Modeling from a cognitive perspective : Theoretical considerations and empirical contributions

Journal article

Schukajlow, Stanislaw, Kaiser, Gabriele Agnes Hildegard and Stillman, Gloria Ann. (2021). Modeling from a cognitive perspective : Theoretical considerations and empirical contributions. Mathematical Thinking and Learning. 25(3), pp. 259-269. https://doi.org/10.1080/10986065.2021.2012631
AuthorsSchukajlow, Stanislaw, Kaiser, Gabriele Agnes Hildegard and Stillman, Gloria Ann
Abstract

Mathematical modeling and applications are an important part of curriculum and considered to be important for students’ current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the current thinking on modeling activities and review empirical results. Subsequently, new findings and implications for research offered by the contributions of the current special issue are described. The contributions of this special issue refer to the relation between cognitive and metacognitive modeling activities to (a) mathematical thinking during building a modeling example, (b) strategic knowledge within modeling activities, (c) solving of data-rich modeling problems and their status from a meta-perspective and (d) individual and social metacognition.

Keywordsmathematical modeling; real-world problems; cognitive perspective
Year2021
JournalMathematical Thinking and Learning
Journal citation25 (3), pp. 259-269
PublisherRoutledge
ISSN1098-6065
Digital Object Identifier (DOI)https://doi.org/10.1080/10986065.2021.2012631
Web address (URL)https://www.tandfonline.com/doi/full/10.1080/10986065.2021.2012631
Research or scholarlyResearch
Page range259-269
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All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online04 Dec 2021
Publication process dates
Accepted27 Nov 2021
Deposited01 Mar 2022
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Pankow, Lena, Kaiser, Gabriele, König, Johannes and Blömeke, Sigrid. (2018). Perception of student errors under time limitations: Are teachers faster than mathematicians or students? ZDM. 50(4), pp. 631 - 642. https://doi.org/10.1007/s11858-018-0945-1
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Heinrichs, Hannah and Kaiser, Gabriele. (2018). Diagnostic competence for dealing with students' errors: fostering diagnostic competence in error situations. In In T. Leuders, K. Philipp and J. Leuders (Ed.). Diagnostic Competence of Mathematics Teachers - Unpacking a Complex Construct in Teacher Education and Teacher Practice pp. 79 - 94 Springer. https://doi.org/10.1007/978-3-319-66327-2_4
Teaching secondary school mathematics : Research and practice for the 21st century
Goos, Merrilyn, Vale, Colleen, Stillman, Gloria, Makar, Katie, Herbert, Sandra and Geiger, Vincent. (2017). Teaching secondary school mathematics : Research and practice for the 21st century Allen & Unwin.
Erratum to: professional competencies of (prospective) mathematics teachers - cognitive versus situated approaches
Kaiser, Gabriele, Blomeke, Sigrid, Konig, Johannes, Busse, Andreas, Dohrmann, Martina and Hoth, Jessica. (2017). Erratum to: professional competencies of (prospective) mathematics teachers - cognitive versus situated approaches. Educational Studies in Mathematics: An international journal. 94(2), pp. 161 - 182. https://doi.org/10.1007/s10649-016-9724-5
Understanding the development of teachers' professional competencies as personally, situationally and socially determined
Blomeke, Sigrid and Kaiser, Gabriele. (2017). Understanding the development of teachers' professional competencies as personally, situationally and socially determined. In In D. J. Clandinin and J. Husu (Ed.). The Sage handbook of research on teacher education pp. 783 - 802 SAGE Publications India.
Crossing boundaries in mathematical modelling and applications educational research and practice
Stillman, Gloria, Blum, Werner and Kaiser, Gabriele. (2017). Crossing boundaries in mathematical modelling and applications educational research and practice. In In G. A. Stillman, W. Blum and G. Kaiser (Ed.). Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education pp. 1 - 22 Springer International Publishing. https://doi.org/10.1007/978-3-319-62968-1
Enabling anticipation through visualisation in mathematising real-world problems in a flipped classroom
Stillman, Gloria. (2017). Enabling anticipation through visualisation in mathematising real-world problems in a flipped classroom. In In G. A. Stilman, W. Blum and G. Kasier (Ed.). Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education pp. 163 - 173 Springer International Publishing. https://doi.org/10.1007/978-3-319-62968-1
Scaffolding complex modelling processes: an in-depth study
Stender, Peter, Krosanke, Nadine and Kaiser, Gabriele. (2017). Scaffolding complex modelling processes: an in-depth study. In In G. A. Stillman, W. Blum and G. Kaiser (Ed.). Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education pp. 467 - 477 Springer International Publishing. https://doi.org/10.1007/978-3-319-62968-1
Professional competencies of (prospective) mathematics teachers cognitive versus situated approaches
Kaiser, Gabriele, Blomeke, Sigrid, Konig, Johannes, Busse, Andreas, Dohrmann, Martina and Hoth, Jessica. (2017). Professional competencies of (prospective) mathematics teachers cognitive versus situated approaches. Educational Studies in Mathematics: An international journal. 94(2), pp. 161 - 182. https://doi.org/10.1007/s10649-016-9713-8
