Session Information
ERG SES H 06, Mathematics education
Parallel Paper Session
Contribution
Mathematics is related with proof, because it’s related with not only what is the correct, but also why it’s true and it tries to convince other people to the correct one (Almedia, 1996). Mathematical proof, the esence of mathematics, is used to find a result, verify it, inform someone else about this verification and also persuade them, and at last it’s used to systematize results in a deductive system (Almedia, 2003).
The process of proving, which is followed to reach a correct judgment, consist of three different but related stages; to put forth the statement that will be proven, design the proof, and explain all the process to someone else (Lee, 2002). The design stage must tested by at least one or two of them for accepted as proof (Hale, 2003):
- Rules of logic
- Other previously proven theorems
- Axioms
- Definitions related to the subject
- Previous stages of the proof.
Mathematical proof is an important part of the mathematics. Similarly, proof teaching and developing proof ability of students are also important for the mathematics teaching. Namely, proof teaching is valuable for mathematics teaching not only for reaching the correct mathematical statement, but also for knowing and doing mathematics correctly, building the basis of mathematical thinking, understanding, using and improving the mathematical knowledge (Hanna and Jahnke,1996; Kitcher,1984; Polya 1981).
Despite the attributed importance, proof teaching takes part mostly in high school and university level, in the process of mathematics education. In Turkey however, students encounter with proof especially in geometry courses, intensively in 9th grade in secondary education and also in further grades. But proof teaching takes part exactly at university level, especially at mathematics and math. education departments. Despite these facts, the number of studies which advocate proof should have a central part at all grade levels of the mathematics education, proof is important at knowing and doing mathematics, and it should be incorporated into the mathematical experiences of even elementary students is increased rapidly (Stylianides, 2007; Ball & Bass, 2003; Ball and others, 2002; Hanna, 1995; NCTM, 2000).
As it mentioned, proof is important for learning mathematics. Namely, it is important for preventing rote learning, providing conceptual learning and meaningful learning. As a result, proof teaching should be adapted to all grade levels and then included to the mathematics elementary curricula.
Adopting proof for all grades is also a dangerous process. The questions, “What is proof?” and “What is the difference between proof and verification?” come into prominence at that point. Sometimes, a verification can be accepted as a proof. According to Stylianides (2007), there are four major elements of an argument which qualifies as proof. These are arguments foundation, formulation, representation, and social dimension.
Consequently, the purpose of study is to investigate 7th grade students performance on proof. In particular, this study is conducted to find the answer of the following research problems:
- How can mathematical proof be adapted to the 7th grade?
- Can 7th grade students prove?
Method
Expected Outcomes
References
• Almedia, D. (1996), Justifying and the Proving in the Mathematics Classroom, Philosophy in Mathematics Education, Exeter University, Philisoph of Mathematical Education Journal, 9. • Almedia, D. (2003), Engendering proof attitudes: Can the genesis of the mathematical knowledge teach us anything? International Journal of Mathematical Education in Science and Technology, 34 (4), p. 479-488. • Ball, D.L.; Bass, H. (2003), Making mathematics reasonable in school, A Research Companion to Principles and Standards for School Mathematics (Ed. J. Kilpatrick, W.G. Martin, D. Schifter), National Council of Teachers of Mathematics, Reston, VA, p. 27–44. • 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, p. 907–920. • Hale, M. (2003), Essentials of Mathematics : Introduction to Theory, Proof, and the Professional Culture, The Mathematical Association of America, USA. • Hana, G. (1995),Challanges to the İmportance of Proof, Fort he Learning of Mathematics, 15(3), p. 42-49. • Hanna, G.; Jahnke, H. N. (1996), Proof and proving. International Handbook of Mathematics Education (Ed. A. J. Bishop, K. Clements, C. Keitel, J. Kilpatric, & C. Laborde), Dordrecht, Netherlands: Kluwer Academic Publishers, p. 877 – 908. • Kitcher, P. (1984), The nature of mathematical knowledge. New York: Oxford University Pres. • LEE J. K. (2002), Philosophical perspectives on proof in mathematics education, Philosophy of Mathematics Education, 16. • National Council of Teachers of Mathematics, (2000). Principles and standards for school mathematics, www.nctm.org • Poyla, G. (1981), Mathematical discovery: on understanding, learning and teaching problem solving . New York: Wiley. • Stylianides, A. J. (2007), Proof and Proving in School Mathematics, Journal for Research in Mathematics Education, 38 (3), p. 289-321.
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