# Using mathematics to solve real world problems : The role of enablers

Journal article

Geiger, Vince, Stillman, Gloria, Brown, Jill P., Galbraith, Peter and Niss, Mogens. (2018). Using mathematics to solve real world problems : The role of enablers.

*Mathematics Education Research Journal.*30(1), pp. 7-19. https://doi.org/10.1007/s13394-017-0217-3

Authors | Geiger, Vince, Stillman, Gloria, Brown, Jill P., Galbraith, Peter and Niss, Mogens |
---|---|

Abstract | The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that Benable^ year 10/11 students to successfully begin themodelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of Benablers^ within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students’ development as modellers. |

Keywords | applications; mathematical modelling; real world problem; mathematisation; formulation; implemented anticipation; anticipatory metacognition; enablers |

Year | 2018 |

Journal | Mathematics Education Research Journal |

Journal citation | 30 (1), pp. 7-19 |

Publisher | Springer |

ISSN | 1033-2170 |

Digital Object Identifier (DOI) | https://doi.org/10.1007/s13394-017-0217-3 |

Scopus EID | 2-s2.0-85041699750 |

Open access | Published as green open access |

Page range | 7-19 |

Funder | Australian Research Council (ARC) |

Research Group | Institute for Learning Sciences and Teacher Education (ILSTE) |

Author's accepted manuscript | License All rights reserved File Access Level Open |

Publisher's version | License All rights reserved File Access Level Controlled |

Output status | Published |

Publication dates | |

Online | 21 Jun 2017 |

Publication process dates | |

Accepted | 05 Jun 2017 |

ARC Funded Research | This output has been funded, wholly or partially, under the Australian Research Council Act 2001 |

Grant ID | DP170101555 |

https://acuresearchbank.acu.edu.au/item/87xz4/using-mathematics-to-solve-real-world-problems-the-role-of-enablers

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Geiger, Vince, Goos, Merrilyn and Forgasz, Helen. (2015). A rich interpretation of numeracy for the 21st century: A survey of the state of the field.*ZDM: The International Journal on Mathematics Education.*47(4), pp. 531 - 548. https://doi.org/10.1007/s11858-015-0708-1

##### 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

Brown, Jill. (2015). Complexities of digital technology use and the teaching and learning of function.*Computers and Education.*87, pp. 112 - 122. https://doi.org/10.1016/j.compedu.2015.03.022

##### The role of digital technologies in numeracy teaching and learning

Geiger, Vince, Goos, Merrilyn and Dole, Shelley. (2015). The role of digital technologies in numeracy teaching and learning.*International Journal of Science and Mathematics Education.*13(5), pp. 1115 - 1137. https://doi.org/10.1007/s10763-014-9530-4

##### Mathematical applications and modelling in the teaching and learning of mathematics

Brown, Jill and Ikeda, Toshikazu. (2015). Mathematical applications and modelling in the teaching and learning of mathematics. In In S.J. Cho (Ed.).*Proceedings of the 12th International Congress on Mathematical Education: Intellectual and Attitudinal Challanges*pp. 469 - 474 Springer. https://doi.org/10.1007/978-3-319-12688-3

##### 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.

##### Conceptualising and enacting numeracy across the curriculum

Goos, Merrilyn, Geiger, Vince and Bennison, Anne. (2015). Conceptualising and enacting numeracy across the curriculum.*Annual Conference of the International Group for the Psychology of Mathematics Education.*Australia: International Group for the Psychology of Mathematics Education. pp. 9 - 16

##### The challenge of publication for English non-dominant-language authors in mathematics education

Geiger, Vince and Straesser, Rudolf. (2015). The challenge of publication for English non-dominant-language authors in mathematics education.*For the Learning of Mathematics.*35(3), pp. 35 - 41.