Reflections on research trends in international comparative studies in mathematics education
Kaiser, Gabriele and Yang, Xinrong. (2017). Reflections on research trends in international comparative studies in mathematics education. In In J. Son, T. Watanabe and J. Lo (Ed.). What Matters? Research Trends in International Comparative Studies in Mathematics Education pp. 395 - 409 Springer. https://doi.org/10.1007/978-3-319-51187-0
Der Einsatz von Unterrichtsvideos in der universitären Ausbildung: Zur Wirksamkeit video- und transkriptgestützter Seminare zur Klassenführung auf pädagogisches Wissen und situationsspezifische Fähigkeiten angehender Lehrkräfte [Using videos in teacher preparation: On the effectiveness of video- and transcriptbased classroom management courses on pre-service teachers general pedagogical knowledge and situation-specific skills]
Kramer, Charlotte, Konig, Johannes, Kaiser, Gabriele, Ligtvoet, Rudy and Blomeke, Sigrid. (2017). Der Einsatz von Unterrichtsvideos in der universitären Ausbildung: Zur Wirksamkeit video- und transkriptgestützter Seminare zur Klassenführung auf pädagogisches Wissen und situationsspezifische Fähigkeiten angehender Lehrkräfte [Using videos in teacher preparation: On the effectiveness of video- and transcriptbased classroom management courses on pre-service teachers general pedagogical knowledge and situation-specific skills]. Zeitschrift fur Erziehungswissenschaft. 20(1), pp. 137 - 164. https://doi.org/10.1007/s11618-017-0732-8
On the occasion of the decennial publication of ZDM mathematics education by springer
Kaiser, Gabriele. (2017). On the occasion of the decennial publication of ZDM mathematics education by springer. ZDM: The International Journal on Mathematics Education. 49(1), pp. 1 - 3. https://doi.org/10.1007/s11858-017-0835-y
Perspectives on (future) teachers' professional competencies
Kaiser, Gabriele and Li, Yeping. (2017). Perspectives on (future) teachers' professional competencies. In B. Kaur, W. Kin Ho and T. L. Toh and B. H. Choy (Ed.). pp. 1 - 81
Developing the roots of modelling conceptions: 'mathematical modelling is the life of the world'
Brown, Jill and Stillman, Gloria. (2017). Developing the roots of modelling conceptions: 'mathematical modelling is the life of the world'. International Journal of Mathematical Education in Science and Technology. 48(3), pp. 353 - 373. https://doi.org/10.1080/0020739X.2016.1245875
The teaching and learning of mathematical modeling
Kaiser, Gabriele. (2017). The teaching and learning of mathematical modeling. In In J. Cai (Ed.). Compendium for Research in Mathematics Education pp. 267 - 291 The National Council of Teachers of Mathematics, Inc..
A mixed-methods-evaluation approach for the study of macro-micro interactions: on the development of teaching- and learning-oriented beliefs of mathematics student teachers in the introductory phase of study
Buchholtz, Nils and Kaiser, Gabriele. (2017). A mixed-methods-evaluation approach for the study of macro-micro interactions: on the development of teaching- and learning-oriented beliefs of mathematics student teachers in the introductory phase of study. Koelner Zeitschrift fuer Soziologie und Sozialpsychologie. 69(Suppl 2), pp. 435 - 458. https://doi.org/10.1007/s11577-017-0465-y
The primacy of 'noticing': a key to successful modelling
Galbraith, Peter, Stillman, Gloria and Brown, Jill. (2017). The primacy of 'noticing': a key to successful modelling. In In G. A. Stillman, W. Blum and G. Kaiser (Ed.). Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education pp. 83 - 94 Springer International Publishing. https://doi.org/10.1007/978-3-319-62968-1
Professional competences of teachers for fostering creativity and supporting high-achieving students
Hoth, Jessica, Kaiser, Gabriele, Busse, Andreas, Dohrmann, Martina, Konig, Johannes and Blomeke, Sigrid. (2017). Professional competences of teachers for fostering creativity and supporting high-achieving students. ZDM: The International Journal on Mathematics Education. 49(1), pp. 107 - 120. https://doi.org/10.1007/s11858-016-0817-5
Eine analyse der sogenannten schlussrechnung - die relevanz der ansatze von arnold kirsch fur aktuelle lernprozesse in der lehrerausbildung
Buchholtz, Nils, Schwarz, Bjorn and Kaiser, Gabriele. (2016). Eine analyse der sogenannten schlussrechnung - die relevanz der ansatze von arnold kirsch fur aktuelle lernprozesse in der lehrerausbildung. Journal fuer Mathematik-Didaktik. 37(1), pp. 31 - 53. https://doi.org/10.1007/s13138-016-0090-8
Uncovering predictors of disagreement: ensuring the quality of expert ratings
Hoth, Jessica, Schwarz, Björn, Kaiser, Gabriele, Busse, Andreas, König, Johannes and Blömeke, Sigrid. (2016). Uncovering predictors of disagreement: ensuring the quality of expert ratings. ZDM Mathematics Education. 48(1-2), pp. 83 - 95. https://doi.org/10.1007/s11858-016-0758-z
Fostering modeling competencies for complex situations
Stender, Peter and Kaiser, Gabriele. (2016). Fostering modeling competencies for complex situations. In In C. R. Hirsch (Ed.). Mathematical modeling and modeling mathematics pp. 107 - 115 National Council of Teachers of Mathematics.
