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001482269 001__ 1482269
001482269 003__ OCoLC
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001482269 008__ 231007s2023\\\\sz\a\\\\o\\\\\000\0\eng\d
001482269 019__ $$a1401961353
001482269 020__ $$a9783031406393$$qelectronic book
001482269 020__ $$a3031406397$$qelectronic book
001482269 020__ $$z3031406389
001482269 020__ $$z9783031406386
001482269 0247_ $$a10.1007/978-3-031-40639-3$$2doi
001482269 035__ $$aSP(OCoLC)1402025028
001482269 040__ $$aEBLCP$$beng$$erda$$cEBLCP$$dYDX$$dGW5XE$$dEBLCP$$dYDX$$dOCLCF
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001482269 049__ $$aISEA
001482269 050_4 $$aQA14.C2$$bA27 2023
001482269 08204 $$a510.71071$$223/eng/20231010
001482269 1001_ $$aAbramovich, Sergei.
001482269 24510 $$aFostering collateral creativity in school mathematics :$$bpaying attention to students' emerging ideas in the age of technology /$$cSergei Abramovich, Viktor Freiman.
001482269 264_1 $$aCham :$$bSpringer International Publishing AG,$$c2023.
001482269 300__ $$a1 online resource (xiii, 130 pages) :$$billustrations (chiefly color).
001482269 336__ $$atext$$btxt$$2rdacontent
001482269 337__ $$acomputer$$bc$$2rdamedia
001482269 338__ $$aonline resource$$bcr$$2rdacarrier
001482269 4901_ $$aMathematics Education in the Digital Era Series ;$$vv.23
001482269 500__ $$aDescription based upon print version of record.
001482269 5050_ $$aIntro -- Preface -- References -- Contents -- 1 Theoretical Foundation and Examples of Collateral Creativity -- 1.1 Introduction -- 1.2 Theories Associated with Collateral Creativity -- 1.3 Collateral Creativity and the Instrumental Act -- 1.4 Three More Examples of Collateral Creativity -- 1.4.1 A Second Grade Example of Collateral Creativity -- 1.4.2 A Fourth Grade Example of Collateral Creativity -- 1.4.3 Collateral Creativity in a Classroom of Secondary Mathematics Teacher Candidates -- 1.5 Collateral Creativity as Problem Posing in the Zone of Proximal Development
001482269 5058_ $$a1.6 Forthcoming Examples of Collateral Creativity Included in the Book -- References -- 2 From Additive Decompositions of Integers to Probability Experiments -- 2.1 Introduction -- 2.2 Artificial Creatures as a Context Inspiring Collateral Creativity -- 2.3 Iterative Nature of Questions and Investigations Supported by the Instrumental Act -- 2.4 The Joint Use of Tactile and Digital Tools Within the Instrumental Act -- 2.5 Tactile Activities as a Window to the Basic Ideas of Number Theory -- 2.6 Historical Account Connecting Decomposition of Integers to Challenges of Gambling -- References
001482269 5058_ $$a3 From Number Sieves to Difference Equations -- 3.1 Introduction -- 3.2 On the Notion of a Number Sieve -- 3.3 Theoretical Value of Practical Outcome of the Instrumental Act -- 3.4 On the Equivalence of Two Approaches to Even and Odd Numbers -- 3.5 Developing New Sieves from Even and Odd Numbers -- 3.6 Polygonal Number Sieves -- 3.7 Connecting Arithmetic to Geometry Explains Mathematical Terminology -- 3.8 Polygonal Numbers and Collateral Creativity -- References -- 4 Explorations with the Sums of Digits -- 4.1 Introduction -- 4.2 About the Sums of Digits -- 4.3 Years with the Difference Nine
001482269 5058_ $$a4.4 Calculating the Century Number to Which a Year Belongs -- 4.5 Finding the Number of Years with the Given Sum of Digits Throughout Centuries -- 4.6 Partitioning n into Ordered Sums of Two Positive Integers -- 4.7 Interpreting the Results of Spreadsheet Modeling -- References -- 5 Collateral Creativity and Prime Numbers -- 5.1 'Low-Level' Questions Require 'High-Level' Thinking -- 5.2 Twin Primes Explorations Motivated by Activities with the Number 2021 -- 5.3 Students' Confusion as a Teaching Moment and a Source of Collateral Creativity -- 5.4 Different Definitions of a Prime Number
001482269 5058_ $$a5.5 Tests of Divisibility and Collateral Creativity -- 5.6 Historically Significant Contributions to the Theory of Prime Numbers -- 5.6.1 The Sieve of Eratosthenes -- 5.6.2 Is There a Formula for Prime Numbers? -- References -- 6 From Square Tiles to Algebraic Inequalities -- 6.1 Introduction -- 6.2 Comparing Fractions Using Parts-Within-Whole Scheme -- 6.3 Collateral Creativity: Calls for Generalization -- 6.4 Collaterally Creative Question Leads to the Discovery of "Jumping Fractions" -- 6.5 Algebraic Generalization -- 6.6 Seeking New Algorithms for the Development of "Jumping Fractions"
001482269 506__ $$aAccess limited to authorized users.
001482269 520__ $$aThis book explores the topic of using technology, both physical and digital, to motivate creative mathematical thinking among students who are not considered mathematically advanced. The book reflects the authors experience of teaching mathematics to Canadian and American teacher candidates and supervising several field-based activities by the candidates. It consists of eight chapters and an Appendix which includes details of constructing computational learning environments. Specifically, the book demonstrates how the appropriate use of technology in the teaching of mathematics can create conditions for the emergence of what may be called collateral creativity, a notion similar to Deweys notion of collateral learning. Just as collateral learning does not result from the immediate goal of the traditional curriculum, collateral creativity does not result from the immediate goal of traditional problem solving. Rather, mathematical creativity emerges as a collateral outcome of thinking afforded by the use of technology. Furthermore, collateral creativity is an educative outcome of ones learning experience with pedagogy that motivates students to ask questions about computer-generated or tactile-derived information and assists them in finding answers to their own or the teachers questions. This book intends to provide guidance to teachers for fostering collateral creativity in their classrooms.
001482269 650_0 $$aMathematics$$xStudy and teaching$$zCanada.$$0(DLC)sh 85001863
001482269 650_0 $$aMathematics$$xStudy and teaching$$zUnited States.$$0(DLC)sh 85001863
001482269 650_0 $$aCreative teaching.$$0(DLC)sh2005005272
001482269 655_0 $$aElectronic books.
001482269 7001_ $$aFreiman, Viktor.
001482269 77608 $$iPrint version:$$aAbramovich, Sergei$$tFostering Collateral Creativity in School Mathematics$$dCham : Springer International Publishing AG,c2023$$z9783031406386
001482269 830_0 $$aMathematics education in the digital era ;$$vv. 23.
001482269 852__ $$bebk
001482269 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-40639-3$$zOnline Access$$91397441.1
001482269 909CO $$ooai:library.usi.edu:1482269$$pGLOBAL_SET
001482269 980__ $$aBIB
001482269 980__ $$aEBOOK
001482269 982__ $$aEbook
001482269 983__ $$aOnline
001482269 994__ $$a92$$bISE