LEADER 06037nam 2200469 450 001 9910631098103321 005 20231110223342.0 010 $a9783658399177$b(electronic bk.) 010 $z9783658399160 035 $a(MiAaPQ)EBC7143544 035 $a(Au-PeEL)EBL7143544 035 $a(CKB)25402380500041 035 $a(PPN)266352855 035 $a(EXLCZ)9925402380500041 100 $a20230329d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical problem posing $econceptual considerations and empirical investigations for understanding the process of problem posing /$fLukas Baumanns 210 1$aWiesbaden :$cSpringer Fachmedien,$d[2022] 210 4$d©2022 215 $a1 online resource (299 pages) 225 1 $aKölner Beiträge Zur Didaktik der Mathematik 311 08$aPrint version: Baumanns, Lukas Mathematical Problem Posing Wiesbaden : Springer Fachmedien Wiesbaden GmbH,c2023 9783658399160 327 $aIntro -- Foreword -- Danksagung -- Abstract -- Contents -- I Introduction -- 1 Motivation -- 2 Objectives -- 3 Thesis Structure -- II Theoretical frame -- 4 Problem posing from a subject-matter didactics perspective -- 4.1 Illustration with a geometric example -- 4.2 Conceptions of problem posing - Four mathematical miniatures -- 4.2.1 Problem posing as generating new problems -- Mathematical miniature -- Summarizing empirical research -- 4.2.2 Problem posing as reformulating a given problem for problem solving -- Mathematical miniature -- Summarizing empirical research -- 4.2.3 Problem posing as reformulating a given problem for investigation -- Mathematical miniature -- Summarizing empirical research -- 4.2.4 Problem posing as constructing tasks for others -- Mathematical miniature -- Summarizing empirical research -- 5 Problem posing and its connection to related constructs in mathematics education -- 5.1 Modelling -- 5.2 Proving -- 5.2.1 Proving through problem posing -- 5.2.2 Problem posing through proving -- 5.3 Problem Solving -- 5.3.1 Problem posing as a subset of problem solving -- 5.3.2 Problem solving as a subset of problem posing -- 5.3.3 Problem posing and problem solving as complementary, but different in nature -- 5.4 Creativity and Giftedness -- III Journal articles -- 6 Rethinking problem-posing situations: A review -- 6.1 Introduction -- 6.2 Theoretical Background -- 6.2.1 What is problem posing? -- 6.2.2 What is posing? -- 6.2.3 What is a problem? -- 6.2.4 Openness of problems -- 6.2.5 Categorisations of problem-posing situations -- 6.2.6 Research questions -- 6.3 Design -- 6.3.1 Data sampling -- 6.3.2 Data analysis -- 6.4 Analysis 1: Is it posing? -- 6.4.1 Discussion of Analysis 1: Mathematical problem posing -- 6.5 Analysis 2: Is it free, semi-structured, or structured?. 327 $a6.5.1 Discussion of Analysis 2: Unstructured situations -- 6.6 Analysis 3: Is it a routine or a non-routine problem? -- 6.6.1 Discussion of Analysis 3: Routine and non-routine initial problems -- 6.7 Conclusion -- 6.7.1 Implications for practice -- 6.7.2 Implications for research -- 7 Developing a framework for characterising problem-posing activities: A review -- 7.1 Introduction -- 7.2 What is problem posing? -- 7.2.1 Definition of problem posing -- 7.2.2 Non-posing activities -- 7.3 The proposed framework -- 7.3.1 Dimension 1: Generating and reformulating -- 7.3.2 Dimension 2: Routine and non-routine problems -- 7.3.3 Dimension 3: Metacognitive behaviour -- 7.4 Procedure of the literature review -- 7.5 Qualitative application of the framework -- 7.5.1 Dimension 1: Generating and reformulating -- 7.5.2 Dimension 2: Routine and non-routine problems -- 7.5.3 Dimension 3: Metacognitive behaviour -- 7.6 Quantitative application of the framework -- 7.7 Conclusion and discussion -- 8 The process of problem posing: Development of a descriptive process model of problem posing -- 8.1 Introduction -- 8.2 Theoretical Background -- 8.2.1 Problem Posing -- 8.2.2 Process of problem posing - State of research -- 8.2.3 Research questions -- 8.3 The study -- 8.3.1 Data collection -- 8.3.2 Data evaluation -- 8.4 Results -- 8.4.1 Category development of episode types in problem posing -- 8.4.2 Derivation of a descriptive phase model for problem posing -- 8.5 Discussion -- 9 Identifying metacognitive behavior in problem-posing processes. Development of a framework and a proof of concept -- 9.1 Introduction -- 9.2 Theoretical Background -- 9.2.1 Problem Posing -- 9.2.2 Metacognition -- 9.2.3 Research on Metacognition in Mathematics Education -- 9.2.4 Research on Metacognition in Problem Posing -- 9.3 Research objectives -- 9.4 Methods. 327 $a9.4.1 Research design for data collection -- 9.4.2 Data analysis - Assessment of metacognitive behavior -- 9.5 Results -- 9.5.1 Development of a framework for identifying problem-posing-specific aspects of metacognitive behavior -- 9.5.2 Proof of concept: The cases of Tino & -- Ulrich and Valerie & -- Wenke -- 9.6 Discussion -- 9.7 Conclusion -- IV Discussion & -- Outlook -- 10 Summary -- 11 Potential for further research -- (1,2): -- (1,3): -- (1,4): -- (2,3): -- (2,4): -- (3,4): -- V Listings -- Bibliography -- List of Tables -- List of Figures -- VI Appendix -- A Online supplement of journal article 2 -- A.1 List of all 47 included articles included in the review -- A.2 Categorisation of all 47 articles within the developed framework -- B Online supplement of journal article 3. 410 0$aKölner Beiträge Zur Didaktik der Mathematik 606 $aMathematics$xStudy and teaching 606 $aMathematics$vHandbooks, manuals, etc 615 0$aMathematics$xStudy and teaching. 615 0$aMathematics 676 $a510.71 700 $aBaumanns$b Lukas$01265007 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910631098103321 996 $aMathematical Problem Posing$92966305 997 $aUNINA