Research into mathematical applications and modelling
Stillman, Gloria Ann, Brown, Jill Patricia, Galbraith, Peter and Ng, Kit Ee Dawn. (2016). Research into mathematical applications and modelling. In In K. Makar, S. Dole and J. Visnovska, M. Goos, A. Bennison & K. Fry (Ed.). Research in mathematics education in Australasia 2012-2015 pp. 281 - 304 Springer Science and Business Media. https://doi.org/10.1007/978-981-10-1419-2_14
Early Career Teachers’ ability to focus on typical students errors in relation to the complexity of a mathematical topic
Pankow, Lena, Kaiser, Gabriele, Busse, Andreas, König, Johannes, Blömeke, Sigrid, Hoth, Jessica and Döhrmann, Martina. (2016). Early Career Teachers’ ability to focus on typical students errors in relation to the complexity of a mathematical topic. ZDM: The International Journal on Mathematics Education. 48(1-2), pp. 55 - 67. https://doi.org/10.1007/s11858-016-0763-2
Theoretical and pedagogical considerations in promoting students' metacognitive modeling competencies
Vorholter, Katrin and Kaiser, Gabriele. (2016). Theoretical and pedagogical considerations in promoting students' metacognitive modeling competencies. In In C. R. Hirsch (Ed.). Mathematical modeling and modeling mathematics pp. 273 - 280 National Council of Teachers of Mathematics.
The relation between content-specific and general teacher knowledge and skills
Blömeke, Sigrid, Busse, Andreas, Kaiser, Gabriele, König, Johannes and Suhl, Ute. (2016). The relation between content-specific and general teacher knowledge and skills. Teaching and Teacher Education. 56, pp. 35 - 46. https://doi.org/10.1016/j.tate.2016.02.003
Early career teachers' ability to focus on typical students errors in relation to the complexity of a mathematical topic
Pankow, Lena, Kaiser, Gabriele, Busse, Andreas, Konig, Johannes, Blomeke, Sigrid, Hoth, Jessica and Dohrmann, Martina. (2016). Early career teachers' ability to focus on typical students errors in relation to the complexity of a mathematical topic. 48, pp. 55 - 67. https://doi.org/10.1007/s11858-016-0763-2
Diagnostic competence of primary school mathematics teachers during classroom situations
Hoth, Jessica, Döhrmann, Martina, Kaiser, Gabriele, Busse, Andreas, König, Johannes and Blömeke, Sigrid. (2016). Diagnostic competence of primary school mathematics teachers during classroom situations. ZDM: The International Journal on Mathematics Education. 48(1-2), pp. 41 - 53. https://doi.org/10.1007/s11858-016-0759-y
Early Career Mathematics Teachers’ General Pedagogical Knowledge and Skills: Do Teacher Education, Teaching Experience, and Working Conditions Make a Difference?
König, Johannes, Blömeke, Sigrid and Kaiser, Gabriele. (2015). Early Career Mathematics Teachers’ General Pedagogical Knowledge and Skills: Do Teacher Education, Teaching Experience, and Working Conditions Make a Difference? International Journal of Science and Mathematics Education. 13(2), pp. 331 - 350. https://doi.org/10.1007/s10763-015-9618-5
Effects of motivation on the belief systems of future mathematics teachers from a comparative perspective
Blömeke, Sigrid and Kaiser, Gabriele. (2015). Effects of motivation on the belief systems of future mathematics teachers from a comparative perspective. In In B. Pepin and B. Roesken-Winter (Ed.). From beliefs to dynamic affect systems in mathematics education: Exploring a mosaic of relationships and interactions pp. 227 - 243 Springer International Publishing.
Teacher Change During Induction: Development of Beginning Primary Teachers’ Knowledge, Beliefs and Performance
Blömeke, Sigrid, Hoth, Jessica, Döhrmann, Martina, Busse, Andreas, Kaiser, Gabriele and König, Johannes. (2015). Teacher Change During Induction: Development of Beginning Primary Teachers’ Knowledge, Beliefs and Performance. International Journal of Science and Mathematics Education. 13(2), pp. 287 - 308. https://doi.org/10.1007/s10763-015-9619-4
Fostering mathematical modelling in secondary schools
Stillman, Gloria. (2015). Fostering mathematical modelling in secondary schools. In In L. N. Hoe and N. K. E. Dawn (Ed.). Mathematical modelling: From theory to practice pp. 125 - 141 World Scientific Publishing.
Modelling competencies: Past development and further perspectives
Kaiser, Gabriele and Brand, Susanne. (2015). Modelling competencies: Past development and further perspectives. In In G. A. Stillman, W. Blum and M. S. Biembengut (Ed.). Mathematical modelling in education research and practice: Cultural, social and cognitive influences pp. 129 - 149 Springer International Publishing.
Facilitating mathematisation in modelling by beginning modellers in secondary school
Stillman, Gloria, Brown, Jill and Geiger, Vince. (2015). Facilitating mathematisation in modelling by beginning modellers in secondary school. In In G. A. Stillman, W. Blum and M. S. Biembengut (Ed.). Mathematical modelling in education research and practice: Cultural, social and cognitive influences pp. 93 - 104 Springer. https://doi.org/10.1007/978-3-319-18272-8_7
Scaffolding in complex modelling situations
Stender, Peter and Kaiser, Gabriele. (2015). Scaffolding in complex modelling situations. ZDM: The International Journal on Mathematics Education. 47(7), pp. 1255 - 1267. https://doi.org/10.1007/s11858-015-0741-0
Mathematical modelling in education, research and practice: Cultural, social, and cognitive influences
Stillman, Gloria, Blum, Werner and Salett Biembengut, Maria. (2015). Mathematical modelling in education, research and practice: Cultural, social, and cognitive influences Springer.
Promotion of mathematical modelling competencies in the context of modelling projects
Kaiser, Gabriele and Grünewald, Susanne. (2015). Promotion of mathematical modelling competencies in the context of modelling projects. In In N. H. Lee and K. E. D. Ng (Ed.). Mathematical modelling from theory to practice pp. 21 - 39 World Scientific Publishing.
