Integrating computers and problem posing in mathematics teacher education:
"This book shares ideas about integrating mathematical problem posing with the use of computing technology in the context of K-12 mathematics teacher preparation. Problem posing has been on the mathematics education agenda for a long time. Over the centuries, it appeared in different didactic f...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2019]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "This book shares ideas about integrating mathematical problem posing with the use of computing technology in the context of K-12 mathematics teacher preparation. Problem posing has been on the mathematics education agenda for a long time. Over the centuries, it appeared in different didactic forms as a way of enriching one's learning experience through investigating mathematical ideas, exploring conjectures, and solving worthwhile problems. In the digital era, mathematics teacher training may include learning the skill of formulating different mathematical problems that the appropriate use of technology affords. As shown in the book, problem posing skills can be supported by two major theoretical positions that stem from technology integration: didactical coherence of a posed problem (Chapter 2) and technology-immune/technology-enabled (TITE) problem posing (Chapter 3). In order to connect theory and practice of mathematical problem posing in the digital era, the book includes examples of problems posed by teacher candidates enrolled in different technology-rich mathematics education courses taught by the author over the years. These examples are analyzed through the lenses of the proposed theory. In addition, the book shows how technology can be used to reformulate rather advanced problems from the traditional (pre-digital era) problem-solving curriculum. The goal of reformulation of such problems is at least two-fold: to make them compatible with the modern-day emphasis on democratizing mathematics education, and to find the right balance between positive and negative affordances of technology. In particular, an argument can be made that through achieving such a balance one uses technology appropriately"... |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xvii, 235 Seiten Illustrationen, Diagramme |
| ISBN: | 9789813273917 |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Preface v Chapter 1 On the Genesis of Problem Posing in Mathematics............................ 1.1 Problems from the first printed arithmetic........................... 1.1.1 Solving a 15th century problem using the modern-day pedagogy................... 1.1.2 Posing 15th century-like problems through conceptualization....................................................... 1.1.3 Using technology for posing 15th century-like problems................................................................... 1.2 From a classic problem to using the modem spreadsheet.... 1.2.1 The birth of the probability theory through problem posing............................................... ....................... 1.2.2 Using a spreadsheet as a problem-posing tool.......... 1.2.3 Duality of the spreadsheet’s use................................ 1.3 The Problem of the Grand Duke of Tuscany...................... 1.4 Conjecturing as posing problems to find proof................... 1.5 Problem posing in a classic context as a springboard into experimental mathematics................................................... 1.5.1 Triangular numbers with identical digits................... 1.5.2 Triangular number sieves.......................................... 1.6 Problem posing as setting up a research program................ 1.7 Summary............................................................................. 19 20 20 22 25 Chapter 2 From a Theory of Problem Posing to Classroom Practice of the Digital
Era........................................................................................... 2.1 Problem posing as educational philosophy......................... 2.2 Problem posing in the modem educational context............. 2.3 Learning to ask questions about posed/solved problems..... 27 27 29 32 xiii 1 1 3 5 6 8 8 11 13 14 17
xiv Integrating Computers and Problem Posing in Mathematics Teacher Education 2.4 Technology as a cultural support of problem posing........... 2.5 Numerical coherence in problem posing............................. 2.5.1 Using a spreadsheet to pose a numerically coherent problem...................................................................... 2.6 Contextual coherence in problem posing............................. 2.7 Pedagogical coherence in problem posing........................... 2.8 Didactical coherence in problem posing.............................. 2.9 Summary.............................................................................. Chapter 3 Posing Technology-Immune/Technology-Enabled (TITE) Problems. 3.1 From teaching machine movement to symbolic computations......... ............................................................... 3.2 Technological advances call for the revision of mathematics curriculum........ ............. 3.3 Definition of a TITE problem and a simple example.......... 3.4 Revisiting classic problems in the digital era under the umbrella of the TITE concept.............................................. 3.5 Conceptual bond and arithmetical word problems............... 3.5.1 Looking at the past to develop new teaching ideas.... 3.5.2 Posing similar problems............................................ 3.6 Revisiting mathematical problems to make them didactically coherent............ ................................................ 3.6.1 From numerical to contextual coherence.................. 3.6.2 Towards pedagogical
