OECD Publishing. https://doi.org/10.1787/b25efab8-en.
• Organisation for Economic Co-operation and Development [OECD]. (2016). PISA 2015 results (Volume I): Excellence and equity in education. OECD Publishing. http://dx.doi.org/10.1787/9789264266490-en
• Özgen, K., & Bindak, R. (2008). Matematik okuryazarlığı öz-yeterlik ölçeğinin geliştirilmesi [The development of self-efficiacy scale for mathematics literacy]. Kastamonu Eğitim Dergisi, 16(2), 517-528.
• Pilten, P. (2008). Üstbiliş stratejileri öğretiminin ilköğretim beşinci sınıf öğrencilerinin matematiksel muhakeme becerilerine etkisi [The effect of metacognitive instruction on mathematical reasoning of fifth grade primary school students]. [Unpublished doctoral thesis]. Gazi University, Ankara.
• Polya, G. (1973). How to solve it (2nd ed.). Princeton University Press.
• Pugalee, D. K. (1999). Constructing a model of mathematical literacy. The Clearing House, 73(1), 19-22.
• 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
• Sáenz, C. (2009). The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA). Educational Studies in Mathematics, 71(2), 123-143. https://doi.org/10.1007/s10649-008-9167-8
• Shuttleworth, M. (2009). Content validity. Retrieved from https://explorable.com/content-validity
• Stacey, K. (2015). The real world and the mathematical world. In K. Stacey & R. Turner (Eds.), Assessing mathematical literacy. The PISA experience (pp. 57–84). Springer.
• Stacey, K., & Turner, R. (2015). Assessing mathematical literacy: The PISA experience. Springer.
• Syeda, T. J. (2015). Perceptions of Private College Teachers of Karachi about the Curriculum Prescribed by Sindh Bureau of Curriculum (BOC). Acta Didactica Napocensia, 8(4), 13-24. Retrieved from https://files.eric.ed.gov/fulltext/EJ1092636.pdf
• Şefik, Ö. & Dost, Ş. (2016). Secondary preservice mathematics teachers' views on mathematical literacy. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 10(2), 320-338. https://doi.org/10.17522/balikesirnef.277935
• Toh, T. L. (2021). School calculus curriculum and the Singapore mathematics curriculum framework. ZDM–Mathematics Education, 53(3), 535-547. https://doi.org/10.1007/s11858-021-01225-6
• Uyangör, S. M., & Övez, F. T. D. (2012). İlköğretim altıncı sınıf matematik dersi öğretim programı cebir öğrenme alanı kazanımlarına ulaşılma düzeyi [Reaching of attainment levels of algebra learning domain in sixth grade of elementary mathematics education program]. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, 6(1), 01-22.
• Ülger, T. K., Bozkurt, I., & Altun, M. (2020). Thematic Analysis of Articles Focusing on Mathematical Literacy in Mathematics Teaching-Learning Process. Education and Science, 45(201), 1-37. http://dx.doi.org/10.15390/EB.2020.8028
• Verschaffel, L., De Corte, E., Lasure, S., Van Vaerenbergh, G., Bogaerts, H., & Ratinckx, E. (1999). Learning to solve mathematical application problems: A design experiment with fifth graders. Mathematical Thinking and Learning, 1(3), 195-229. https://doi.org/10.1207/s15327833mtl0103_2
• Wardono, Waluya, S. B., Scolastika, M., & Candra, D. (2016). Mathematics literacy on problem based learning with indonesian realistic mathematics education approach assisted e-learning edmodo. In Journal of Physics: Conference Series, 693(1), 1-10. IOP Publishing.
• Wheater, R., R. Ager, B. Burge, & J. Sizmur. (2014). Achievement of 15-year-olds in England: PISA 2012 national report (OECD Programme for International Student Assessment). Retrieved from https://dera.ioe.ac.uk/19484/1/programme-for-international-student-assessment-pisa-2012-national-report-for-england.pdf
• Yazgan, Y. (2007). Dördüncü ve beşinci sınıf öğrencilerinin rutin olmayan problem çözme stratejileriyle ilgili gözlemler [Observations about fourth and fifth grade students’ strategies to solve non-routine problems]. İlköğretim Online, 6(2), 249-263.
• Yazgan, Y., & Bintaş, J. (2005). İlköğretim dördüncü ve beşinci sınıf öğrencilerinin problem çözme stratejilerini kullanabilme düzeyleri: Bir öğretim deneyi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 28, 210-218.
• Yenilmez, K., & Uysal, E. (2011). Sekizinci sınıf öğrencilerinin matematik okuryazarlığı düzeyi [The mathematics literacy level of eighth grade students]. Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi, 12(2), 1-15.
• Yıkmış, A. (1999). Zihin engelli çocuklara temel toplama ve çıkarma işlemlerinin kazandırılmasında etkileşim ünitesi ile sunulan bireyselleştirilmiş öğretim materyalinin etkililiği [The effectiveness of the individualized teaching materials presented with interactive unit on the teaching of the basic addition and subtraction skills to the student with mental retardation]. [Unpublished doctoral thesis]. Anadolu University, Eskişehir.
• Yıldırım, A. (1996). Disiplinlerarası öğretim kavramı ve programlar açısından doğurduğu sonuçlar. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 12, 89-94.
• Yılmaz, K., & Altınkurt, Y. (2011). Öğretmen adaylarının Türk eğitim sisteminin sorunlarına ilişkin görüşleri [Prospective teachers’ views about the problems of Turkish educational system]. Uluslararası insan bilimleri dergisi, 8(1), 942-973.