About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers’ Competence
Kaiser, Gabriele, Busse, Andreas, Hoth, Jessica, König, Johannes and Blömeke, Sigrid. (2015). About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers’ Competence. International Journal of Science and Mathematics Education. 13(2), pp. 369 - 387. https://doi.org/10.1007/s10763-015-9616-7
Early career mathematics teachers' general pedagogical knowledge and skills: do teacher education, teaching experience, and working conditions make a difference?
Konig, Johannes, Blomeke, Sigrid and Kaiser, Gabriele. (2015). Early career mathematics teachers' general pedagogical knowledge and skills: do teacher education, teaching experience, and working conditions make a difference? International Journal of Science and Mathematics Education. 13(2), pp. 331 - 350. https://doi.org/10.1007/s10763-015-9618-5
Cultural, social, cognitive and research influences on mathematical modelling education
Stillman, Gloria, Blum, Werner and Biembengut, Maria. (2015). Cultural, social, cognitive and research influences on mathematical modelling education. In In G. A. Stillman, W. Blum and M. S. Biembengut (Ed.). Mathematical modelling in education research and practice: Cultural, social and cognitive influences pp. 1 - 32 Springer. https://doi.org/10.1007/978-3-319-18272-8_1
Applications and modelling research in secondary classrooms : What have we learnt?
Stillman, Gloria. (2015). Applications and modelling research in secondary classrooms : What have we learnt? In In S. J. Cho (Ed.). Selected regular lectures from the 12th International Congress on Mathematical Education pp. 791 - 805 Springer. https://doi.org/10.1007/978-3-319-17187-6_44
Erfassung berufsbezogener kompetenzen von studierenden: Ein kommentar
Kaiser, Gabriele. (2015). Erfassung berufsbezogener kompetenzen von studierenden: Ein kommentar. Zeitschrift fuer Paedagogik. Beiheft. 61, pp. 136 - 143.
Wissen und Fähigkeiten in Fachdidaktik und Pädagogik
Busse, Andreas and Kaiser, Gabriele. (2015). Wissen und Fähigkeiten in Fachdidaktik und Pädagogik. Zeitschrift für Pädagogik. 61(3), pp. 328 - 344.
Exploring interconnections between real-world and application tasks: Case study from Singapore
Ng, Kit Ee Dawn and Stillman, Gloria. (2015). Exploring interconnections between real-world and application tasks: Case study from Singapore. In In G. A. Stillman, W. Blum and M. S. Biembengut (Ed.). Mathematical modelling in education research and practice: Cultural, social and cognitive influences pp. 207 - 217 Springer. https://doi.org/10.1007/978-3-319-18272-8_16
Preface for the special issue on "video-based research on teacher expertise"
Blömeke, Sigrid, Kaiser, Gabriele and Clarke, David J.. (2015). Preface for the special issue on "video-based research on teacher expertise". International Journal of Science and Mathematics Education. 13(2), pp. 257 - 266. https://doi.org/10.1007/s10763-015-9629-2
Problem finding and problem posing for mathematical modelling
Stillman, Gloria. (2015). Problem finding and problem posing for mathematical modelling. In In L. N. Hoe and N. K. E. Dawn (Ed.). Mathematical modelling: From theory to practice pp. 41 - 56 World Scientific Publishing.
The conceptualisation of mathematics competencies in the International Teacher Education Study TEDS-M
Döhrmann, Martina, Kaiser, Gabriele and Blömeke, Sigird. (2014). The conceptualisation of mathematics competencies in the International Teacher Education Study TEDS-M. In In S. Blömeke, F.-J. Hsieh and G. Kaiser & W. H. Schmidt (Ed.). International perspectives on teacher knowledge, beliefs and opportunities to learn: TEDS-M results pp. 431 - 456 Springer. https://doi.org/10.1007/978-94-007-6437-8_20
Resolving the chicken-or-egg causality dilemma: The longitudinal interplay of teacher knowledge and teacher beliefs
Blömeke, Sigrid, Buchholz, Nils, Suhl, Ute and Kaiser, Gabriele. (2014). Resolving the chicken-or-egg causality dilemma: The longitudinal interplay of teacher knowledge and teacher beliefs. Teaching and Teacher Education. 37, pp. 130 - 139. https://doi.org/10.1016/j.tate.2013.10.007
Von der Lehrerausbildung in den Beruf – Fachbezogenes Wissen als Voraussetzung für Wahrnehmung, Interpretation und Handeln im Unterricht
Blömeke, Sigrid, König, Johannes, Busse, Andreas, Suhl, Ute, Benthien, Jessica, Döhrmann, Martina and Kaiser, Gabriele. (2014). Von der Lehrerausbildung in den Beruf – Fachbezogenes Wissen als Voraussetzung für Wahrnehmung, Interpretation und Handeln im Unterricht. Zeitschrift für Erziehungswissenschaft. 17(3), pp. 509 - 542. https://doi.org/10.1007/s11618-014-0564-8
The cultural dimension of beliefs: An investigation of future primary teachers' epistemological beliefs concerning the nature of mathematics in 15 countries
Felbrich, Anja, Kaiser, Gabriele and Schmotz, Christiane. (2014). The cultural dimension of beliefs: An investigation of future primary teachers' epistemological beliefs concerning the nature of mathematics in 15 countries. In In S. Blömeke, F.-J. Hsieh and G. Kaiser & W. H. Schmidt (Ed.). pp. 209 - 229 Springer. https://doi.org/10.1007/978-94-007-6437-8_10
Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional and teacher educational perspectives
