Future teachers' professional knowledge on argumentation and proof: A case study from universities in three countries

Journal article

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
AuthorsSchwarz, Bjorn, Leung, Issic K. C., Bucholtz, Nils, Kaiser, Gabriele, Stillman, Gloria, Brown, Jill Patricia and Vale, Colleen
Abstract

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.

Year2008
JournalZDM
Journal citation40 (5), pp. 791 - 811
PublisherSpringer
ISSN1863-9690
Digital Object Identifier (DOI)https://doi.org/10.1007/s11858-008-0150-8
Scopus EID2-s2.0-79957965319
Page range791 - 811
Research GroupInstitute for Learning Sciences and Teacher Education (ILSTE)
Place of publicationGermany
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https://acuresearchbank.acu.edu.au/item/852q9/future-teachers-professional-knowledge-on-argumentation-and-proof-a-case-study-from-universities-in-three-countries

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Context and understanding: the case of linear models
Brown, Jill. (2017). Context and understanding: the case of linear models. In In G. A. Stillman, W. Blum and G. Kaiser (Ed.). Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education pp. 211 - 221 Springer International Publishing. https://doi.org/10.1007/978-3-319-62968-1
Crossing boundaries in mathematical modelling and applications educational research and practice
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Enabling anticipation through visualisation in mathematising real-world problems in a flipped classroom
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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
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Reflections on research trends in international comparative studies in mathematics education
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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
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Perspectives on (future) teachers' professional competencies
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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
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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
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Teachers' perspectives of changes in their practice during a technology in mathematics education research project
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The primacy of 'noticing': a key to successful modelling
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Professional competences of teachers for fostering creativity and supporting high-achieving students
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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
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Fostering modeling competencies for complex situations
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Research into mathematical applications and modelling
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Early Career Teachers’ ability to focus on typical students errors in relation to the complexity of a mathematical topic
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Theoretical and pedagogical considerations in promoting students' metacognitive modeling competencies
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The relation between content-specific and general teacher knowledge and skills
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Early career teachers' ability to focus on typical students errors in relation to the complexity of a mathematical topic
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Diagnostic competence of primary school mathematics teachers during classroom situations
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Early Career Mathematics Teachers’ General Pedagogical Knowledge and Skills: Do Teacher Education, Teaching Experience, and Working Conditions Make a Difference?
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Effects of motivation on the belief systems of future mathematics teachers from a comparative perspective
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Teacher Change During Induction: Development of Beginning Primary Teachers’ Knowledge, Beliefs and Performance
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Visualisation tactics for solving real world tasks
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Fostering mathematical modelling in secondary schools
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Modelling competencies: Past development and further perspectives
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Facilitating mathematisation in modelling by beginning modellers in secondary school
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Scaffolding in complex modelling situations
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Mathematical modelling in education, research and practice: Cultural, social, and cognitive influences
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Promotion of mathematical modelling competencies in the context of modelling projects
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About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers’ Competence
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Early career mathematics teachers' general pedagogical knowledge and skills: do teacher education, teaching experience, and working conditions make a difference?
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Cultural, social, cognitive and research influences on mathematical modelling education
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Applications and modelling research in secondary classrooms : What have we learnt?
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Erfassung berufsbezogener kompetenzen von studierenden: Ein kommentar
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Wissen und Fähigkeiten in Fachdidaktik und Pädagogik
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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
Complexities of digital technology use and the teaching and learning of function
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Mathematical applications and modelling in the teaching and learning of mathematics
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Preface for the special issue on "video-based research on teacher expertise"
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Problem finding and problem posing for mathematical modelling
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The conceptualisation of mathematics competencies in the International Teacher Education Study TEDS-M
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Student strategies in enacting affordances
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Resolving the chicken-or-egg causality dilemma: The longitudinal interplay of teacher knowledge and teacher beliefs
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Von der Lehrerausbildung in den Beruf – Fachbezogenes Wissen als Voraussetzung für Wahrnehmung, Interpretation und Handeln im Unterricht
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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
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Is teachers' general pedagogical knowledge a premise for noticing and interpreting classroom situations? A video-based assessment approach
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Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries
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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
