Holdings: Puzzles in mathematics education

Puzzles in mathematics education:

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Bibliographic Details
Main Author:	Danesi, Marcel 1946- (Author)
Format:	Book
Language:	English
Published:	München LINCOM GmbH 2017
Series:	Interdisciplinary studies on the nature of mathematics 04
Subjects:	Mathematikunterricht Unterhaltungsmathematik Mathematik Pädagogik Rätsel
Online Access:	Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	iii, 200 Seiten Illustrationen 25 cm, 680 g
ISBN:	9783862888276 3862888274

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MARC


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Record in the Search Index

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adam_text	T ABLE OF C ONTENTS INTRODUCTION..................................................................................................................................... 1 1 PUZZLES AND MATHEMATICS........................................................................................................3 1.1 MATH PUZZLES........................................................................................................................ 4 1.1.1 RIDDLES.........................................................................................................................5 1.1.2 PROBLEMS..................................................................................................................... 6 1.1.3 PUZZLES.........................................................................................................................8 1.1.4 GAMES........................................................................................................................ 13 1.2 PUZZLES AND MATH EDUCATION.............................................................................................. 15 1.2.1 THE AHMES PAPYRUS.................................................................................................. 15 1.2.2 MEDIEVAL MATH EDUCATION........................................................................................17 1.2.3 PUZZLES AND MATH EDUCATION AFTER FIBONACCI ........................................................ 22 1.2.4 PEDAGOGICAL FEATURES O F PUZZLES............................................................................26 1.3 PUZZLES AND MATHEMATICAL METHOD...................................................................................28 1.3.1 THE GENERALIZATION PRINCIPLE.................................................................................. 30 1.3.2 THE PUZZLE PRINCIPLE.................................................................................................31 1.3.3 THE SERENDIPITY PRINCIPLE ........................................................................................ 34 1.4 RECREATIONAL MATHEMATICS.................................................................................................37 1.4.1 EDUCATIONAL RECREATIONAL MATHEMATICS ................................................................. 38 1.4.2 MATH FLUENCY............................................................................................................ 42 2 MATHEMATICAL STRUCTURE........................................................................................................46 2.1 PUZZLES IN ARITHMETIC.........................................................................................................47 2.1.1 COUNTING AND MEASURING PUZZLES............................................................................48 2.1.2 MAGIC SQUARES.......................................................................................................... 56 2.1.3 ALGORITHMIC IMPLICATIONS ......................................................................................... 58 2.2 CIYPTARITHMETIC.................................................................................................................. 62 2.2.1 CRYPTARITHMS............................................................................................................. 63 2.2.2 ALPHAMETICS.............................................................................................................. 64 2.3 LUDIC STRUCTURE.................................................................................................................. 69 2.3.1 LUDIC ARITHMETIC.......................................................................................................69 2.3.2 LUDIC ALGEBRA............................................................................................................72 2.4 HIDDEN STRUCTURE............................................................................................................. 75 2.4.1 JOSEPHUS S PROBLEM.................................................................................................. 76 2.4.2 THE TANGRAM.............................................................................................................78 2.4.3 MAZES AND PATHS........................................................................................................80 3 THE PUZZLE PRINCIPLE...............................................................................................................83 3.1 PUZZLE ARCHETYPES..............................................................................................................85 3.1.1 ALCUIN S RIVER CROSSING PUZZLES .............................................................................. 86 3.1.2 EULER S KOENIGSBERG BRIDGES PUZZLE......................................................................... 90 3.1.3 FIBONACCI S RABBIT PUZZLE........................................................................................96 3.2 MEMETICS............................................................................................................................101 3.2.1 IBN KALLIKAN S CHESS PUZZLE................................................................................... 102 3.2.2 THE TOWERS O F HANOI PUZZLE................................................................................... 104 3.2.3 MEME THEORY........................................................................................................... 106 3.3 DISCOVERY...........................................................................................................................110 3.3.1 PROBABILITY THEORY..................................................................................................110 3.3.2 ZENO S PARADOXES....................................................................................................112 3.4 PEDAGOGICAL IMPLICATIONS..................................................................................................114 3.4.1 PUZZLES AS DISCOVERY FORMATS................................................................................114 3.4.2 PUZZLES AS EXPLORATIONS.......................................................................................... 115 4 PUZZLES AND MATH COGNITION............................................................................................... 118 4.1 MATH COGNITION................................................................................................................. 120 4.1.1 AHA INSIGHTS............................................................................................................. 121 4.1.2 THE BIRTHDAY PUZZLE.................................................................................................123 4.1.3 NUMEROSITY............................................................................................................... 125 4.2 PROBABILITY REASONING.......................................................................................................128 4.2.1 THE MONTY HALL PROBLEM........................................................................................ 129 4.2.2 THE PROSECUTOR S FALLACY....................................................................................... 131 4.3 SPATIAL REASONING............................................................................................................. 132 4.3.1 CHESS PUZZLES.......................................................................................................... 134 4.3.2 THE RUBIK S CUBE....................................................................................................136 4.3.3 THE FOUR COLOR PROBLEM........................................................................................ 137 4.3.4 GET O FF THE EARTH PUZZLE......................................................................................... 139 4.4 LOGICAL REASONING............................................................................................................143 4.4.1 PROOF........................................................................................................................ 145 4.4.2 SUDOKU..................................................................................................................... 147 4.5 AHA THINKING.................................................................................................................... 153 4.5.1 THE NINE-DOT PUZZLE REVISITED...............................................................................155 4.5.2 DISSECTION PUZZLES.................................................................................................. 157 5 RECREATIONAL MATHEMATICS IN THE CLASSROOM...................................................................160 5.1 PUZZLES AS ACQUISITION DEVICES.......................................................................................162 5.1.1 FIATLAND................................................................................................................... 163 5.1.2 DECONSTRUCTION PUZZLES.......................................................................................... 167 5.2 THE PSYCHOLOGY O F PUZZLES.............................................................................................. 170 5.2.1 THE MODAL FLOW PRINCIPLE.....................................................................................172 5.2.2 ANCILLARY VERSUS INTEGRAL PUZZLE USE.................................................................... 174 5.2.3 THE MODAL FOCUSING PRINCIPLE...............................................................................176 5.3 MATH PEDAGOGY.................................................................................................................179 5.3.1 PUZZLE-BASED LEARNING........................................................................................... 180 5.3.2 THE EUREKA FACTOR.................................................................................................. 181 5.4 CONCLUDING REM ARKS....................................................................................................... 184 REFERENCES......................................................................................................................................189 INDEX............................................................................................................................................... 196
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author	Danesi, Marcel 1946-
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dewey-full	510
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	510 - Mathematics
dewey-raw	510
dewey-search	510
dewey-sort	3510
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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title	Puzzles in mathematics education
title_auth	Puzzles in mathematics education
title_exact_search	Puzzles in mathematics education
title_full	Puzzles in mathematics education Marcel Danesi
title_fullStr	Puzzles in mathematics education Marcel Danesi
title_full_unstemmed	Puzzles in mathematics education Marcel Danesi
title_short	Puzzles in mathematics education
title_sort	puzzles in mathematics education
topic	Mathematikunterricht (DE-588)4037949-8 gnd Unterhaltungsmathematik (DE-588)4124357-2 gnd
topic_facet	Mathematikunterricht Unterhaltungsmathematik
url	http://d-nb.info/1136623736/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029919671&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT danesimarcel puzzlesinmathematicseducation AT lincomeuropamunchen puzzlesinmathematicseducation

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