Fikret CİHAN, Hatice AKKOÇ

32216

Meslek Yüksekokulu Öğrencilerinin Matematiksel Problem Çözmeye İlişkin Metaforik Algıları

Problem çözme üniversite düzeyindeki matematik derslerinde önemli bir yere sahip olduğundan üniversite öğrencilerinin problem çözme ile ilgili algılarını belirlemek alana katkı sağlayabilir. Bu doğrultuda, bu çalışmanın amacı meslek yüksekokulu öğrencilerinin matematiksel problem çözme algılarını metaforlar aracılığıyla belirlemektir. Bunun için bu çalışmada örnek olay tarama modeli tercih edilmiştir. Araştırmanın katılımcıları 2019-2020 eğitim-öğretim yılı güz döneminde Türkiye’deki bir devlet üniversitesinin meslek yüksekokulunun çeşitli programlarında öğrenim gören 234 öğrencidir. “Matematiksel Problem Çözme Metafor Anketi” veri toplama aracı olarak kullanılmıştır. Bu ankette katılımcılardan matematiksel problem çözme ile ilgili bir metafor üretmeleri ve bunu gerekçelendirmeleri istenmiştir. Katılımcıların yazılı yanıtları içerik analizi ile analiz edilmiştir. Verilerin analizi katılımcıların matematiksel problem çözme ile ilgili 105 geçerli metafor ürettiğini göstermiştir. Katılımcıların en sık “hayat”, “labirent”, “satranç oynamak” ve “yapboz yapmak” metaforlarını ürettikleri saptanmıştır. Ayrıca katılımcıların ürettikleri metaforlar on farklı kavramsal kategori altında kategorize edilmiştir. Üretilen metaforlar en sık “komplike” ve “stratejik aşamalı” kategorilerinde toplanmıştır. Bu kategorilerin katılımcıların öğrenim gördükleri programlarla istatistiksel olarak anlamlı bir ilişkiye sahip olduğu saptanmıştır. Kategorilere dayalı olarak, öğrencilerin matematiksel problem çözme algıları tartışılmıştır. Ayrıca öğrencilerin olumsuz algılarının nasıl değiştirilebileceğine ilişkin öğretimsel çıkarımlar tartışılmıştır.
Anahtar Kelimeler:

Matematiksel problem çözme, metafor, algı, meslek yüksekokulu öğrencileri

Metaphorical Perceptions of Vocational High School Students on Mathematical Problem Solving

Since problem solving has an important place in university level mathematics courses, determining university students' perceptions about problem solving can contribute to the field. In this regard, the aim of this study is to determine the mathematical problem solving perceptions of vocational high school students through metaphors. The case survey method was preferred for this study. Participants were 234 students studying in various programs of a vocational high school of a public university in Turkey in the fall semester of the 2019-2020 academic year. “Mathematical Problem Solving Metaphor Survey” were used as data collection tool. This survey included items that asked them to produce a metaphor for mathematical problem solving and its justification. Their written responses were analyzed using content analysis. Analysis of data indicated that participants produced 105 valid metaphors for mathematical problem solving. The most commonly used metaphors were “life”, “labyrinth”, “playing chess”, and “jigsaw puzzles”. Also, the metaphors produced by the participants were categorized under ten different conceptual categories. Metaphors were mostly gathered in the categories of “complicated” and “strategically progressive”. These categories have a statistically significant relationship with the programs in which the participants study at. Based on the categories, students’ perceptions of mathematical problem solving were discussed. Also, the study discusses instructional implications regarding how to change negative perceptions of students.
Keywords:

Mathematical problem solving, metaphor, perception, vocational high school students,