##### Student strategies in enacting affordances

Brown, Jill P.. (2014). Student strategies in enacting affordances. 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: International Group for the Psychology of Mathematics Education. pp. 201 - 208

##### The role of social aspects of teaching and learning in transforming mathematical activity: Tools, tasks, individuals and learning communities

Geiger, Vince. (2014). The role of social aspects of teaching and learning in transforming mathematical activity: Tools, tasks, individuals and learning communities. In In Rezat, S., Hattermann, M. and Peter-Koop, A. (Ed.).*Transformation - A Fundamental Idea of Mathematics Education*pp. 203 - 221 Springer. https://doi.org/10.1007/978-1-4614-3489-4_11

##### 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

##### Curriculum intent, teacher professional development and student learning in numeracy

Geiger, Vince, Goos, Merrilyn and Dole, Shelley. (2014). Curriculum intent, teacher professional development and student learning in numeracy. In In Y. Li and G. Lappan (Ed.).*Mathematics Curriculum in School Education*pp. 473 - 492 Springer. https://doi.org/10.1007/978-94-007-7560-2_22

##### Devising principles of design for numeracy tasks

Geiger, Vince, Goos, Merrilyn and Forgasz, Helen. (2014). Devising principles of design for numeracy tasks. 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. 239 - 246

##### 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

##### Transforming professional practice in numeracy teaching

Goos, Merrilyn, Geiger, Vince and Dole, Shelley. (2014). Transforming professional practice in numeracy teaching. In In Y. Li, E. Silver and S. Li (Ed.).*Transforming Mathematics Instruction: Multiple Approaches and Practices*Springer. https://doi.org/10.1007/978-3-319-04993-9_6

##### 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

##### 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

##### Exploring the demands and opportunities for numeracy in the Australian curriculum: English

Geiger, Vince, Goos, Merrilyn, Dole, Shelley, Forgasz, Helen and Bennison, Anne. (2013). Exploring the demands and opportunities for numeracy in the Australian curriculum: English.*Mathematics Education: Yesterday, Today and Tomorrow (MERGA36).*Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 330 - 337

##### Designing mathematical modelling tasks in a technology rich secondary school context

Geiger, Vince and Redmond, Trevor. (2013). Designing mathematical modelling tasks in a technology rich secondary school context. In C. Margolinas (Ed.).*Task Design in Mathematics Education.*Oxford. United Kingdom: International Commission on Mathematical Instruction. pp. 121 - 130

##### 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

##### Strasser's Didactic Tetrahedron as a basis for theorising mathematical modelling activity within social contexts

Geiger, Vince. (2013). Strasser's Didactic Tetrahedron as a basis for theorising mathematical modelling activity within social contexts. In In GA Stillman, G Kaiser and W Blum & JP Brown (Ed.).*Teaching mathematical modelling: connecting to research and practice*pp. 107 - 116 Springer. https://doi.org/10.1007/978-94-007-6540-5_9

##### 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

##### 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

##### Mathematical applications, modelling and technology as windows into industry based mathematical practice

Geiger, Vince. (2013). Mathematical applications, modelling and technology as windows into industry based mathematical practice. In In A. Damlamian, J. F. Rodrigues and R. Straser (Ed.).*Educational Interfaces between Mathematics and Industry*pp. 271 - 278 Springer. https://doi.org/10.1007/978-3-319-02270-3_27

##### Inducting year 6 students into a culture of mathematising as a practice

Brown, Jill P.. (2013). Inducting year 6 students into a culture of mathematising as a practice. In In G. A. Stillman, G. Kaiser and W. Blum & J. P. Brown (Ed.).*Teaching mathematical modelling: connecting to research and practice*pp. 295 - 306 Springer. https://doi.org/10.1007/978-94-007-6540-5_24

##### Teacher professional development on mathematical modelling: initial perspectives from Singapore

Geiger, Vince. (2013). Teacher professional development on mathematical modelling: initial perspectives from Singapore. In In GA Stillman, G Kaiser and W Blum & JP Brown (Ed.).*Teaching mathematical modelling: connecting to research and practice*pp. 437 - 442 Springer. https://doi.org/10.1007/978-94-007-6540-5_37

##### Taking advantage of incidental school events to engage with the application of mathematics: The case of surviving the reconstruction

Geiger, Vince, Goos, Merrilyn and Dole, Shelley. (2013). Taking advantage of incidental school events to engage with the application of mathematics: The case of surviving the reconstruction. In In GA Stillman, G Kaiser and W Blum & JP Brown (Ed.).*Teaching mathematical modelling: connecting to research and practice*pp. 175 - 184 Springer. https://doi.org/10.1007/978-94-007-6540-5_15

