Explanation and Proof in Mathematics [electronic resource] : Philosophical and Educational Perspectives / edited by Gila Hanna, Hans Niels Jahnke, Helmut Pulte.
Erişim Adresi
ISBN
9781441905765
Dil Kodu
İngilizce
Yer Numarası
DK/10495
Basım Bildirimi
1st ed. 2010.
Yayın Bilgisi
New York, NY : Springer US : Imprint: Springer, 2010.
Fiziksel Niteleme
VIII, 294 p. online resource.
İçindekiler Notu
Reflections on the Nature and Teaching of Proof -- The Conjoint Origin of Proof and Theoretical Physics -- Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity -- Preaxiomatic Mathematical Reasoning: An Algebraic Approach -- Completions, Constructions, and Corollaries -- Authoritarian Versus Authoritative Teaching: Polya and Lakatos -- Proofs as Bearers of Mathematical Knowledge -- Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach -- Proof and Cognitive Development -- Bridging Knowing and Proving in Mathematics: A Didactical Perspective -- The Long-Term Cognitive Development of Reasoning and Proof -- Historical Artefacts, Semiotic Mediation and Teaching Proof -- Proofs, Semiotics and Artefacts of Information Technologies -- Experiments, Diagrams and Proofs -- Proof as Experiment in Wittgenstein -- Experimentation and Proof in Mathematics -- Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching -- Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols -- Proof in the Wording: Two Modalities from Ancient Chinese Algorithms.
Özet, vb.
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece Proof as bearers of mathematical knowledge Bridging knowing and proving in mathematical reasoning The role of mathematics in long-term cognitive development of reasoning Proof as experiment in the work of Wittgenstein Relationships between mathematical proof, problem-solving, and explanation Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
Konu
Learning, Psychology of.
Education.
Mathematics.
Mathematics __ Study and teaching .
Education __ Philosophy.
Instructional Psychology.
Education.
Mathematics.
Mathematics Education.
Philosophy of Education.
Education.
Mathematics.
Mathematics __ Study and teaching .
Education __ Philosophy.
Instructional Psychology.
Education.
Mathematics.
Mathematics Education.
Philosophy of Education.
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Eseri Alıntıla
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250 |a1st ed. 2010.
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505 0 |aReflections on the Nature and Teaching of Proof -- The Conjoint Origin of Proof and Theoretical Physics -- Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity -- Preaxiomatic Mathematical Reasoning: An Algebraic Approach -- Completions, Constructions, and Corollaries -- Authoritarian Versus Authoritative Teaching: Polya and Lakatos -- Proofs as Bearers of Mathematical Knowledge -- Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach -- Proof and Cognitive Development -- Bridging Knowing and Proving in Mathematics: A Didactical Perspective -- The Long-Term Cognitive Development of Reasoning and Proof -- Historical Artefacts, Semiotic Mediation and Teaching Proof -- Proofs, Semiotics and Artefacts of Information Technologies -- Experiments, Diagrams and Proofs -- Proof as Experiment in Wittgenstein -- Experimentation and Proof in Mathematics -- Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching -- Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols -- Proof in the Wording: Two Modalities from Ancient Chinese Algorithms.
520 |aIn the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece Proof as bearers of mathematical knowledge Bridging knowing and proving in mathematical reasoning The role of mathematics in long-term cognitive development of reasoning Proof as experiment in the work of Wittgenstein Relationships between mathematical proof, problem-solving, and explanation Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
650 0|aLearning, Psychology of.
650 0|aEducation.
650 0|aMathematics.
650 0|aMathematics|xStudy and teaching .
650 0|aEducation|xPhilosophy.
650 14|aInstructional Psychology.
650 24|aEducation.
650 24|aMathematics.
650 24|aMathematics Education.
650 24|aPhilosophy of Education.
700 1 |aHanna, Gila.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aJahnke, Hans Niels.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aPulte, Helmut.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
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024 7 |a10.1007/978-1-4419-0576-5|2doi
041 |aeng
049 |aTürk Tarih Kurumu Kütüphanesi
050 4|aLB1060-1077
072 7|aJNC|2bicssc
072 7|aEDU009000|2bisacsh
072 7|aJNC|2thema
082 04|a370.15|223
090 |aDK/10495
245 10|aExplanation and Proof in Mathematics|h[electronic resource] :|bPhilosophical and Educational Perspectives /|cedited by Gila Hanna, Hans Niels Jahnke, Helmut Pulte.
250 |a1st ed. 2010.
264 1|aNew York, NY :|bSpringer US :|bImprint: Springer,|c2010.
300 |aVIII, 294 p.|bonline resource.
336 |atext|btxt|2rdacontent
337 |acomputer|bc|2rdamedia
338 |aonline resource|bcr|2rdacarrier
347 |atext file|bPDF|2rda
505 0 |aReflections on the Nature and Teaching of Proof -- The Conjoint Origin of Proof and Theoretical Physics -- Lakatos, Lakoff and Núñez: Towards a Satisfactory Definition of Continuity -- Preaxiomatic Mathematical Reasoning: An Algebraic Approach -- Completions, Constructions, and Corollaries -- Authoritarian Versus Authoritative Teaching: Polya and Lakatos -- Proofs as Bearers of Mathematical Knowledge -- Mathematicians’ Individual Criteria for Accepting Theorems and Proofs: An Empirical Approach -- Proof and Cognitive Development -- Bridging Knowing and Proving in Mathematics: A Didactical Perspective -- The Long-Term Cognitive Development of Reasoning and Proof -- Historical Artefacts, Semiotic Mediation and Teaching Proof -- Proofs, Semiotics and Artefacts of Information Technologies -- Experiments, Diagrams and Proofs -- Proof as Experiment in Wittgenstein -- Experimentation and Proof in Mathematics -- Proof, Mathematical Problem-Solving, and Explanation in Mathematics Teaching -- Evolving Geometric Proofs in the Seventeenth Century: From Icons to Symbols -- Proof in the Wording: Two Modalities from Ancient Chinese Algorithms.
520 |aIn the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece Proof as bearers of mathematical knowledge Bridging knowing and proving in mathematical reasoning The role of mathematics in long-term cognitive development of reasoning Proof as experiment in the work of Wittgenstein Relationships between mathematical proof, problem-solving, and explanation Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.
650 0|aLearning, Psychology of.
650 0|aEducation.
650 0|aMathematics.
650 0|aMathematics|xStudy and teaching .
650 0|aEducation|xPhilosophy.
650 14|aInstructional Psychology.
650 24|aEducation.
650 24|aMathematics.
650 24|aMathematics Education.
650 24|aPhilosophy of Education.
700 1 |aHanna, Gila.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aJahnke, Hans Niels.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
700 1 |aPulte, Helmut.|eeditor.|4edt|4http://id.loc.gov/vocabulary/relators/edt
710 2 |aSpringerLink (Online service)
773 0 |tSpringer Nature eBook
776 08|iPrinted edition:|z9781441905758
776 08|iPrinted edition:|z9781441905772
776 08|iPrinted edition:|z9781489982735
856 40|uhttps://doi.org/10.1007/978-1-4419-0576-5
912 |aZDB-2-SHU
912 |aZDB-2-SXED
950 |aHumanities, Social Sciences and Law (SpringerNature-11648)
950 |aEducation (R0) (SpringerNature-43721)
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