coherence................................ 3.7 From modeling data to a general formula using technology 3.8 Formulating and solving a didactically coherent problem... 3.9 Maple-based mathematical induction proof........................ 3.10 Summary.............................................................................. 35 36 38 41 44 48 49 51 51 54 58 60 67 67 68 71 71 73 74 75 78 82 Chapter 4 Linking Algorithmic Thinking and Conceptual Knowledge through Problem Posing... ................................................................... 85 4.1 On the hierarchy of two types of knowledge....................... 85 4.2 A simple question leads to revealing hidden creativity....... 89 4.3 Two levels of conceptual understanding.............................. 92
Contents XV 4.4 Solving a problem seeking information............................ . 4.5 Problem posing leads to conceptual knowledge and collateral learning................................................................. 4.6 Using conceptual bond in posing problems with technology 4.7 Summary.......................................................... 93 95 99 102 Chapter 5 Using Graphing Software for Posing Problems in Advanced High School Algebra.......................................................... 5.1 Introduction............................. 105 5.2 Location of roots of quadratics about an interval................. 107 5.3 Digital fabrication................................................................ 110 5.4 Connecting the coordinate plane with the plane of coefficients....................................................................... 112 5.4.1 ThecaseRREE.......................................................... 112 5.4.2 The case RERE.......................... ........... .... .............. 113 5.4.3 The case REER....................................... .............. . 113 5.4.4 The caseERER........... ................................. ............. 114 5.4.5 The case EERR................................... ...................... 115 5.4.6 ThecaseERRE......................................................... .116 5.5 Using Vieta’s Theorem........................ 116 5.6 Posing TITE problems in the plane of parameters............... 119 5.7 Geometric probabilities and the partitioning diagram......... 123 5.8 Making mathematical
connections....................................... 125 5.9 Revealing hidden concepts through collateral learning....... 128 5.10 Summary........................... 130 Chapter 6 Einstellung Effect and Problem Posing .................. ........................... 6.1 Examples of Einstellung effect.... ...... 6.2 Water jar experiments and Einstellung effect............. 6.3 Posing and solving problems as a remediation of Einstellung effect.... ..... .... ........................... .................... 6.4 Posing problems for water jar experiments using a spreadsheet.............................................. 6.5 Einstellung effect in finding areas on a geoboard.... ............ 133 133 138 141 144 105
xvi Integrating Computers and Problem Posing in Mathematics Teacher Education 6.6 Einstellung effect in solving algebraic equations and inequalities........................................................................... 6.7 Einstellung effect in solving trigonometricinequalities........ 6.8 Using technology to pose problems that might lead to Einstellung effect ................................................................. 6.9 Einstellung effect in solving logarithmic inequalities........... 6.9.1 Simultaneous extension and contraction of solution set................................................................. 6.9.2 Extension of solution set........................................... 6.10 Solving logarithmic inequality (6.21) in the general case.... 6.10.1 The case n = 2k.......................................................... 6.10.2 The case n = 2k+ 1................................. ................... 6.11 Summary.............................................................................. 149 153 156 159 159 162 166 166 172 176 Chapter 7 Explorations with Integer Sequences as TITE Problem Posing.......... 179 7.1 Introduction.......................................................................... 179 7.2 Exploring patterns formed by the last digits of the sums of powers of integers................................................................ 180 7.3 Discovering patters in the last digits of the polygonal numbers.............................. 186 7.3.1 The triangular number sieves.................................... 186 7.3.2 Triangular number sieves
and the last digits of their terms.......... ....................................................... 188 7.3.3 Rises and falls in permutations.................................. 189 7.3.4 Connecting triangular and square numbers within the multiplication table.................................................... 189 7.3.5 The square number sieves......................................... 191 7.3.6 The pentagonal number sieves.................................. 193 7.3.7 The general case of the m-gonal number sieves........ 195 7.4 Patterns in the behavior of the greatest common divisors of two polygonal numbers......................................................200 7.5 Exploring sequences formed by the sums of powers of integers................... 202 7.6 Exploring sieves developed from the sums of powers of integers...................................................................................204