Cai, Jinfa, Cirillo, Michelle, Pelesko, John, Bommero Ferri, Rita, Borba, Marcelo, Geiger, Vince, Stillman, Gloria, English, Lyn, Wake, Geoff and Kaiser, Gabriele. (2014). Mathematical modeling in school education: Mathematical, cognitive, curricular, instructional and teacher educational perspectives. In P Liljedahl, S Oesterle and C Nicol (Ed.). Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education. Canada: Springer. pp. 145 - 172
Learning from the Eastern and the Western Debate: The case of mathematics teacher education
Kaiser, Gabriele and Blömeke, Sigrid. (2014). Learning from the Eastern and the Western Debate: The case of mathematics teacher education. In In S. Blömeke, F.-J. Hsieh and G. Kaiser & W. H. Schmidt (Ed.). International perspectives on teacher knowledge, beliefs and opportunities to learn: TEDS-M results pp. 517 - 539 Routledge. https://doi.org/10.1007/978-94-007-6437-8_24
Is teachers' general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach
König, Johannes, Blömeke, Sigrid, Klein, Patricia, Suhl, Ute, Busse, Andreas and Kaiser, Gabriele. (2014). Is teachers' general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach. Teaching and Teacher Education. 38, pp. 76 - 88. https://doi.org/10.1016/j.tate.2013.11.004
Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries
Blömeke, Sigrid, Suhl, Ute, Kaiser, Gabriele and Döhrmann, Martina. (2014). Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries. In In S. Blömeke, F.-J. Hsieh and G. Kaiser & W. H. Schmidt (Ed.). International perspectives on teacher knowledge, beliefs and opportunities to learn: TEDS-M results pp. 327 - 353 Routledge. https://doi.org/10.1007/978-94-007-6437-8_15
Overcoming the gap between university and school mathematics: The impact of an innovative program in mathematics teacher education at the Justus-Liebig University in Giessen
Kaiser, Gabriele. (2014). Overcoming the gap between university and school mathematics: The impact of an innovative program in mathematics teacher education at the Justus-Liebig University in Giessen. In In S. Rezat, M. Hattermann and A. Peter-Koop (Ed.). Transformation — A fundamental Idea of mathematics education pp. 85 - 105 Springer. https://doi.org/10.1007/978-1-4614-3489-4_5
Affordances: Ten Years On
Brown, Jill and Stillman, Gloria. (2014). Affordances: Ten Years On. In J Anderson, M Cavanagh and A Prescott (Ed.). Curriculum in focus: Research guided practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia). Australia: Mathematics Education Research Group of Australasia. pp. 111 - 118
Views of cognition: Different lenses for 'looking-in' on classrooms
Stillman, Gloria Ann. (2014). Views of cognition: Different lenses for 'looking-in' on classrooms. ZDM: The International Journal on Mathematics Education. 46(3), pp. 493 - 496. https://doi.org/10.1007/s11858-014-0601-3
Modelling in mathematics classroom instruction an innovative approach for transforming mathematics education
Vorhölter, Kartin, Kaiser, Gabriele and Borromeo Ferri, Rita. (2014). Modelling in mathematics classroom instruction an innovative approach for transforming mathematics education. In In Y. Li, E. A. Silver and S. Li (Ed.). Transforming mathematics instruction: Multiple approaches and practices pp. 21 - 36 Springer. https://doi.org/10.1007/978-3-319-04993-9_3
Evidence of implemented anticipation in mathematising by beginning modellers
Stillman, Gloria and Brown, Jill. (2014). Evidence of implemented anticipation in mathematising by beginning modellers. Mathematics Education Research Journal. 26(4), pp. 763 - 789. https://doi.org/10.1007/s13394-014-0119-6
Teacher Education Effectiveness: Quality and Equity of Future Primary Teachers’ Mathematics and Mathematics Pedagogical Content Knowledge
Blömeke, Sigrid, Suhl, Ute and Kaiser, Gabriele. (2014). Teacher Education Effectiveness: Quality and Equity of Future Primary Teachers’ Mathematics and Mathematics Pedagogical Content Knowledge. In International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn: TEDS-M Results pp. 91 - 114 Springer. https://doi.org/10.1007/978-94-007-6437-8_5
Theoretical Framework, Study Design and Main Results of TEDS-M
Blömeke, Sigrid and Kaiser, Gabriele. (2014). Theoretical Framework, Study Design and Main Results of TEDS-M. In International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn: TEDS-M Results pp. 19 - 47 Springer. https://doi.org/10.1007/978-94-007-6437-8_2
Homogeneity or Heterogeneity? Profiles of Opportunities to Learn in Primary Teacher Education and Their Relationship to Cultural Context and Outcomes
Blömeke, Sigrid and Kaiser, Gabriele. (2014). Homogeneity or Heterogeneity? Profiles of Opportunities to Learn in Primary Teacher Education and Their Relationship to Cultural Context and Outcomes. In In S. Blömeke, G. Kaiser and F. Hsieh & W. H. Schmidt (Ed.). International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn: TEDS-M Results pp. 299 - 325 Springer. https://doi.org/10.1007/978-94-007-6437-8_14
Mathematical modelling: Connecting to teaching and research practices - the impact of globalisation
