LEADER 05876nam 22007693u 450 001 9910451574103321 005 20210114013433.0 010 $a1-280-66949-7 010 $a9786613646422 010 $a981-4350-85-0 035 $a(CKB)2550000000101574 035 $a(EBL)919077 035 $a(OCoLC)794328374 035 $a(SSID)ssj0000657294 035 $a(PQKBManifestationID)12198258 035 $a(PQKBTitleCode)TC0000657294 035 $a(PQKBWorkID)10653684 035 $a(PQKB)11144695 035 $a(MiAaPQ)EBC919077 035 $a(EXLCZ)992550000000101574 100 $a20131125d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Thinking$b[electronic resource] $eHow to Develop It in the Classroom 210 $aSingapore $cWorld Scientific Publishing Company$d2012 215 $a1 online resource (318 p.) 225 1 $aMonographs on Lesson Study for Teaching Mathematics and Sciences 300 $aDescription based upon print version of record. 311 $a981-4350-83-4 327 $aPreface to the Book; Preface to the Series; Acknowledgements; Contents; Introductory Chapter: Problem Solving Approach to Develop Mathematical Thinking; 1.1 The Teaching Approach as the Result of Lesson Study; 1.1.1 Learning mathematics by/for themselves; 1.1.2 The difference between tasks and problems (problematic); 1.1.3 Teachers' questioning, and changing and adding representations; 1.1.4 Extending the ideas which we have already learned; 1.2 Setting the Activities for Explaining, Listening, Reflecting, and Appreciating in Class; 1.2.1 Structure of Problem Solving Approaches 327 $a1.2.2 Diversity of solutions and the objective of the class1.2.3 Comparison based on the problematic; 1.2.4 Using the blackboard for illustrating children's thinking process; 1.3 The Roles of the Curriculum and Textbooks; 1.4 Perspectives for Developing Mathematical Thinking; 1.4.1 Mathematical thinking: a major research topic of lesson study; 1.4.2 Mathematical thinking: a bird's-eye view; References; Part I Mathematical Thinking: Theory of Teaching Mathematics to Develop Children Who Learn Mathematics for Themselves; Chapter 1 Mathematical Thinking as the Aim of Education 327 $a1.1 Developing Children Who Learn Mathematics for Themselves1.2 Mathematical Thinking as an Ability to Think and to Make Decisions; 1.3 The Hierarchy of Ability and Thinking; Chapter 2 The Importance of Cultivating Mathematical Thinking; 2.1 The Importance of Teaching Mathematical Thinking; 2.1.1 The driving forces in pursuing knowledge and skills; 2.1.2 Achieving independent thinking and the ability to learn independently; 2.2 Example: How Many Squares Are There?; 2.2.1 The usual lesson process; 2.2.2 Problems with this method; 2.2.3 The preferred method 327 $a2.2.4 Mathematical thinking is the key ability hereChapter 3 The Mindset and Mathematical Thinking; 3.1 Mathematical Thinking; 3.1.1 Focus on the mindset: attitude and disposition; 3.1.2 Three variables for thinking mathematically; 3.1.3 Importance of Denotative understanding of mathematical thinking; 3.1.4 Mathematical thinking is the driving force behind knowledge and skills; 3.2 Structure of Mathematical Thinking; Chapter 4 Mathematical Methods; 4.1 Inductive Thinking; Meaning; Examples; Important aspects about teaching inductive thinking; 4.2 Analogical Thinking; Meaning; Examples 327 $aImportant aspects about teaching analogical thinking4.3 Deductive Thinking; Meaning; Examples; Important aspect about teaching deductive thinking; 4.4 Integrative Thinking; Meaning; Type I integration (high-level integration); Type II integration (comprehensive integration); Type III integration (extensional thinking); Example for type I; Example 2 for type II; Example 3 for type III; Important aspects about teaching integrative thinking; 4.5 Developmental Thinking; Meaning; Examples; Important aspects about teaching developmental thinking; 4.6 Abstract Thinking (Abstraction); Meaning 327 $aExamples 330 $aDeveloping mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples. 410 0$aMonographs on Lesson Study for Teaching Mathematics and Sciences 606 $aEffective teaching 606 $aMathematical ability 606 $aMathematics -- Study and teaching 606 $aMathematics$xStudy and teaching (Primary) 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aElementary Mathematics & Arithmetic$2HILCC 606 $aMathematics Teaching & Research$2HILCC 608 $aElectronic books. 615 4$aEffective teaching. 615 4$aMathematical ability. 615 4$aMathematics -- Study and teaching. 615 0$aMathematics$xStudy and teaching (Primary) 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aElementary Mathematics & Arithmetic 615 7$aMathematics Teaching & Research 676 $a510.71 700 $aIsoda$b Masami$0915051 701 $aKatagiri$b Shigeo$0927133 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9910451574103321 996 $aMathematical Thinking$92083087 997 $aUNINA