Yıl 2018, Cilt 5, Sayı 2, Sayfalar 339 - 369 2018-04-20

High School Students’ Performances on Proof Comprehension Tests

Bahattin İnam [1] , Işıkhan Uğurel [2] , Burcak Boz Yaman Boz Yaman [3]

25 413

This study is a part of a large scale project in which an action research design is used to teach proof to 11th grade students. This part of the project aims to identify students’ comprehension level through five proof comprehension tests developed by the researchers based on the National Geometry Curriculum. Data were analyzed by considering the framework of Yang and Lin’s (2008) multilevel model. Results showed none of the students were successful at the most sophisticated level of the proof comprehension tests which requires conducting a proof in various ways or proving different theorems by using the same proof methods. Moreover, the highest proof comprehension was obtained from the level containing knowledge about definition, properties, and meanings of symbols. Achievement and comprehension decreased for components of a proof needing higher level mathematical skills. Based on the study’s results, suggestions about teaching proof are provided.
Proof, proving, Comprehension of proof, Proof comprehension test, High school student, Mathematics education
  • Alcock, L., & Wilkinson, N. (2011). e-Proofs: Design of a resource to support proof comprehension in mathematics. Educational Designer, 1(4), Article 14.
  • Almeida, D. (2003). Engendering Proof Attitudes: Can The Genesis of Mathematical Knowledge Teach Us Anything?. International Journal of Mathematical Education in Science and Technology, 34(4), 479-488.
  • Atwood, P.R. (2001). Learning to Construct Proofs in a First Course on Mathematical Proof. Doctoral dissertation, Western Michigan University.
  • Ball, D.L., Hoyles, C., Jahnke, H.N., & Movshovitz-Hadar, N. (2002). The Teaching of Proof. ICM, 3, 907-920.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö.E., Karadeniz, Ş., & Demirel, F. (2014). Bilimsel Araştırma Yöntemleri. (16th ed.). Ankara: Pegem Akademi.
  • Conradie, J., & Frith, J. (2000). Comprehension Tests in Mathematics. Educational Studies in Mathematics, 42(3), 225-235.
  • Creswell, J. W. (2003). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. 2nd ed. Sage, Thousand Oaks
  • Di Martino, P., & Maracci, M. (2009). The Secondary-Tertiary Transition: Beyond the Purely Cognitive. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of 33rd Conference of the International Group for the Psychology of Mathematics Education (pp.401-408). Thessaloniki, Greece: PME.
  • Duval, R. (2002). Proof understanding in mathematics: What ways for students. In Proceedings of the 2002 International Conference on Mathematics: Understanding Proving and Proving to Understand (pp.61-77).
  • Edwards, B.S., & Ward, M.B. (2004). Surprises from mathematics education research: Student (mis)use of mathematical definitions. American Mathematical Monthly, 111, 411-424.
  • Heinze, A., Cheng, Y. H., & Yang, K. L. (2004). Students’ performance in reasoning and proof in Taiwan and Germany: Results, paradoxes and open questions. ZDM, 36(5), 162-171. doi:10.1007/BF02655668
  • Hemmi, K. (2008). Students’ encounter with proof: the condition of transparency. ZDM, The Special Issue on Proof, 40(3), 413-426.
  • Houston, S. K. (1993a). Comprehension Tests in Mathematics. Teaching Mathematics and its Applications, 12(2), 60-73.
  • Houston, S. K. (1993b). Comprehension Tests in Mathematics: II. Teaching Mathematics and its Applications, 12(2), 113-120.
  • Knapp, J. L. (2006). Students’ appropriation of proving practices in advanced calculus. Doctoral dissertation, Arizona State University.
  • Koshy, V. (2005). Action Research for Improving Practice. London: Paul Chapman Publishing.
  • Leron, U. (1983). Structuring Mathematical Proof. American Mathematical Monthly, 90(3), 174-185.
  • Lin, F. L., & Yang, K. L. (2007). The Reading Comprehension of Geometric Proofs: The Contribution of Knowledge and Reasoning. International Journal of Science and Mathematics Education, 5(4), 729-754.
  • MEB [Milli Eğitim Bakanlığı] (2010). 11.Sınıf Geometri Öğretim Programı. Ankara: MEB. Retrieved from http://ogm.meb.gov.tr/
  • MEB [Milli Eğitim Bakanlığı] (2013). Ortaöğretim Matematik Dersi (9, 10, 11 ve 12. Sınıflar) Öğretim Programı. Ankara: MEB. Retrieved from http://ogm.meb.gov.tr/