Stillman, Gloria, Kaiser, Gabriele, Blum, Werner and Brown, Jill P.. (2013). Mathematical modelling: Connecting to teaching and research practices - the impact of globalisation. In In GA Stillman, G Kaiser and W Blum & JP Brown (Ed.). Teaching mathematical modelling: connecting to research and practice pp. 1 - 24 Springer. https://doi.org/10.1007/978-94-007-6540-5_1
Future mathematics teachers' professional knowledge of elementary mathematics from an advanced standpoint
Buchholtz, Nils, Leung, Frederick KS, Ding, Lin, Kaiser, Gabriele, Park, Kyungmee and Schwarz, Bjorn. (2013). Future mathematics teachers' professional knowledge of elementary mathematics from an advanced standpoint. ZDM - International Journal on Mathematics Education. https://doi.org/10.1007/s11858-012-0462-6
Authentic complex modelling problems in mathematics education
Kaiser, Gabriele, Bracke, Martin, Göttlich, Simone and Kaland, Christine. (2013). Authentic complex modelling problems in mathematics education. In In A. Damlamian, J. F. Rodrigues and R. Sträßer (Ed.). Educational interfaces between mathematics and industry: Report on an ICMI-ICIAM-Study pp. 287 - 297 Springer. https://doi.org/10.1007/978-3-319-02270-3_29
Complex modelling problems in co-operative, self-directed learning environments
Kaiser, Gabriele and Stender, Peter. (2013). Complex modelling problems in co-operative, self-directed learning environments. In In G. A. Stillman, G. Kaiser and W. Blum & J. P. Brown (Ed.). pp. 277 - 293 Springer. https://doi.org/10.1007/978-94-007-6540-5_23
Challenges in modelling challenges: Intents and purposes
Stillman, Gloria, Brown, Jill P. and Galbraith, Peter. (2013). Challenges in modelling challenges: Intents and purposes. In In GA Stillman, G Kaiser and W Blum & JP Brown (Ed.). Teaching mathematical modelling: connecting to research and practice pp. 217 - 227 Springer. https://doi.org/10.1007/978-94-007-6540-5_19
Educational interfaces between mathematics and industry at school level: Report on WG 4
Kaiser, Gabriele, van der Kooij, Henk and Wake, Geoff. (2013). Educational interfaces between mathematics and industry at school level: Report on WG 4. In In A. Damlamian, J. F. Rodrigues and R. Sträßer (Ed.). Educational interfaces between mathematics and industry: Report on an ICMI-ICIAM-Study pp. 263 - 270 Springer. https://doi.org/10.1007/978-3-319-02270-3_26
Improving mathematics teacher education in Germany: empirical results from a longitudinal evaluation of innovative programs
Bucholtz, Nils and Kaiser, Gabriele. (2013). Improving mathematics teacher education in Germany: empirical results from a longitudinal evaluation of innovative programs. International Journal of Science and Mathematics Education. 11(4), pp. 949 - 977. https://doi.org/10.1007/s10763-013-9427-7
The role of textbooks in developing a socio-critical perspective on mathematical modelling in secondary classrooms
Stillman, Gloria, Brown, Jill P., Faragher, Rhonda Muriel, Geiger, Vince and Galbraith, Peter. (2013). The role of textbooks in developing a socio-critical perspective on mathematical modelling in secondary classrooms. In In GA Stillman, G Kaiser and W Blum & JP Brown (Ed.). Teaching mathematical modelling: connecting to research and practice pp. 361 - 373 Springer. https://doi.org/10.1007/978-94-007-6540-5_30
Implementation of IBL in Europe from an Australasian perspective
Stillman, Gloria Ann. (2013). Implementation of IBL in Europe from an Australasian perspective. ZDM Mathematics Education. 45(6), pp. 911 - 918. https://doi.org/10.1007/s11858-013-0545-z
Preface to Section IV
Kaiser, Gabriele. (2013). Preface to Section IV. In In Y. Li and R. Huang (Ed.). How Chinese Teach Mathematics and Improve Teaching pp. 384 - 390 Routledge. https://doi.org/10.4324/9780203110119
Spiegelt sich pädagogisches Wissen in den Kompetenzselbsteinschätzungen angehender Lehrkräfte?
König, Johannes, Kaiser, Gabriele and Felbrich, Anja. (2012). Spiegelt sich pädagogisches Wissen in den Kompetenzselbsteinschätzungen angehender Lehrkräfte? Zeitschrift für Pädagogik. 58(4), pp. 476 - 491.
Mathematical modelling: Some issues and reflections
Stillman, Gloria and Galbraith, Peter. (2012). Mathematical modelling: Some issues and reflections. In In W Blum, R B Ferri and K Maass (Ed.). pp. 97 - 105 Springer.
Empirical evidence for Niss' implemented anticipation in mathematising realistic situations
Stillman, Gloria and Brown, Jill P.. (2012). Empirical evidence for Niss' implemented anticipation in mathematising realistic situations. In J. Dindyal, L. P. Cheng and S. F. Ng (Ed.). Mathematics education: Expanding horizons. Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 682 - 689
Editorial: To engage or not to engage
Stillman, Gloria and Brown, Jill. (2012). Editorial: To engage or not to engage. Australian Senior Mathematics Journal. 26(1), pp. 1 - 5.
Editorial: Envisioning the future of the mathematical sciences and mathematics teaching
Brown, Jill and Stillman, Gloria. (2012). Editorial: Envisioning the future of the mathematical sciences and mathematics teaching. Australian Senior Mathematics Journal. 26(2), pp. 4 - 5.
Mathematical modelling: Some issues and reflections
Stillman, Gloria and Galbraith, Peter. (2012). Mathematical modelling: Some issues and reflections. In In W Blum, R B Ferri and K Maass (Ed.). pp. 97 - 105 Springer.
