ERG SES D 14, Education and Teachers' Practice
Mathematical proof is important in mathematics teaching in terms of the comprehension of mathematical knowledge. Thus, proof has critical value in the teaching process in terms of the prevention of memorization in mathematics, the construction of conceptual knowledge, and the realization of meaningful learning. Again, the tendency to consider proof as only a subject requiring advanced level mathematical knowledge is continuing. It would not be a mistake to say that report of “The Principles and Standards for School Mathematics” published by NCTM in 2000 created an important breaking point for this tendency. In this report, NCTM discussed proof as an important component of mathematics teaching for every age group and has led to interest and discussions being directed to this area. NCTM does not consider proof as a special activity of certain subjects of the curriculum conducted at certain times. Proof and reasoning must be a part of the process of teaching a lesson no matter what the subject is (NCTM, 2000).
“Reasoning and proof”, which NCTM dealt with as a process standard, is an important method of the comprehension of mathematical content and knowledge. NCTM mentions of the importance of comprehending proof in the understanding mathematics. Contrary to this, the most recent primary school and middle school curriculum attempting to largely include the process and content standards of NCTM in its content is observed to not emphasizing proof at the same degree.
In Turkey, with the transition to the practice of 12 years of compulsory education, curriculums were updated in 2013. Together with this correction, when curriculums are examined, it can be observed that proof is not included in the primary school and middle school curriculum as a concept. In the curriculum, proof is dealt with in the curriculums of the 9th and 11th grades as mathematical skills and competencies that are aimed to be developed.
In parallel with the increase of teaching of proof in high school and advanced levels of education, a large proportion of studies conducted regarding proof discuss the teaching of proof in primary and middle school and some studies can even state that proof in school mathematics is suitable for students in the advanced secondary education level and middle school students do not understand and do formal proof (Bell, 1976; Fischbein, 1982; Knuth, 2002). Contrary to these discussions, recently there is an increase in studies advocating that proof teaching can start in the early age group starting from preschool education (Ball et al., 2002; Cyr, 2011; Stylianides, 2007). In addition to this, most of the research shows that students who are attaining at all grade of school levels, tend to accept emprical arguments as proofs of mathematical generalizations (Healy & Hoyles, 2000; Goetting, 1995; Stylianides & Stylianides, 2009).
Studies conducted in this area in our country are relatively limited. The title of “the relation of early age period and proof” for students in Turkey is an unknown title. Can middle school students prove? Can they understand the difference between emprical argument and proof?
For the purpose of finding some answers to the problems above to some extent, the concept of proof could be acquired by 7th grade students was aimed in this study. First of all in the study, applications that 7th grade students can perform proof were focused on and after these performed applications, their perceptions and skills towards proof were attempted to be determined with the test and interview conducted subsequently.
Ball, D.L.; Hoyles, C.; Jahnke, H.N.; Movshovitz-Hadar, N. (2002). The teaching of proof, Proceedings of the International Congress of Mathematicians (Ed. L.I.Tatsien), Vol. III, Higher Education Press, Beijing, 907–920. Bell, A. W. (1976). A Study Of Pupıls' Proof-Explanatıons In Mathematıcal Sıtuatıons, Educational Studies in Mathematics, 7, 23-40. Cyr, S. (2011). Development of beginning skills in proving and proof writing by elementary school students, Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education, University of Rzeszów, Poland. Fischbein, E. (1982). Intuition and Proof. For The Learning of Mathematics, 3 (2), 9-18. Goetting, M. (1995). The college students ' understanding of mathematical proof. Unpublished doctoral dissertation. University of Maryland, College Park. Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31 (4), 396-428. Knuth, E. J. (2002). Teachers’ conceptions of proof in the context of secondary school mathematics. Journal of Mathematics Teachers Education, 5, 61 – 88. NCTM (National Council of Teachers of Mathematics), (2000). Principles and standards for school mathematics, www.nctm.org Stylianides, A. J. (2007), Proof and Proving in School Mathematics, Journal for Research in Mathematics Education, 38 (3), 289-321. Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40 (3). Yıldırım, A.; Şimşek, H. (2005). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (5. Baskı), Ankara: Seçkin Yayınevi.
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