  • Mejia-Ramos, J. P. (2008). The construction and evaluation of arguments in undergraduate mathematics: A theoretical and a longitudinal multiple-case study. Doctoral dissertation. University of Warwick, U.K.
  • Mejia-Ramos, J. P., Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An Assessment Model for Proof Comprehension in Undergraduate Mathematics. Educational Studies in Mathematics, 79(1), 3-18.
  • Moore, R. C. (1994) Making the Transition to Formal Proof. Educational Studies in Mathematics, 27(3), 249-266.
  • NCTM [National Council of Teachers of Mathematics]. (2000). NCTM Principles and Standards for School Mathematics. Reston. VA: NCTM.
  • Özer, Ö., & Arıkan, A. (2002). Lise matematik derslerinde öğrencilerin ispat yapabilme düzeyleri. V. Ulusal Fen ve Matematik Eğitimi Kongresi bildirisi, ODTÜ, Ankara. Retrieved from http://old.fedu.metu.edu.tr/ufbmek-5/b_kitabi/PDF/Matematik/Bildiri/t245d.pdf
  • Remillard, K. S. (2010). Exploring the learning of mathematical proof by undergraduate mathematics majors through discourse analysis. In Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education. Raleigh, NC: RUME (published online). Retrieved from http://sigmaa.maa.org/rume/crume2010/Archive/Remillard.pdf
  • Roy, S., Alcock, L., & Inglis, M. (2010). Supporting Proof Comprehension: A Comparative Study of Three Forms of Presentation. In Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education. Raleigh, NC: RUME (published online). Retrieved from http://sigmaa.maa.org/rume/crume2010/Archive/Roy%20et%20al.pdf
  • Sarı, M. (2011). Üniversite Öğrencilerinin Matematiksel Kanıt ile İlgili Güçlükleri ve Kanıt Öğretimi. Doctoral dissertation, Hacettepe University, Ankara.
  • Schoenfeld, A. (1994). Reflections on doing and teaching Mathematics. In A. Schoenfeld (Ed.). Mathematical Thinking and Problem Solving (pp.53-69). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Selden, J., & Selden, A. (1995). Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29(2), 123-151.
  • Stylianides, A.J. (2007). Proof and proving in school mathematics. Journal of Research in Mathematics Education, 38(3), 289-321.
  • Tall, D. (1992). The Transition to Advanced Mathematical Thinking: Functions, Limits, Infinity and Proof. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp.495-511). Reston, VA: National Council of Teachers of Mathematics/Macmillan.
  • Uğurel, I., & Moralı, S. (2010). Bir Ortaöğretim Matematik Dersindeki İspat Yapma Etkinliğine Yönelik Sınıf içi Tartışma Sürecine Öğrenci Söylemleri Çerçevesinde Yakından Bakış. Buca Eğitim Fakültesi Dergisi, 28, 135-154.
  • Weber, K., & Mejia-Ramos, J.P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76(3), 329-344.
  • Weber, K., Brophy, A., & Lin, K. (2008). Learning about advanced mathematical concepts by reading text. In Proceedings of the 11th Conference on Research in Undergraduate Mathematics Education. San Diego, California: RUME (published online). Retrieved from http://sigmaa.maa.org/rume/crume2008/Proceedings/Weber%20LONG.pdf
  • Yang, K. L. (2012). Structures of Cognitive and Metacognitive Reading Strategy Use for Reading Comprehension of Geometry Proof. Educational Studies in Mathematics, 80(3), 307-326.
  • Yang, K. L., & Lin, F. L. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), 59-76.
  • Yang, K. L., Lin, F. L., & Wang, Y.T. (2008). The effects of proof features and question probing on understanding geometry proof. Contemporary Educational Research Quarterly, 16(2), 77-100.
  • Yıldırım, A., & Şimşek, H. (2013). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (9th ed.). Ankara: Seçkin Yayıncılık.
  • Yıldız, G. (2006). Lisans Seviyesinde Genel Matematik Dersindeki Teorem ve İspatları Anlamaya Yönelik Kavrama Testinin Hazırlanması Uygulanması ve Öğrenci Görüşlerinin Değerlendirmesi. Unpublished Master’s thesis, Gazi University, Ankara.
  • Zazkis, R., & Zazkis, D. (2014). Proof scripts as a lens for exploring proof comprehension. In T. Fukawa-Connolly, G. Karakok, K. Keene, & M. Zandieh (Eds.), Proceedings of the 17th Annual Conference for Research in Undergraduate Mathematics Education (pp.1198-1204). Denver, CO
Birincil Dil en
Konular Eğitim Bilimleri
Yayımlanma Tarihi July
Dergi Bölümü Makaleler
Yazarlar

