Proofs and refutations the logic of mathematical discovery pdf
Proofs and Refutations: The Logic of Mathematical Discovery - PDF Free DownloadMachine Learning pp Cite as. To learn, a learner needs to formulate plans, monitor the plan execution to detect violated expectations, and then diagnose and rectify errors which the dis-confirming data reveal. In this paper, five heuristic methods are presented for repairing flawed beliefs. These beliefs are considered as theories that predict effects of actions. Theories presuppose particular structural characteristics.
Using Proofs and Refutations to Learn from Experience
Examining the method of proofs and refutations in pre-service teachers education. There is some evidence in the mathematics education literature that Lakatos' proofs and refutation methods can be useful to examining students' conjecture production and proof construction process. The purpose of this study was to determine how the Lakatos method goes and which steps of the method works in the teacher education program. The population sample for this study consists of 24 senior pre-service teachers in elementary mathematics education in Turkey 16 women and 8 men. Pre-service teachers were given a problem in which they examined the relation between perimeter and area of a rectangle. Data was collected with a camera, field notes, and groups' written solutions and analyzed on the basis of framework included in Larsen and Zandieh's study. The finding revealed that Lakatos' method was usable in the teacher education program.
Proofs and Refutations is a book by philosopher Imre Lakatos expounding his view of the progress of mathematics. The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron. A central theme is that definitions are not carved in stone, but often have to be patched up in the light of later insights, in particular failed proofs. This gives mathematics a somewhat experimental flavour. At the end of the Introduction, Lakatos explains that his purpose is to challenge formalism in mathematics , and to show that informal mathematics grows by a logic of "proofs and refutations". Many important logical ideas are explained in the book.
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