Mechanical linkages, interactive geometry software, and argumentation » książka
Mechanical linkages, interactive geometry software, and argumentation
ISBN-13: 9783838300139 / Angielski / Miękka / 2010 / 412 str.
It is proof which sets mathematics apart from the empirical sciences, and forms the foundation of our mathematical knowledge, yet students often fail to understand the purpose of proof, they are unable to construct proofs, and instead readily accept empirical evidence or the authority of textbooks or teachers. This research focuses on the role of mechanical linkages (devices based on systems of hinged rods) and interactive geometric software as cognitive bridges between empirical justification and deductive reasoning. The provision of motivating contexts was found to foster conjecturing and argumentation, during which the eighth grade students in the project engaged in sustained deductive reasoning in support of their conjectures and achieved high levels of success with geometric proof. Mechanical linkages and their dynamic geometry computer simulations were shown by this research to be highly suitable contexts for bridging empirical and deductive reasoning.
It is proof which sets mathematics apart from theempirical sciences, and forms the foundation of ourmathematical knowledge, yet students often fail tounderstand the purpose of proof, they are unable toconstruct proofs, and instead readily acceptempirical evidence or the authority of textbooks orteachers. This research focuses on the role ofmechanical linkages (devices based on systems ofhinged rods) and interactive geometric software ascognitive bridges between empirical justification anddeductive reasoning. The provision of motivatingcontexts was found to foster conjecturing andargumentation, during which the eighth grade studentsin the project engaged in sustained deductivereasoning in support of their conjectures andachieved high levels of success with geometric proof.Mechanical linkages and their dynamic geometrycomputer simulations were shown by this research tobe highly suitable contexts for bridging empiricaland deductive reasoning.
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