Orcid: orcid.org/0000-0002-6212-8013
Yazar: Bahattin İnam
E-posta: bahattin_inam67@yahoo.com
Kurum: Mugla Sitki Kocman University, TURKEY
Ülke: Turkey


Orcid: orcid.org/0000-0003-4067-1522
Yazar: Işıkhan Uğurel
E-posta: isikhann@gmail.com
Ülke: Turkey


Orcid: orcid.org/0000-0002-0922-3652
Yazar: Burcak Boz Yaman Boz Yaman (Sorumlu Yazar)
E-posta: burcakboz@gmail.com
Ülke: Turkey


Bibtex @araştırma makalesi { ijate416261, journal = {International Journal of Assessment Tools in Education}, issn = {}, address = {İzzet KARA}, year = {2018}, volume = {5}, pages = {339 - 369}, doi = {10.21449/ijate.416261}, title = {High School Students’ Performances on Proof Comprehension Tests}, key = {cite}, author = {Uğurel, Işıkhan and Boz Yaman, Burcak Boz Yaman and İnam, Bahattin} }
APA İnam, B , Uğurel, I , Boz Yaman, B . (2018). High School Students’ Performances on Proof Comprehension Tests. International Journal of Assessment Tools in Education, 5 (2), 339-369. DOI: 10.21449/ijate.416261
MLA İnam, B , Uğurel, I , Boz Yaman, B . "High School Students’ Performances on Proof Comprehension Tests". International Journal of Assessment Tools in Education 5 (2018): 339-369 <http://dergipark.gov.tr/ijate/issue/35703/416261>
Chicago İnam, B , Uğurel, I , Boz Yaman, B . "High School Students’ Performances on Proof Comprehension Tests". International Journal of Assessment Tools in Education 5 (2018): 339-369
RIS TY - JOUR T1 - High School Students’ Performances on Proof Comprehension Tests AU - Bahattin İnam , Işıkhan Uğurel , Burcak Boz Yaman Boz Yaman Y1 - 2018 PY - 2018 N1 - doi: 10.21449/ijate.416261 DO - 10.21449/ijate.416261 T2 - International Journal of Assessment Tools in Education JF - Journal JO - JOR SP - 339 EP - 369 VL - 5 IS - 2 SN - -2148-7456 M3 - doi: 10.21449/ijate.416261 UR - http://dx.doi.org/10.21449/ijate.416261 Y2 - 2018 ER -
EndNote %0 International Journal of Assessment Tools in Education High School Students’ Performances on Proof Comprehension Tests %A Bahattin İnam , Işıkhan Uğurel , Burcak Boz Yaman Boz Yaman %T High School Students’ Performances on Proof Comprehension Tests %D 2018 %J International Journal of Assessment Tools in Education %P -2148-7456 %V 5 %N 2 %R doi: 10.21449/ijate.416261 %U 10.21449/ijate.416261