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AN ANALYSIS OF PROVING METHODS FOR VALIDITY OF THE LOGICAL ARGUMENTS BY STUDENTS FROM THE DEPARTMENT OF MATHEMATICS EDUCATION

Yıl 2013, Sayı: 12, 129 - 148, 01.06.2013
https://doi.org/10.14520/adyusbd.441

Öz

This study aimed to determine the methods to prove the validity of logical arguments used by the college students, from the department of mathematics education, and to reveal students’ reasons for selection of the method they used. Among the qualitative research designs, case study was the methodology of the current study. The participants of the study consisted of 76 students who were in their third year in college and who were registered for Introduction to Algebra course. One result of the study was that all three solution methods (classical mathematical operations, truth table, rules of inference) were utilized by the students while the rules of inferences were the most preferred solution method among all. Moreover, the fact that students who applied the rules of inferences were more successful in reaching the correct solution than the rest also confirmed the efficacy of the method of rules of inferences. Another result of the study was that students’ reasons for selecting the method of rules of inferences mainly included that it requires less steps and that it is more applicable. Moreover, students utilizing the rules of inferences also stated that the rules of inferences helped them to reveal the concepts behind the logical arguments beside the fact that this method was more efficient in acquiring the solution. On the other hand, students using the truth table or classical mathematical operations techniques highlighted that their preferences were mainly due to their confidence in using these techniques since they were instructed on these techniques in their past courses.

Kaynakça

  • Ainsworth, S. (2006). DeFT: “A Conceptual Framework for Considering Learning with Multiple Representations”. Learning and Instruction, 16, 183-198.
  • Balcı, A. (2000). Sosyal bilimlerde araştırma: Yöntem, teknik ve ilkeler. Ankara: Pegem A Yayıncılık.
  • Bromme, R., & Stahl E. (2002). Learning By Producing Hypertext From Reader Perspectives: Cognitive Flexibility Theory Reconsidered. R. Bromme, E. Stahl (Eds.), Writing Hypertext and Learning: Conceptual And Empirical Approaches. Pergamon, London.
  • Clifton, R. A. (1997). “The Effects of Social Psychological Variables and Gender on the Grade Point Averages and Educational Expectations of University Students: A Case Study”. Canadian Journal of Higher Education,27 (2), 67–90.
  • Copi, I. M. (1979). Symbolic logic (5th ed.). New York, NY: Macmillan.
  • Crocker, L., & Schmitt, A. (1987). “Improving Multiple-Choice Test Performance for Examinees with Different Levels of Test Anxiety”. The Journal of Experimental Education, 55(4), 201–205.
  • De Jong, T., Ainsworth, S., Dobson, M., van der Hulst, A., Levonen, J., & Reimann P. (1998). Acquiring Knowledge in Science and Mathematics: the Use of Multiple Representations In Technology-Based Learning Environments. M. Van Someren, P. Reimann, H. Boshuizen, T. De Jong (Eds.), Learning With Multiple Representations. Elsevier Sciences, Oxford.
  • Gibbons, F. X., Blanton, H., Gerrard, M., Buunk, B., & Eggleston, T. (2000). “Does Social Comparison Make A Difference? Optimism as A Moderator of the Relation Between Comparison Level and Academic Performance.” Personal and Social Psychology Bulletin, 26(5), 637–648.
  • Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.), London & Thousand Oaks, California: Sage
  • Moralı, S., Köroğlu, H., & Çelik, A. (2004). “Buca Eğitim Fakültesi Matematik Öğretmen Adaylarının Soyut Matematik Dersine Yönelik Tutumları Ve Rastlanan Kavram Yanılgıları.” Gazi Eğitim Fakültesi Dergisi, 24(1), 161-175.
  • Perry, R. P. (1991). Perceived Control In College Students: Implications for Instruction In Higher Education. In: Smart, J. (ed.), Higher Education: Handbook of Theory and Research (Vol. 7), Agathon Press, New York.
  • Perry, R. P. (1997b). Teaching Effectively: Which Students? What Methods? In: Perry, R. P., and Smart, J. (eds.), Effective Teaching in Higher Education: Research and Practice, Agathon Press, New York.
  • Schoenfeld, A .H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. Grouws D. (Ed.), Handbook for Research on Mathematics Teaching and Learning, MacMillan, New York. Schönwetter, D. J., Clifton, R. A., & Perry, R. P. (2002). “Content Familiarity: Differential Impact of Effective Teaching on Student Achievement Outcomes.” Research in Higher Education, 43(6), 625-655.
  • Sinnott-Armstrong, W., & Fogelin, R.J. (2010). Understanding arguments: an introduction to informal logic. Wadsworth Cengage learning.
  • Stigler, J.W., Gallimore, R., & Hiebert, J. (2000). Using video surveys to compare classrooms and teaching across cultures: Examples and lessons from the TIMSS video studies. Educational Psychologist, 35, 87–100.
  • Tabachneck, H. J. M., Koedinger, K.R., & Nathan M. J. (1994). Toward a theoretical account of strategy use and sense-making in mathematics problem solving. Proceedings of the 16th annual conference of the cognitive science society. Erlbaum, Hillsdale, NJ.
  • Van Someren, M.W., Boshuizen, H. P. A., De Jong, T., & Reimann P. (1998). Introduction. M. van Someren, P. Reimann, H. Boshuizen, T. De Jong (Eds.), Learning with multiple representations. Elsevier Sciences, Oxford.
  • Yıldırım, A. & Şimşek, H. (1999). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayınevi
  • Yin, R. K. (1984). Case study research: Design and methods. Beverly Hills, CA: Sage