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Views of cognition: Different lenses for 'looking-in' on classrooms
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Modelling in mathematics classroom instruction an innovative approach for transforming mathematics education
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Evidence of implemented anticipation in mathematising by beginning modellers
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Teacher Education Effectiveness: Quality and Equity of Future Primary Teachers’ Mathematics and Mathematics Pedagogical Content Knowledge
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Theoretical Framework, Study Design and Main Results of TEDS-M
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Homogeneity or Heterogeneity? Profiles of Opportunities to Learn in Primary Teacher Education and Their Relationship to Cultural Context and Outcomes
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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
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Authentic complex modelling problems in mathematics education
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Complex modelling problems in co-operative, self-directed learning environments
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Challenges in modelling challenges: Intents and purposes
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Educational interfaces between mathematics and industry at school level: Report on WG 4
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Improving mathematics teacher education in Germany: empirical results from a longitudinal evaluation of innovative programs
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The role of textbooks in developing a socio-critical perspective on mathematical modelling in secondary classrooms
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Inducting year 6 students into a culture of mathematising as a practice
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Implementation of IBL in Europe from an Australasian perspective
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Preface to Section IV
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Teaching roles in technology-rich teaching and learning environments (TRTLE's)
Brown, Jill. (2013). Teaching roles in technology-rich teaching and learning environments (TRTLE's). In V. Steinle, L. Ball and C. Bardini (Ed.). Mathematics Education: Yesterday, Today and Tomorrow (MERGA36). Australia: Mathematics Education Research Group of Australasia. pp. 106 - 113
Demonstration lessons in mathematics education: Teachers' observation foci and intended changes in practice
Clarke, Doug, Roche, Anne, Wilkie, Karina, Wright, Vince, Brown, Jill, Downton, Ann, Horne, Marjorie, Knight, Rose, McDonough, Andrea, Sexton, Matthew and Worrall, Chris. (2013). Demonstration lessons in mathematics education: Teachers' observation foci and intended changes in practice. Mathematics Education Research Journal. 25(2), pp. 207 - 230. https://doi.org/10.1007/s13394-012-0058-z
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.
Modelling tasks: insight into mathematical understanding
Brown, Jill P. and Edwards, Ian. (2011). Modelling tasks: insight into mathematical understanding. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 187 - 197 Springer. https://doi.org/10.1007/978-94-007-0910-2_20
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
Concept Maps: Implications for the Teaching of Function for Secondary School Students
Brown, Jill Patricia. (2009). Concept Maps: Implications for the Teaching of Function for Secondary School Students. In R. Hunter, B. Bicknell and T. Burgess (Ed.). Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). Palmerston North, NZ: Mathematics Education Research Group of Australasia. pp. 65 - 72
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
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
Early notions of functions in a technology-rich teaching and learning environment (TRTLE)
Brown, Jill Patricia. (2007). Early notions of functions in a technology-rich teaching and learning environment (TRTLE). 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. 153 - 162
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.
Looking through zones at the teacher's role in technology-rich teaching and learning environments (TRTLE's)
Brown, Jill Patricia. (2006). Looking through zones at the teacher's role in technology-rich teaching and learning environments (TRTLE's). In C. Hoyles, J-b. Lagrange and L. H. Son (Ed.). Digital technologies and mathematics teaching and learning: Rethinking the terrain, Proceedings of the seventeenth ICMI Study: 'Technology revisited'. Hanoi, Vietnam: International Commission on Mathematical Instruction. pp. 56 - 65
Manifestations of affordances of a technology-rich teaching and learning environment (TRTLE)
Brown, Jill Patricia. (2006). Manifestations of affordances of a technology-rich teaching and learning environment (TRTLE). In J. Novotna, H. Moraova and M. Kratke (Ed.). Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (PME),. Prague, Czech Republic: International Group for the Psychology of Mathemati.... pp. 241 - 248
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
Affordances of a technology-rich teaching and learning environment
Brown, Jill Patricia. (2005). Affordances of a technology-rich teaching and learning environment. In P. Clarkson, A. Downton and D. Gronn (Ed.). Building Connections, Theory, Research and Practice: Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia. Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 177 - 184
Identification of affordances of a technology-rich teaching and learning environment (TRTLE)
Brown, Jill Patricia. (2005). Identification of affordances of a technology-rich teaching and learning environment (TRTLE). In H. Chick and J. Vincent (Ed.). Proceedings of the 29th annual conference of the International Group for the Psychology of Mathematics Education (PME). Melbourne, Australia: International Group for the Psychology of Mathemati.... pp. 185 - 192
Enabling teachers to perceive the affordances of a technologically rich learning environment for linear functions in order to design units of work incorporating best practice
Brown, Jill Patricia. (2004). Enabling teachers to perceive the affordances of a technologically rich learning environment for linear functions in order to design units of work incorporating best practice. In W. C. Yang, S. C. Chu and T. de Alwis (Ed.). Proceedings of the 9th Asian Technology Conference in Mathematics. Singapore, Singapore: Advanced Technology Council in Mathematics Inc. pp. 242 - 251
A difficult function
Brown, Jill. (2004). A difficult function. Australian Mathematics Teacher. 60(2), pp. 6 - 11.
Teacher approaches to graphing a difficult cubic function
Brown, Jill Patricia. (2004). Teacher approaches to graphing a difficult cubic function. 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. 111 - 118
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
Defining moments in determining a complete graph in a graphing calculator teaching and learning environment
Brown, Jill Patricia. (2003). Defining moments in determining a complete graph in a graphing calculator teaching and learning environment. In L. Bragg, C. Campbell and G. Herbert (Ed.). Mathematics Education Research: Innovation, networking, opportunity. Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia (MERGA). Geelong, Australia: Mathematics Education Research Group of Australasia. pp. 168 - 175