PDF

___

  • Agresti, A. (1990). Categorical data analysis. New York: John Wiley & Sons. Retrieved March 20, 2020 from https://books.google.com.tr/books/about/Categorical_Data_Analysis.html?id=MCnvAAAAMAAJ&redir_esc=y
  • Botha, E. (2009). Why metaphor matters in education. South African Journal of Education, 29(4), 431-444. https://dx.doi.org/10.15700/saje.v29n4a287
  • Buerk, D. (1988). Mathematical metaphors from advanced placement students. Humanistic Mathematics Network Journal, 1(3), Article 10. https://dx.doi.org/10.5642/hmnj.198801.03.10
  • Cai, J. (2004). Why do U.S. and Chinese students think differently in mathematical problem solving?: Impact of early algebra learning and teachers’ beliefs. The Journal of Mathematical Behavior, 23(2), 135-167. https://doi.org/10.1016/j.jmathb.2004.03.004
  • Callejo, M. L., & Vila, A. (2009). Approach to mathematical problem solving and students’ belief systems: two case studies. Educational Studies in Mathematics, 72(1), 111-126. https://doi.org/10.1007/s10649-009-9195-z
  • Chapman, O. (1997). Metaphors in the teaching of mathematical problem solving. Educational Studies in Mathematics, 32(3), 201-228. https://doi.org/10.1023/A:1002991718392
  • Chiu, M. M. (2001). Using metaphors to understand and solve arithmetic problems: Novices and experts working with negative numbers. Mathematical Thinking and Learning, 3(2-3), 93-124. https://doi.org/10.1080/10986065.2001.9679970
  • Cochran, W. G. (1954). Some methods for strengthening the common χ2 tests. Biometrics, 10(4), 417-451. https://dx.doi.org/10.2307/3001616
  • Creswell, J. W. (2014). Research design: qualitative, quantitative and mixed methods approaches (4th ed.). Thousand Oaks, CA: Sage. Retrieved March 10, 2020 from https://study.sagepub.com/creswellrd4e
  • Department for Education. (2014). Statutory guidance national curriculum in England: Mathematics programmes of study. Retrieved December 10, 2019 from https://www.gov.uk/government/publications/national-curriculum-in-england-mathematics-programmes-of-study/national-curriculum-in-england-mathematics-programmes-of-study
  • Diaz-Rojas, D., & Soto-Andrade, J. (2017, February). Enactive metaphors in mathematical problem solving. In T. Dooley & G. Gueudet (Eds.), Proceedings of CERME10 (pp. 3904-3911). DCU Institute of Education and ERME, Dublin, Ireland. Retrieved February 11, 2020 from https://hal.archives-ouvertes.fr/hal-01950551
  • Ergen, Y. (2020). ‘Does mathematics fool us?’ A study on fourth grade students’ non-routine maths problem solving skills. Issues in Educational Research, 30(3), 845-865. Retrieved October 11, 2021 from http://www.iier.org.au/iier30/ergen.pdf
  • Fisher, R. A. (1925). Statistical methods for research workers. Edinburgh, Scotland: Oliver and Boyd. Retrieved March 20, 2020 from https://books.google.com.tr/books/about/Statistical_Methods_for_Research_Workers.html?id=I0NBAAAAIAAJ&redir_esc=y
  • Font, V., Bolite, J., & Acevedo, J. (2010). Metaphors in mathematics classrooms: analyzing the dynamic process of teaching and learning of graph functions. Educational Studies in Mathematics, 75(2), 131-152. https://doi.org/10.1007/s10649-010-9247-4
  • Freeman, G. H., & Halton, J. H. (1951). Note on exact treatment of contingency, goodness of fit and other problems of significance. Biometrika, 38(1-2), 141-149. https://dx.doi.org/10.2307/2332323
  • Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication and Technology Journal, 30(4), 233-252. https://doi.org/10.1007/BF02765185
  • Guest, G., MacQueen, K. M., & Namey, E. E. (2012). Applied thematic analysis. Thousand Oaks, CA: Sage. https://dx.doi.org/10.4135/9781483384436
  • Hannula, M. S. (2002). Attitude towards mathematics: emotions, expectations and values. Educational Studies in Mathematic, 49(1), 25-46. https://dx.doi.org/10.1023/A:1016048823497
  • Hannula, M. S. (2015). Emotions in problem solving. In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 269-288). New York: Springer. https://doi.org/10.1007/978-3-319-17187-6_16
  • Hendriana, H., & Rohaeti, E. E. (2017). The importance of metaphorical thinking in the teaching of mathematics. Current Science, 113(11), 2160-2164. https://doi.org/10.18520/cs/v113/i11/2160-2164