İLKÖĞRETİM MATEMATİK ÖĞRETMENLİĞİ PROGRAMI ÖĞRENCİLERİNİN MANTIKSAL ARGÜMANLARI KANITLAMA YÖNTEMLERİNİN İNCELENMESİ

Yıl 2013, Sayı: 12, 129 - 148, 01.06.2013
https://doi.org/10.14520/adyusbd.441

Öz

Bu çalışma, İlköğretim Matematik Öğretmenliği Programında okuyan öğrencilerin bir argümanın geçerliliğinin kanıtında kullandıkları yöntemleri belirlemeyi ve yöntem tercih nedenlerini ortaya koymayı amaçlamaktadır. Bu araştırmada nitel araştırma yaklaşımı desenlerinden durum çalışması (case study) deseni kullanılmıştır. Katılımcılar, İlköğretim Matematik Öğretmenliği Programı 3. sınıfta öğrenim gören ve Cebire Giriş dersine kayıt yaptırmış 76 öğrenciden oluşmaktadır. Araştırmanın sonuçlarından birisi öğrencilerin çözümlerinde her üç çözüm yönteminin (klasik, doğruluk tablosu, çıkarım kuralları) de kullanıldığı ancak çıkarım kuralları yönteminin diğer yöntemlere kıyasla çok daha büyük bir oranda tercih edildiğidir. Ayrıca, öğrencilerin çözümlerinde ki başarı oranlarının yine çıkarım kuralları yönteminde diğerlerine göre çok daha yüksek olması bu yöntemin sorunun çözümünde daha etkili olduğunu göstermektedir. Araştırmanın bir diğer bulgusu ise öğrencilerin çıkarım kurallarının kullanma nedenlerinin genel olarak bu yöntemin diğer yöntemlere göre daha az işlem içermesi ve bu yöntemi daha uygulanabilir bulmalarıdır. Çıkarım kurallarını kullanan öğrenciler bu yöntemin, kendilerinin doğru sonuca daha çabuk ulaşmalarına yardımcı olmasının yanında mantıksal ifadelerin altında yatan anlamları da düşünmeye/araştırmaya sevk ettiğini dile getirmişlerdir. Diğer taraftan, doğruluk tablosu ve klasik matematiksel işlemler yöntemini kullanan öğrenciler, genel olarak bu yöntemleri daha önceki derslerinde de kullanmalarından (deneyim) dolayı kendine bu yöntemlerde daha çok güvenmelerini tercih nedenleri olarak ön plana çıkarmışlardır.

