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identifierLAKATOSX c,n S \ xex[Nev [GMathematical educational study of Lakatos's conjectures and refutations1992P!Y YP!
tTŐYP P!YMastertǅlMaster's ThesisRLakatos K. PopperX D $XX@ G. PolyaX Y , YX | \ lX ƥD D Y X 1D 'Ʌ 'X |\h $X . Lakatos ɅD 'X !D !<\ tXՔp tt XՔ 't| p, t\ ɅD Euler t Ȭ\ $X . Ʌ Xt !D XՔ pȬ iմ̕@ 'X |'@ 'TX |'tX x itp, 'Ʌ X )'t|ĳ .
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t\ LakatosX t`@ Ʌ Yյ ȩ . l LakatosX Ʌ D 8 ȩX | l1t X.;Lakatos was effected by K. Popper's critical falliblism and G. Polya's mathematical heuristic and the study of the logic of mathematical discovery and he explained the growth of mathematical knowledge by the logic of 'Proofs and Refutations'. Lakatos said that proof is 'thought-experiment which leads to decomposition of the original conjecture into subconjectures', and this proof is explained by Euler's polyhedron theorem. That the method of lemma-incorporation improves conjectures by proofs is intrinsic unity between the 'logic of discovery' and the 'logic of justification', the method of lemma-incorporation is also called 'the method of proofs and refutations'.
Through this study, we can obtain suggestions like this. When teachers teach mathematics, they must make student develop reasoning ability. Class must have a flexibility, which is not uniformed but could be utilized various ideas. Also, that the significance of a theorem and understanding of its underlying concepts is more important than rigorous proof. Teachers must enhance students' creative action and informal intuition and urge students to guess themselves. In order to this, systematic textbook study for thought-education, experiment for Lakatos's theory can be applied to method and field, and teachers' re-education are needed.
This Lakatos's theory can be applicable to proof learning. I made examples that this Lakatos's proofs and refutations was applied to class and problem.~http://dspace.ewha.ac.kr/handle/2015.oak/197166;
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