  • Hodgen, J., Wake, G., & Dalby, D. (2017). Mathematics in the successful technical education of 16-19 year olds. London: Gatsby. Retrieved January 17, 2020 from https://www.gatsby.org.uk/uploads/education/reports/pdf/maths-in-international-systems.pdf
  • Innis, R. E. (1982). From perception to metaphor. In K. Bühler (Ed.), Semiotic foundations of language theory (pp. 43-53). Boston, MA: Springer. https://doi.org/10.1007/978-1-4757-0923-0_4
  • Julien, H. (2008). Content analysis. In L. M. Given (Ed.), The Sage encyclopedia of qualitative research methods (Vol 1, pp. 120-122). Los Angeles, California: Sage Publications, Inc. https://dx.doi.org/10.4135/9781412963909
  • Lachner, A., & Nückles, M. (2016). Tell me why! Content knowledge predicts process-orientation of math researchers’ and math teachers’ explanations. Instructional Science, 44(3), 221-242. https://doi.org/10.1007/s11251-015-9365-6
  • Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and thought (2nd ed., pp. 202-251). Cambridge: Cambridge University Press. Retrieved January 11, 2020 from https://escholarship.org/content/qt4nv3j5j9/qt4nv3j5j9.pdf
  • Lakoff, G., & Johnson, M. (1980a). Metaphors we live by. Chicago: The University of Chicago Press. Retrieved January 11, 2020 from https://books.google.com.tr/books/about/Metaphors_We_Live_By.html?id=r6nOYYtxzUoC&redir_esc=y
  • Lakoff, G., & Johnson, M. (1980b). Conceptual metaphor in everyday language. The Journal of Philosophy, 77(8), 453-486. https://dx.doi.org/10.2307/2025464
  • Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books. Retrieved January 11, 2020 from https://pages.ucsd.edu/~rnunez/COGS252_Readings/Preface_Intro.PDF
  • Larsson, R. (1993). Case survey methodology: Quantitative analysis of patterns across case studies. Academy of management Journal, 36(6), 1515-1546. https://doi.org/10.5465/256820
  • Latterell, C. M., & Wilson, J. L. (2016). Math is like a lion hunting a sleeping gazelle: Preservice elementary teachers’ metaphors of mathematics. European Journal of Science and Mathematics Education, 4(3), 283-292. Retrieved January 25, 2020 from https://eric.ed.gov/?id=EJ1107832
  • Latterell, C. M., & Wilson, J. L. (2017). Metaphors and mathematical identity: Math is like a tornado in Kansas. Journal of Humanistic Mathematics, 7(1), 46-61. https://dx.doi.org/ 10.5642/jhummath.201701.05
  • Lester, F. K., & Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems: advances and new perspectives (pp. 117-135). Buenos Aires: Springer Publishing. https://doi.org/10.1007/978-3-319-28023-3_8
  • Mailisman, N., Ikhsan, M., & Hajidin. (2020). Mathematics problem-solving skills of vocational high school students related to the 21st-century education. Journal of Physics: Conference Series, 1460(1):012014. https://doi.org/10.1088/1742-6596/1460/1/012014
  • Markovits, Z., & Forgasz, H. (2017). “Mathematics is like a lion”: Elementary students’ beliefs about mathematics. Educational Studies in Mathematics, 96(1), 49-64. https://doi.org/10.1007/s10649-017-9759-2
  • Martin, M. O., von Davier, M., & Mullis, I. V. S. (2020). Methods and procedures: TIMSS 2019 technical report. T. P. I. S. Center. Lynch School of Education, Boston College. Retrieved January 10, 2020 from https://timssandpirls.bc.edu/timss2019/methods/pdf/TIMSS-2019-MP-Technical-Report.pdf
  • Mason, L. (2003). High school students’ beliefs about maths, mathematical problem solving and their achievement in maths: a cross sectional study. Educational Psychology, 23(1), 73-85. https://doi.org/10.1080/01443410303216
  • Mathieu, A. (2009). Metaphors in mathematics: introduction and the case of algebraic geometry. http://dx.doi.org/10.2139/ssrn.1478871
  • McLeod, D. B. (1988). Affective issues in mathematical problem solving: some theoretical considerations. Journal for Research in Mathematics Education, 19(2), 134-141. https://doi.org/10.5951/jresematheduc.19.2.0134
  • Measuring, Selection and Placement Center [MSPC]. (2019). Yükseköğretim Kurumları sınavı (YKS) klavuzu [Council of Higher Education (CoHE) exam guide]. Retrieved January 18, 2020 https://www.osym.gov.tr/TR,15615/2019.html
  • Metha, C. R., & Patel, N. R. (1989). IBM SPSS exact tests. Cambridge, MA: IBM Corporation. Retrieved March 20, 2020 from https://www.ibm.com/docs/en/SSLVMB_27.0.0/pdf/en/IBM_SPSS_Exact_Tests.pdf
