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Proof in Mathematics Education
Journal of Education, 1996The development of reasoning ability is one of the major goals of education, and mathematics as reasoning is one of the objectives of the standards created by the National Council of Teachers of Mathematics. As students develop reasoning power, they progress toward the highest levels of Bloom's taxonomy and encounter the need to synthesize or prove ...
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Comprehension of Mathematical Proofs
1999Narrative comprehension has been an area of continuous inquiry in cognitive psychology since the late 1970s (e.g., Bower, Black, & Turner, 1979; Mandler & Johnson, 1977). During the last 15 years, much of this research has focused on the role that causality plays in the representation and processing of narratives.
Corrine M. Baron +2 more
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Experimentation and Proof in Mathematics
2009This paper examines the role and function of experimentation in mathematics with reference to some historical examples and some of my own, in order to provide a conceptual frame of reference for educational practise. I identify, illustrate, and discuss the following functions: conjecturing, verification, global refutation, heuristic refutation, and ...
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A blockchain consensus mechanism that uses Proof of Solution to optimize energy dispatch and trading
Nature Energy, 2022Sijie Chen +8 more
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On Proofs and Writing Mathematics
2018In this chapter, we study proof techniques by providing general guidelines and going over commented examples of proofs, in the context of arithmetic and elementary number theory, basic set-theory, and more. We go over direct proofs, proofs by contraposition, proofs by contradiction, the role of counterexamples, proof by induction including arguments ...
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2002
The basic elements of mathematics are“undefinables”(Subsection 3.1.1). Since every new piece of terminology is defined in terms of old pieces of terminology, we must begin with certain terms that have no definition.
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The basic elements of mathematics are“undefinables”(Subsection 3.1.1). Since every new piece of terminology is defined in terms of old pieces of terminology, we must begin with certain terms that have no definition.
openaire +2 more sources