##### 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

##### Designing rich numeracy tasks

Goos, Merrilyn, Geiger, Vince and Dole, Shelley. (2013). Designing rich numeracy tasks.*ICMI Study 22: Task Design in Mathematics.*United Kingdom: International Commission on Mathematical Instruction. pp. 589 - 597

##### 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

##### Auditing the numeracy demands of the Australian curriculum

Goos, Merrilyn, Dole, Shelley and Geiger, Vince. (2012). Auditing the numeracy demands of the Australian curriculum. In J. Dindyal, L. P. Cheng and S. F. Ng (Ed.).*Mathematics education: Expanding horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 314 - 321

##### Connecting social perspectives on mathematics teacher education in online environments

Goos, Merrilyn and Geiger, Vince. (2012). Connecting social perspectives on mathematics teacher education in online environments.*ZDM Mathematics Education.*44(6), pp. 705 - 715. https://doi.org/10.1007/s11858-012-0441-y

##### Male students' perspectives concerning the relevance of mathematics: Pilot study findings

Easey, Michael, Warren, Elizabeth A. and Geiger, Vince. (2012). Male students' perspectives concerning the relevance of mathematics: Pilot study findings. In J. Dindyal, L. P. Cheng and S. F. Ng (Ed.).*Mathematics education: Expanding horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 242 - 249

##### Numeracy for what's in the news and building an expressway

Willis, Kym, Geiger, Vince, Goos, Merrilyn and Dole, Shelley. (2012). Numeracy for what's in the news and building an expressway.*Australian Mathematics Teacher.*68(1), pp. 9 - 15.

##### Teaching experiments and professional learning

Lamb, Janeen Therese and Geiger, Vince. (2012). Teaching experiments and professional learning. In In N. M. Seel (Ed.).*Encyclopedia of the sciences of learning*pp. 3276 - 3277 Springer. https://doi.org/10.1007/978-1-4419-1428-6_1017

##### Numeracy across the curriculum

Goos, Merrilyn, Dole, Shelley and Geiger, Vince. (2012). Numeracy across the curriculum.*Australian Mathematics Teacher.*68(1), pp. 3 - 7.

##### 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.##### Numeracy in society and environment

Cooper, Cath, Dole, Shelley, Geiger, Vince and Goos, Merrilyn. (2012). Numeracy in society and environment.*Australian Mathematics Teacher.*68(1), pp. 16 - 20.

##### 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.

##### Technology in mathematics education

Geiger, Vince, Forgasz, Helen, Tan, Hazel and Calder, Nigel. (2012). Technology in mathematics education. In In B Perry, T Lowrie and T Logan, A MacDonald & J Greenlees (Ed.). pp. 111 - 141 Sense Publishers.##### Numeracy in secondary school mathematics

Gibbs, Melissa, Goos, Merrilyn, Geiger, Vince and Dole, Shelley. (2012). Numeracy in secondary school mathematics.*Australian Mathematics Teacher.*68(1), pp. 29 - 35.

##### Numeracy in health and physical education

Peters, Colleen, Geiger, Vince, Goos, Merrilyn and Dole, Shelley. (2012). Numeracy in health and physical education.*Australian Mathematics Teacher.*68(1), pp. 21-27.

##### 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.##### 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.

##### Teachers' personal conceptions of numeracy

Goos, Merrilyn, Geiger, Vince and Dole, Shelley. (2011). Teachers' personal conceptions of numeracy. In B. Ubuz (Ed.).*Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education: developing mathematical thinking.*Turkey: International Group for the Psychology of Mathemati.... pp. 457 - 464

##### 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

##### 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.##### The role of digital technologies in numeracy

Geiger, Vince, Dole, Shelley and Goos, Merrilyn. (2011). The role of digital technologies in numeracy. In B. Ubuz (Ed.).*Proceedings of the 35th conference of the International Group for the Psychology of Mathematics Education: developing mathematical thinking.*Turkey: International Group for the Psychology of Mathematics Education. pp. 385 - 392

##### Improving numeracy education in rural schools: A professional development approach

Goos, Merrilyn, Dole, Shelley and Geiger, Vince. (2011). Improving numeracy education in rural schools: A professional development approach.*Mathematics Education Research Journal.*23(2), pp. 129 - 148. https://doi.org/10.1007/s13394-011-0008-1

##### 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.

##### Factors affecting teachers' adoption of innovative practices with technology and mathematical modelling

Geiger, Vince. (2011). Factors affecting teachers' adoption of innovative practices with technology and mathematical modelling. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 305 - 314 Springer.##### 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.