CERME7 Working Group 6: Applications and modelling
Kaiser, Gabriele, Carreira, Susana, Lingefjard, Thomas and Wake, Geoff. (2012). CERME7 Working Group 6: Applications and modelling. Research in Mathematics Education. 14(2), pp. 195 - 196. https://doi.org/10.1080/14794802.2012.694287
Mathematical Modelling Challenge
Brown, Jill and Stillman, Gloria. (2011). Mathematical Modelling Challenge. Vinculum. 26(4), pp. 16 - 19.
Mathematical Modelling Challenge
Brown, Jill and Stillman, Gloria. (2011). Mathematical Modelling Challenge. Prime Number. 26(4), pp. 15 - 16.
Mathematical Modelling and Applications
Stillman, Gloria and Brown, Jill. (2011). Mathematical Modelling and Applications. Vinculum. 48(2), pp. 20 - 20.
Evolution of applications and modelling in a senior secondary curriculum
Stillman, Gloria and Galbraith, P.. (2011). Evolution of applications and modelling in a senior secondary curriculum. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 689 - 699 Springer. https://doi.org/10.1007/978-94-007-0910-2_66
'Get down and get dirty in the mathematics': Technology and mathematical modelling in senior secondary
Stillman, Gloria and Brown, Jill. (2011). 'Get down and get dirty in the mathematics': Technology and mathematical modelling in senior secondary. In J. Clark, B. Kissane and J. Mousley (Ed.). Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference. Australia: AAMT and MERGA. pp. 711 - 718
Reflections and future prospects
Kaiser, Gabriele and Li, Yeping. (2011). Reflections and future prospects. In In Y. Li and G. Kaiser (Ed.). Expertise in mathematics instruction: An international perspective pp. 343 - 353 Springer. https://doi.org/10.1007/978-1-4419-7707-6_16
Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school
Stillman, Gloria. (2011). Applying metacognitive knowledge and strategies in applications and modelling tasks at secondary school. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 165 - 180 Springer.
Equity and the quality of the language used in mathematics education
Schütte, Marcus and Kaiser, Gabriele. (2011). Equity and the quality of the language used in mathematics education. In In B. Atweh, M. Graven and W. Secada & P. Valero (Ed.). Mapping equity and quality in mathematics education pp. 237 - 251 Springer. https://doi.org/10.1007/978-90-481-9803-0_17
Expertise in mathematics instruction: Advancing research and practice from an international perspective
Li, Yeping and Kaiser, Gabriele. (2011). Expertise in mathematics instruction: Advancing research and practice from an international perspective. In In Y. Li and G. Kaiser (Ed.). Expertise in mathematics instruction: An international perspective pp. 3 - 15 Springer. https://doi.org/10.1007/978-1-4419-7707-6_1
Editorial: To err is human
Brown, Jill and Stillman, Gloria. (2011). Editorial: To err is human. Australian Senior Mathematics Journal. 25(2), pp. 4 - 5.
Bedingungsfaktoren des fachbezogenen Kompetenzerwerbs von Lehrkraften. Zum Einfluss von Ausbildungs-, Personlichkeits- und Kompositionsmerkmalen in der Mathematiklehrerausbildung fur die Sekundarstufe I
Blömeke, Sigrid, Kaiser, Gabriele and Döhrmann, Martina. (2011). Bedingungsfaktoren des fachbezogenen Kompetenzerwerbs von Lehrkraften. Zum Einfluss von Ausbildungs-, Personlichkeits- und Kompositionsmerkmalen in der Mathematiklehrerausbildung fur die Sekundarstufe I. Zeitschrift für Pädagogik. 57, pp. 77 - 103.
Trends in Teaching and Learning of Mathematical Modelling (ICTMA 14)
Stillman, Gloria, Ferri, Rita Borromeo, Blum, Werner and Kaiser, Gabriele. (2011). Trends in Teaching and Learning of Mathematical Modelling (ICTMA 14) Springer.
Editorial: Historical sources and historical development of statistical ideas
Brown, Jill and Stillman, Gloria. (2011). Editorial: Historical sources and historical development of statistical ideas. Australian Senior Mathematics Journal. 25(1), pp. 4 - 6.
Pre-service secondary mathematics teachers' affinity with using modelling tasks in teaching years 8-10
Stillman, Gloria and Brown, Jill P.. (2011). Pre-service secondary mathematics teachers' affinity with using modelling tasks in teaching years 8-10. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 289 - 298 Springer. https://doi.org/10.1007/978-94-007-0910-2_29
Turning ideas into modeling problems
Galbraith, Peter L., Stillman, Gloria and Brown, Jill P.. (2010). Turning ideas into modeling problems. In pp. 133 - 144 Springer. https://doi.org/10.1007/978-1-4419-0561-1_11
Identifying challenges within transition phases of mathematical modeling activities at Year 9
Stillman, Gloria, Brown, Jill and Galbraith, Peter. (2010). Identifying challenges within transition phases of mathematical modeling activities at Year 9. In In R. Lesh, P. L. Galbraith and C. R. Haines & A. Hurford (Ed.). Modeling students' mathematical modeling competencies: ICTMA13 pp. 385 - 398 Springer.