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: an expanded sourcebook (2nd ed.). Thousand Oaks, CA, US: Sage Publications, Inc. Retrieved July 19, 2018 from https://books.google.com.tr/books?id=U4lU_-wJ5QEC&printsec=frontcover&hl=tr#v=onepage&q&f=false
  • Ministry of Education [MoE]. (2012). Mathematics syllabus: primary one to six. Retrieved December 11, 2019 from https://www.moe.gov.sg/education/syllabuses/sciences/
  • Ministry of National Education [MoNE]. (2018a). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar [Mathematics curriculum (Primary and secondary schools 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, and 8th grades)]. Ankara: MoNE Board of Education and Discipline. Retrieved January 27, 2019 http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=329
  • Ministry of National Education [MoNE]. (2018b). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [High school mathematics curriculum (9th, 10th, 11th, and 12th grades)]. Ankara: MoNE Board of Education and Discipline. Retrieved January 27, 2019 http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=343
  • Ministry of National Education [MoNE]. (2019). Millî Eğitim Bakanlığı ortaöğretime geçiş yönergesi [Ministry of National Education the transition to secondary education directive]. Retrieved November 09, 2019 http://www.meb.gov.tr/meb_iys_dosyalar/2019_04/03134342_Yonerge2019.pdf
  • Mohd, N., & Mahmood, T. F. P. T. (2011). The effects of attitude towards problem solving in mathematics achievements. Australian Journal of Basic and Applied Sciences, 5(12), 1857-1862. Retrieved February 26, 2020 from http://www.ir.unikl.edu.my/jspui/handle/123456789/2129
  • National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, Va: National Council of Teachers of Mathematics. Retrieved January 27, 2019 https://www.nctm.org/standards-and-positions/principles-and-standards/
  • Or., M. B., & Bal, A. P. (2021). Ortaokul öğrenci̇leri̇ni̇n problem çözme algıları ile matematik başarıları arasındaki i̇li̇şki̇ni̇n incelenmesi [Investigation of the relationship between the problem-solving perception levels and mathematics achievement of secondary school students]. Journal of Çukurova University Institute of Social Sciences, 30(2), 154-165. https://doi.org/10.35379/cusosbil.906891
  • Organization of Economic Co-operation and Development [OECD]. (2016). PISA 2015 assessment and analytical framework: science, reading, mathematic and financial literacy. Paris: PISA, OECD Publishing. https://dx.doi.org/10.1787/9789264255425-en
  • Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: a path analysis. Journal of Educational Psychology, 86(2), 193-203. https://dx.doi.org/10.1037//0022-0663.86.2.193
  • Patton, M. Q. (2001). Qualitative research & evaluation methods. (4th ed.). Saint Paul, MN: Sage Publications. Retrieved March 10, 2020 from https://us.sagepub.com/en-us/nam/qualitative-research-evaluation-methods/book232962
  • Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
  • Purwasi, L. A., & Fitriyana, N. (2021, January). The enhancement of mathematical reasoning and problem solving ability through metaphorical thinking approach. Journal of Physics Conference Series, (Vol. 1731, No. 1, p. 012040). IOP Publishing. https://dx.doi.org/10.1088/1742-6596/1731/1/012040
  • Reyes, L. H. (1984). Affective variables and mathematics education. The Elementary School Journal, 84(5), 558-581. Retrieved February 27, 2020 from https://www.jstor.org/stable/1001237
  • Sağlam, Y., & Dost, S. (2014). Preservice science and mathematics teachers’ beliefs about mathematical problem solving. Procedia-Social and Behavioral Sciences, 116, 303-306. https://doi.org/10.1016/j.sbspro.2014.01.212
  • Saka, E., & Durmuş, M. (2021). Sınıf öğretmeni adaylarının matematiksel problem çözmeye yönelik inançlarının ve metaforik algılarının incelenmesi [Investigation of prospective primary school teachers’ beliefs and metaforic perceptions related to mathematical problem solving]. Ekev Academic Review, 85, 129-150. https://doi.org/10.17753/Ekev1794
  • Schinck, A. G., Neale, H. W., Pugalee, D. K., & Cifarelli, V. V. (2008). Using metaphors to unpack student beliefs about mathematics. School Science and Mathematics, 108(7), 326-333. https://dx.doi.org/10.1111/j.1949-8594.2008.tb17845.x