##### Teacher professional learning in numeracy: Trajectories through a model for numeracy in the 21st century

Geiger, Vince, Goos, Merrilyn and Dole, Shelley. (2011). Teacher professional learning in numeracy: Trajectories through a model for numeracy in the 21st century. 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. 297 - 305

##### 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##### Theoretical perspectives on mathematics teacher change

Goos, Merrilyn and Geiger, Vince. (2010). Theoretical perspectives on mathematics teacher change.*Journal of Mathematics Teacher Education.*13(6), pp. 499 - 507. https://doi.org/10.1007/s10857-010-9166-4

##### Technology, communication, and collaboration: Re-thinking communities of inquiry, learning and practice

Beatty, Ruth and Geiger, Vince. (2010). Technology, communication, and collaboration: Re-thinking communities of inquiry, learning and practice. In In C. Hoyles and J. Lagrange (Ed.).*Mathematics Education and Technology-Rethinking the Terrain*pp. 251 - 284 Springer. https://doi.org/10.1007/978-1-4419-0146-0_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.

##### A teacher pair approach to adopting effective numeracy teaching practice

Lamb, Geiger, Vince and PhD, Janeen Therese Lamb. (2010). A teacher pair approach to adopting effective numeracy teaching practice. In L. Sparrow, B. Kissane and C. Hurst (Ed.).*33rd Annual Conference of the Mathematics Education Research Group of Australasia.*John Curtin College of the Arts, Fremantle, Western Australia, Australia 03 - 07 Jul 2010 Australia: Mathematics Education Research Group of Australasia. pp. 312 - 319

##### Auditing the numeracy demands of the middle years curriculum

Goos, Merrilyn, Geiger, Vince and Dole, Shelley. (2010). Auditing the numeracy demands of the middle years curriculum. In L. Sparrow, B. Kissane and C. Hurst (Ed.).*33rd Annual Conference of the Mathematics Education Research Group of Australasia.*John Curtin College of the Arts, Fremantle, Western Australia, Australia 03 - 07 Jul 2010 Australia: Mathematics Education Research Group of Australasia. pp. 210 - 217

##### 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.##### Cas-enabled technologies as 'agents provocateurs' in teaching and learning mathematical modelling in secondary school classrooms

Geiger, Vince, Faragher, Rhonda Muriel and Goos, Merrilyn. (2010). Cas-enabled technologies as 'agents provocateurs' in teaching and learning mathematical modelling in secondary school classrooms.*Mathematics Education Research Journal.*22(2), pp. 48 - 68. https://doi.org/10.1007/BF03217565

##### A social perspective on technology-enhanced mathematical learning: From collaboration to performance

Gadanidis, George and Geiger, Vince. (2010). A social perspective on technology-enhanced mathematical learning: From collaboration to performance.*ZDM.*42(1), pp. 91 - 104. https://doi.org/10.1007/s11858-009-0213-5

##### An Approach to Student-Lecturer Collaboration in the Design of Assessment Criteria and Standards Schemes

Mulholland, Judith Anne, Geiger, Vince, Lamb, Janeen Therese and Jacobs, Rachael Frances. (2009). An Approach to Student-Lecturer Collaboration in the Design of Assessment Criteria and Standards Schemes. In J. Milton, K. Hall and J. Lang (Ed.).*Proceedings of the ATN Assessment Conference 2009: Assessment in Different Dimensions.*Melbourne, Australia: Learning and Teaching Unit, RMIT University. pp. 137 - 145

##### The Master, Servant, Partner, Extension-of-self Framework in Individual, Small Group and Whole Class Contexts

Geiger, Vince. (2009). The Master, Servant, Partner, Extension-of-self Framework in Individual, Small Group and Whole Class Contexts. In R. Hunter, B. Bricknell and T. Burgess (Ed.).*Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA).*Wellington, New Zealand: Mathematics Education Research Group of Australasia. pp. 201 - 208