Contents 7.7 xvii Summary.............................................................................. 207 Appendix..............................................................................................209 8.1 Spreadsheets included in Chapter 1....................................... 209 8.2 Spreadsheets included in Chapter 2....................................... 210 8.3 Spreadsheets included in Chapter 3....................................... 211 8.4 Spreadsheets included in Chapter 4....................................... 212 8.5 Spreadsheets included in Chapter 6....................................... 212 8.6 Spreadsheets included in Chapter 7....................................... 213 Bibliography 217 Index 233
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| spelling | Abramovich, Sergei (DE-588)141706333 aut Integrating computers and problem posing in mathematics teacher education by Sergei Abramovich New Jersey World Scientific [2019] xvii, 235 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "This book shares ideas about integrating mathematical problem posing with the use of computing technology in the context of K-12 mathematics teacher preparation. Problem posing has been on the mathematics education agenda for a long time. Over the centuries, it appeared in different didactic forms as a way of enriching one's learning experience through investigating mathematical ideas, exploring conjectures, and solving worthwhile problems. In the digital era, mathematics teacher training may include learning the skill of formulating different mathematical problems that the appropriate use of technology affords. As shown in the book, problem posing skills can be supported by two major theoretical positions that stem from technology integration: didactical coherence of a posed problem (Chapter 2) and technology-immune/technology-enabled (TITE) problem posing (Chapter 3). In order to connect theory and practice of mathematical problem posing in the digital era, the book includes examples of problems posed by teacher candidates enrolled in different technology-rich mathematics education courses taught by the author over the years. These examples are analyzed through the lenses of the proposed theory. In addition, the book shows how technology can be used to reformulate rather advanced problems from the traditional (pre-digital era) problem-solving curriculum. The goal of reformulation of such problems is at least two-fold: to make them compatible with the modern-day emphasis on democratizing mathematics education, and to find the right balance between positive and negative affordances of technology. In particular, an argument can be made that through achieving such a balance one uses technology appropriately"... Mathematics teachers Training of Mathematics Study and teaching Technological innovations Educational technology Study and teaching Problem-based learning Ausbildung (DE-588)4112628-2 gnd rswk-swf Mathematiklehrer (DE-588)4037946-2 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Problemlösen (DE-588)4076358-4 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 s Problemlösen (DE-588)4076358-4 s Mathematiklehrer (DE-588)4037946-2 s Ausbildung (DE-588)4112628-2 s 1\p DE-604 DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030914012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Abramovich, Sergei Integrating computers and problem posing in mathematics teacher education Mathematics teachers Training of Mathematics Study and teaching Technological innovations Educational technology Study and teaching Problem-based learning Ausbildung (DE-588)4112628-2 gnd Mathematiklehrer (DE-588)4037946-2 gnd Mathematikunterricht (DE-588)4037949-8 gnd Problemlösen (DE-588)4076358-4 gnd |
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| title | Integrating computers and problem posing in mathematics teacher education |
| title_auth | Integrating computers and problem posing in mathematics teacher education |
| title_exact_search | Integrating computers and problem posing in mathematics teacher education |
| title_full | Integrating computers and problem posing in mathematics teacher education by Sergei Abramovich |
| title_fullStr | Integrating computers and problem posing in mathematics teacher education by Sergei Abramovich |
| title_full_unstemmed | Integrating computers and problem posing in mathematics teacher education by Sergei Abramovich |
| title_short | Integrating computers and problem posing in mathematics teacher education |
| title_sort | integrating computers and problem posing in mathematics teacher education |
| topic | Mathematics teachers Training of Mathematics Study and teaching Technological innovations Educational technology Study and teaching Problem-based learning Ausbildung (DE-588)4112628-2 gnd Mathematiklehrer (DE-588)4037946-2 gnd Mathematikunterricht (DE-588)4037949-8 gnd Problemlösen (DE-588)4076358-4 gnd |
| topic_facet | Mathematics teachers Training of Mathematics Study and teaching Technological innovations Educational technology Study and teaching Problem-based learning Ausbildung Mathematiklehrer Mathematikunterricht Problemlösen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030914012&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT abramovichsergei integratingcomputersandproblemposinginmathematicsteachereducation |