The other side of the coin :attempts to embed authentic real world tasks in the secondary curriculum
Stillman, Gloria and Ng, Dawn. (2010). The other side of the coin :attempts to embed authentic real world tasks in the secondary curriculum. In A. Araujo, Fernandes and A. Azevedo (Ed.). Proceedings of the EIMI 2010 Conference: Educational interfaces between mathematics and industry. Portugal: Centro Internacional de Matematica. pp. 491 - 500
Implementing applications and modelling in secondary school: Issues for teaching and learning
Stillman, Gloria. (2010). Implementing applications and modelling in secondary school: Issues for teaching and learning. In pp. 300 - 322 World Scientific Publishing.
Preservice secondary teachers' competencies in proof
Brown, Jill Patricia and Stillman, Gloria. (2009). Preservice secondary teachers' competencies in proof. In Fuo-Lai Lin, Feng-Jui Hsieh and Gila Hanna (Ed.). Proof and Proving in Mathematics Education: ICMI Study 19 Conference Proceedings. Taipei, Taiwan: National Taiwan Normal University. pp. 94 - 99
Research into the teaching and learning of applications and modelling in Australasia
Stillman, Gloria, Brown, Jill Patricia and Galbraith, Peter. (2008). Research into the teaching and learning of applications and modelling in Australasia. In Research in Mathematics Education in Australasia 2004-2007 pp. 141 - 164 Sense Publishers.
Competencies in argumentation and proof :A comparative study of future mathematics teachers from Australia, Germany and Hong Kong
Schwarz, Bjorn, Vale, Colleen, Brown, Jill Patricia, Stillman, Gloria, Kaiser, Gabriele, Buchholtz, Nils and Leung, Issic. (2008). Competencies in argumentation and proof :A comparative study of future mathematics teachers from Australia, Germany and Hong Kong. In Gabriele Kaiser (Ed.). Discussion Group 14: International Comparisons in Mathematics Education. Monterrey, Mexico: International Commission on Mathematical Instruction. pp. 1 - 6
Future teachers' professional knowledge on argumentation and proof: A case study from universities in three countries
Schwarz, Bjorn, Leung, Issic K. C., Bucholtz, Nils, Kaiser, Gabriele, Stillman, Gloria, Brown, Jill Patricia and Vale, Colleen. (2008). Future teachers' professional knowledge on argumentation and proof: A case study from universities in three countries. ZDM. 40(5), pp. 791 - 811. https://doi.org/10.1007/s11858-008-0150-8
The case of mathematical proof in lower secondary school :Knowledge and competencies of pre-service teachers
Brown, Jill Patricia, Stillman, Gloria, Schwarz, Bjorn and Kaiser, Gabriele. (2008). The case of mathematical proof in lower secondary school :Knowledge and competencies of pre-service teachers. In Merrilyn Goos, Ray Brown and Katie Makar (Ed.). Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia. Brisbane, Australia: Mathematics Education Research Group of Australasia. pp. 85 - 91
A framework for success in implementing mathematical modelling in the secondary classroom
Stillman, Gloria, Brown, Jill Patricia, Edwards, I. and Galbraith, Peter. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J Watson and K Beswick (Ed.). 30th annual conference of the Mathematics Education Research Group of Australasia. Wrest Point Hotel Casino, Hobart, Tasmania, Australia 02 - 06 Jul 2007 Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 688 - 707
Challenges in formulating an extended modelling task at Year 9
Stillman, Gloria and Brown, Jill Patricia. (2007). Challenges in formulating an extended modelling task at Year 9. In H. Reeves, K. Milton and T. Spencer (Ed.). Mathematics: Essential for learning, essential for life Proceedings of the 21st Biennial Conference of the Australian Association of Mathematics Teachers Inc.. Adelaide, Australia: Australian Association of Mathematics Teachers. pp. 224 - 231
Identifying challenges within transition phases of mathematical modelling activity at Year 9
Stillman, Gloria, Brown, Jill and Galbraith, Peter. (2007). Identifying challenges within transition phases of mathematical modelling activity at Year 9. Conference Proceedings Of the Thirteenth International Conference on the Teaching of Mathematical Modelling and Applications. International Conference on the Teaching of Mathematical Modelling and Applications. pp. 1 - 10
Facilitating middle secondary modelling competencies
Galbraith, Peter, Stillman, Gloria, Brown, Jill Patricia and Edwards, I. (2007). Facilitating middle secondary modelling competencies. In In C. Haines, P. Galbraith and W. Blum et al. (Ed.). Mathematical modelling (ICTMA12): Education, engineering and economics pp. 130 - 140 Horwood Press.
Defining moments in the graphing calculator solution of a cubic function task
Brown, Jill and Stillman, Gloria. (2006). Defining moments in the graphing calculator solution of a cubic function task. Nordisk Matematikkdidaktikk (Nordic Studies in Mathematics). 11(3), pp. 57 - 84.
Identifying key transition activities for enhanced engagement in mathematical modelling
Galbraith, Peter, Stillman, Gloria Ann and Brown, Jill Patricia. (2006). Identifying key transition activities for enhanced engagement in mathematical modelling. In P.Grootenboer, R. Zevenbergen and M. Chinnappan (Ed.). Identities, cultures and learning spaces, Proceedings of the Twenty Ninth annual conference of the Mathematics Education Research Group of Australasia (MERGA). Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 237 - 245
Can the notion of affordances be of use in the design of a technology enriched mathematics curriculum?
Stillman, Gloria, Brown, Jill Patricia and Herberts, Sandra. (2004). Can the notion of affordances be of use in the design of a technology enriched mathematics curriculum? In I. Putt, R. Faragher and M. McLean (Ed.). Mathematics Education for the third millennium: Towards 2010, Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia. Townsville, Australia: Mathematics Education Research Group of Australasia. pp. 119 - 126