##### 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

##### CAS enabled devices as provocative agents in the process of mathematical modelling

Faragher, Rhonda Muriel, Redmond, Trevor, Lowe, Jim and Geiger, Vince. (2008). CAS enabled devices as provocative agents in the process of mathematical modelling. In M. Goos, R. Brown and K. Maker (Ed.).*Navigating Currents and Charting Directions: Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia.*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 246 - 253

##### The emergence of social perspectives on the use of technology in Mathematics education

Geiger, Vince. (2008). The emergence of social perspectives on the use of technology in Mathematics education. In Marcelo C. Borba and Mariolina Bartolini Bussi (Ed.).*Symposium on the Occasion of the 100th Anniversary of ICMI: Resources and Technology Throughout the History of ICMI.*Rome, Italy: International Congress on Mathematical Education. pp. 1 - 3

##### 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

##### 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

##### More Than Tools: Mathematically Enabled Technologies As Partner and Collaborator

Geiger, Vince. (2006). More Than Tools: Mathematically Enabled Technologies As Partner and Collaborator. In P.C. Hoyles, J. Lagrange and L. Son (Ed.).*Technology Revisited: Digital Technologies; Rethinking the Terrain: Proceedings of the 17th ICMI Study Conference.*London, England: International Commission on Mathematical Instruction. pp. 182 - 189

##### 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

##### In search of practical wisdom: A conversation between a researcher and a teacher

Goos, Merrilyn and Geiger, Vince. (2006). In search of practical wisdom: A conversation between a researcher and a teacher.*For the Learning of Mathematics.*26(2), pp. 33 - 35.

##### Standing on the Outside: A Tale of How Technology Can Engage Those Working on the Margins of a Community of Inquiry

Geiger, Vince. (2006). Standing on the Outside: A Tale of How Technology Can Engage Those Working on the Margins of a Community of Inquiry. In P. Grootenboer, R. Zevenbergen and M. Chinnappan (Ed.).*Identities; Cultures and Learning Spaces: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia.*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 246 - 253

##### Living in the Gap: A Tale of Two Different Types of Researchers

Geiger, Vince and Goos, Merrilyn. (2006). Living in the Gap: A Tale of Two Different Types of Researchers. In P. Grootenboer, R. Zevenbergen and M. Chinnappan (Ed.).*Identities; Cultures and Learning Spaces: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia.*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 254 - 261

##### 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

##### Master, servant, partner and extension of self: A finer grained view of this taxonomy

Geiger, Vince. (2005). Master, servant, partner and extension of self: A finer grained view of this taxonomy. 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.*Sydney, Australia: Mathematics Education Research Group of Australasia. pp. 369 - 376

##### 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

##### Choosing and using technology for secondary mathematical modelling tasks: Choosing the right peg for the right hole

Geiger, Vince, Galbraith, Peter, Renshaw, Peter and Goos, Merrilyn. (2003). Choosing and using technology for secondary mathematical modelling tasks: Choosing the right peg for the right hole. In*Mathematical Modelling in Education and Culture*Chichester Horwood.

##### Technology-enriched classrooms: Some implications for teaching applications and modelling

Galbraith, Peter, Renshaw, Peter, Goos, Merrilyn and Geiger, Vince. (2003). Technology-enriched classrooms: Some implications for teaching applications and modelling. In*Mathematical Modelling in Education and Culture*Chichester Horwood.

##### Perspectives on technology mediated learning in secondary school mathematics classrooms

Goos, Merrilyn, Galbraith, Peter, Renshaw, Peter and Geiger, Vince. (2003). Perspectives on technology mediated learning in secondary school mathematics classrooms.*The Journal of Mathematical Behavior.*22(1), pp. 73 - 89. https://doi.org/10.1016/S0732-3123(03)00005-1

##### What Students Say: Analysis of Structured Survey Data in Relation to Technology and Mathematics

Geiger, Vince. (2003). What Students Say: Analysis of Structured Survey Data in Relation to Technology and Mathematics. In L. Bragg, C. Campbell and G. Herbert (Ed.).*MERINO - Mathematics Education Research: Innovation, Networking, Opportunity: Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia.*Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 380 - 387

##### 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