  • Schoenfeld, A. H., & Herrmann, D. J. (1982). Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology: Learning, Memory, and Cognition, 8(5), 484-494. https://doi.org/10.1037/0278-7393.8.5.484
  • Schommer-Aikins, M., Duell, O. K., & Hutter, R. (2005). Epistemological beliefs, mathematical problem-solving beliefs, and academic performance of middle school students. The Elementary School Journal, 105(3), 289-304. https://dx.doi.org/10.1086/428745
  • Sezgin-Memnun, D. (2015). Ortaokul öğrencilerinin matematik problemine ilişkin sahip oldukları metaforlar ve bu metaforların sınıf düzeylerine göre değişimi [Secondary school students’ metaphors about mathematical problem and change of metaphors according to grade levels]. Necatibey Faculty of Education, Electronic Journal of Science and Mathematics Education, 9(1), 351-374. https://dx.doi.org/10.17522/nefefmed.30643
  • Son, J. W., & Lee, M. Y. (2021). Exploring the relationship between preservice teachers’ conceptions of problem solving and their problem-solving performances. International Journal of Science and Mathematics Education, 19(1), 129-150. https://doi.org/10.1007/s10763-019-10045-w
  • Sturm, N., & Bohndick, C. (2021). The influence of attitudes and beliefs on the problem-solving performance. Frontiers in Education, 6, 525923. https://doi.org/10.3389/feduc.2021.525923
  • Thibodi, O. (2017). Metaphors for learning mathematics: An interpretation based on learners’ responses to an exploratory questionnaire on mathematics and learning. International Journal of Secondary Education, 5(6), 70-74. http://dx.doi.org/10.11648/j.ijsedu.20170506.11
  • Tsao, Y. (2004). A comparison of American and Taiwanese students: their math perception. Journal of Instructional Psychology, 31(3), 206-213. Retrieved July 17, 2020 from https://eric.ed.gov/?id=EJ774094
  • Turhan-Türkkan, B., & Yeşilpınar-Uyar, M. (2016). The metaphors of secondary school students towards the concept of “mathematical problem”. Çukurova University Faculty of Education Journal, 45(1), 99-130. Retrieved July 27, 2019 from https://dergipark.org.tr/tr/pub/cuefd/issue/27005/283888
  • Uygun, T., Gökkurt, B., & Usta, N. (2016). Üniversite öğrencilerinin matematik problemine ilişkin algılarının metafor yoluyla analiz edilmesi [Analysis of the perceptions of the university students about mathematics problem through metaphor]. Bartin University Journal of Faculty of Education, 5(2), 536-556. https://dx.doi.org/10.14686/buefad.v5i2.5000187677
  • van Merriënboer, J. J. G. (2013). Perspectives on problem solving and instruction. Computers & Education, 64(1), 153-160. https://dx.doi.org/10.1016/j.compedu.2012.11.025
  • Wilson, J. W., Fernandez, M. L., & Hadaway, N. (1993). Mathematical problem solving. In P. S. Wilson (Ed.), Research ideas for the classroom: high school mathematics (pp. 57- 78). New York, NY: MacMillan. Retrieved May 7, 2020 from https://eric.ed.gov/?q=Charles+AND+W.L&id=ED404144
  • Wolodko, B. L., Willson, K. J., & Johnson, R. E. (2003). Preservice teachers’ perceptions of mathematics: Metaphors as a vehicle for exploring. Teaching Children Mathematics, 10(4), 224-229. Retrieved January 17, 2020 from https://link.gale.com/apps/doc/A111453661/AONE?u=anon~b7dea5df&sid=googleScholar&xid=e60ed9e5
  • Yee, S. P. (2017). Students’ and teachers’ conceptual metaphors for mathematical problem solving. School Science and Mathematics, 117(3-4), 146-157. https://dx.doi.org/10.1111/ssm.12217
Fen Matematik Girişimcilik ve Teknoloji Eğitimi Dergisi-Cover
  • ISSN: 2667-5323
  • Yayın Aralığı: Yılda 3 Sayı
  • Başlangıç: 2018
  • Yayıncı: Oregda
Arşiv
Sayıdaki Diğer Makaleler

Meslek Yüksekokulu Öğrencilerinin Matematiksel Problem Çözmeye İlişkin Metaforik Algıları

Fikret CİHAN, Hatice AKKOÇ

Lise Öğrencilerinin Matematik Okuryazarlığı Öz Yeterlikleri ile Problem Çözme Beceri Algıları Arasındaki İlişkinin İncelenmesi

Taliha KELEŞ

Dezavantajlı Bölgelerde Görev Yapan Sınıf Öğretmenlerinin Karşılaştığı Güçlükler: Ordu İli Örneği

Nurullah KERECİ, Hatice KERECİ, Tuncay Osman GÖK

Sınır Tanımayan Bilim: Özel Gereksinimli Bireylere Yönelik Bilim ve Teknoloji Şenliğinin Etkililiği

Esra YALÇINTAŞ, Muhammed Muzaffer ÖZHAN, Abdulmüttalip AKKAYA

Teknoloji Destekli Öğretimin Bölme İşlemi Konusunu Anlamaya Etkisi

Yeliz ÜNAL, Mustafa YEŞİLYURT