Mathematical problem posing : conceptual considerations and empirical investigations for understanding the process of problem posing / / Lukas Baumanns

• Autore: Baumanns Lukas
• Pubblicazione: Wiesbaden : , : Springer Fachmedien, , [2022]; ©2022
• Descrizione fisica: 1 online resource (299 pages)
• Disciplina: 510.71
• Soggetto topico: Mathematics - Study and teaching; Mathematics
• Nota di contenuto: Intro -- 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?. ; 6.5.1 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. ; 9.4.1 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.
• Titolo autorizzato: Mathematical Problem Posing
• ISBN: 9783658399177; 9783658399160
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910631098103321
• Lo trovi qui: Univ. Federico II
• Serie: Kölner Beiträge Zur Didaktik der Mathematik