Kaynakça

  • Ainsworth, S. (2006). DeFT: “A Conceptual Framework for Considering Learning with Multiple Representations”. Learning and Instruction, 16, 183-198.
  • Balcı, A. (2000). Sosyal bilimlerde araştırma: Yöntem, teknik ve ilkeler. Ankara: Pegem A Yayıncılık.
  • Bromme, R., & Stahl E. (2002). Learning By Producing Hypertext From Reader Perspectives: Cognitive Flexibility Theory Reconsidered. R. Bromme, E. Stahl (Eds.), Writing Hypertext and Learning: Conceptual And Empirical Approaches. Pergamon, London.
  • Clifton, R. A. (1997). “The Effects of Social Psychological Variables and Gender on the Grade Point Averages and Educational Expectations of University Students: A Case Study”. Canadian Journal of Higher Education,27 (2), 67–90.
  • Copi, I. M. (1979). Symbolic logic (5th ed.). New York, NY: Macmillan.
  • Crocker, L., & Schmitt, A. (1987). “Improving Multiple-Choice Test Performance for Examinees with Different Levels of Test Anxiety”. The Journal of Experimental Education, 55(4), 201–205.
  • De Jong, T., Ainsworth, S., Dobson, M., van der Hulst, A., Levonen, J., & Reimann P. (1998). Acquiring Knowledge in Science and Mathematics: the Use of Multiple Representations In Technology-Based Learning Environments. M. Van Someren, P. Reimann, H. Boshuizen, T. De Jong (Eds.), Learning With Multiple Representations. Elsevier Sciences, Oxford.
  • Gibbons, F. X., Blanton, H., Gerrard, M., Buunk, B., & Eggleston, T. (2000). “Does Social Comparison Make A Difference? Optimism as A Moderator of the Relation Between Comparison Level and Academic Performance.” Personal and Social Psychology Bulletin, 26(5), 637–648.
  • Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.), London & Thousand Oaks, California: Sage
  • Moralı, S., Köroğlu, H., & Çelik, A. (2004). “Buca Eğitim Fakültesi Matematik Öğretmen Adaylarının Soyut Matematik Dersine Yönelik Tutumları Ve Rastlanan Kavram Yanılgıları.” Gazi Eğitim Fakültesi Dergisi, 24(1), 161-175.
  • Perry, R. P. (1991). Perceived Control In College Students: Implications for Instruction In Higher Education. In: Smart, J. (ed.), Higher Education: Handbook of Theory and Research (Vol. 7), Agathon Press, New York.
  • Perry, R. P. (1997b). Teaching Effectively: Which Students? What Methods? In: Perry, R. P., and Smart, J. (eds.), Effective Teaching in Higher Education: Research and Practice, Agathon Press, New York.
  • Schoenfeld, A .H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. Grouws D. (Ed.), Handbook for Research on Mathematics Teaching and Learning, MacMillan, New York. Schönwetter, D. J., Clifton, R. A., & Perry, R. P. (2002). “Content Familiarity: Differential Impact of Effective Teaching on Student Achievement Outcomes.” Research in Higher Education, 43(6), 625-655.
  • Sinnott-Armstrong, W., & Fogelin, R.J. (2010). Understanding arguments: an introduction to informal logic. Wadsworth Cengage learning.
  • Stigler, J.W., Gallimore, R., & Hiebert, J. (2000). Using video surveys to compare classrooms and teaching across cultures: Examples and lessons from the TIMSS video studies. Educational Psychologist, 35, 87–100.
  • Tabachneck, H. J. M., Koedinger, K.R., & Nathan M. J. (1994). Toward a theoretical account of strategy use and sense-making in mathematics problem solving. Proceedings of the 16th annual conference of the cognitive science society. Erlbaum, Hillsdale, NJ.
  • Van Someren, M.W., Boshuizen, H. P. A., De Jong, T., & Reimann P. (1998). Introduction. M. van Someren, P. Reimann, H. Boshuizen, T. De Jong (Eds.), Learning with multiple representations. Elsevier Sciences, Oxford.
  • Yıldırım, A. & Şimşek, H. (1999). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayınevi
  • Yin, R. K. (1984). Case study research: Design and methods. Beverly Hills, CA: Sage
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Lütfi İncikabı Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2013
Yayımlandığı Sayı Yıl 2013 Sayı: 12

Kaynak Göster

APA İncikabı, L. (2013). İLKÖĞRETİM MATEMATİK ÖĞRETMENLİĞİ PROGRAMI ÖĞRENCİLERİNİN MANTIKSAL ARGÜMANLARI KANITLAMA YÖNTEMLERİNİN İNCELENMESİ. Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi(12), 129-148. https://doi.org/10.14520/adyusbd.441