# Problem finding and problem posing for mathematical modelling

Book chapter

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.

Authors | Stillman, Gloria |
---|---|

Editors | L. N. Hoe and N. K. E. Dawn |

Page range | 41 - 56 |

Year | 2015 |

Book title | Mathematical modelling: From theory to practice |

Publisher | World Scientific Publishing |

Place of publication | Switzerland |

ISBN | 9789814546911 |

Research Group | School of Education |

Publisher's version | File Access Level Controlled |

Permalink -

https://acuresearchbank.acu.edu.au/item/85488/problem-finding-and-problem-posing-for-mathematical-modelling

## Restricted files

### Publisher's version

*(1 files)*

##### 152

total views##### 1

total downloads##### 0

views this month##### 0

downloads this month

*These values are for the period from 19th October 2020, when this repository was created.*

## Export as

## Related outputs

##### Teachers' perception of and reflection on students' metacognitive knowledge in mathematical modelling processes

Wendt, Lisa, Krüger, Alexandra and Stillman, Gloria Ann. (2022). Teachers' perception of and reflection on students' metacognitive knowledge in mathematical modelling processes. In In Buchholtz, Nils, Schwarz, Björn and Vorhölter, Katrin (Ed.).*Initiationen mathematikdidaktischer forschung : Festschrift zum 70. Geburtstag von Gabriele Kaiser*pp. 137-154 Springer Spektrum. https://doi.org/10.1007/978-3-658-36766-4_7

##### Modeling the phenomenon versus modeling the data set

Stillman, Gloria Ann and Brown, Jill. (2021). Modeling the phenomenon versus modeling the data set.*Mathematical Thinking and Learning.*25(3), pp. 270-295. https://doi.org/10.1080/10986065.2021.2013144

##### Modeling from a cognitive perspective : Theoretical considerations and empirical contributions

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

##### Mathematical modelling education in the cultural contexts of west and east

Leung, Frederick Koon Shing, Stillman, Gloria, Kaiser, Gabriele and Wong, Ka Lok. (2021). Mathematical modelling education in the cultural contexts of west and east. In In Leung, Frederick Koon Shing, Stillman, Gloria, Kaiser, Gabriele and Wong, Ka Lok (Ed.).*Mathematical modelling education in east and west*pp. 3-16 Springer. https://doi.org/10.1007/978-3-030-66996-6_1

##### Sense-making in mathematical modelling and applications educational research and practice

Stillman, Gloria Ann, Kaiser, Gabriele and Lampen, Christine Erna. (2020). Sense-making in mathematical modelling and applications educational research and practice. In In Stillman, Gloria Ann, Kaiser, Gabriele and Lampen, Christine Erna (Ed.).*Mathematical modelling education and sense-making*pp. 15-29 Springer Nature. https://doi.org/10.1007/978-3-030-37673-4_2

##### Yes, mathematicians do X so students should do X, but it’s not the X you think!

Stillman, Gloria, Brown, Jill and Czocher, Jennifer. (2020). Yes, mathematicians do X so students should do X, but it’s not the X you think!*ZDM.*52(6), pp. 1211-1222. https://doi.org/10.1007/s11858-020-01183-5

##### State of the art on modelling in mathematics education--lines of inquiry

Stillman, Gloria Ann. (2019). State of the art on modelling in mathematics education--lines of inquiry. In In Stillman, Gloria Ann and Brown, Jill P. (Ed.).*Lines of inquiry in mathematical modelling research in education*pp. 1-20 SpringerOpen. https://doi.org/10.1007/978-3-030-14931-4_1

##### A modelling challenge: students modelling problems of their choice

Galbraith, Peter L., Stillman, Gloria and Brown, Jill. (2018). A modelling challenge: students modelling problems of their choice. In In S. Schukajlow and W. Blum (Ed.).*Evaluierte Lernumgebungen zum Modellieren [Evaluated Learning Environments for Modeling]*pp. 193 - 214 https://doi.org/10.1007/978-3-658-20325-2

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

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

##### Verification and validation: what do we mean?

Czocher, Jennifer, Stillman, Gloria and Brown, Jill. (2018). Verification and validation: what do we mean? In J. Hunter, P. Perger and L. Darragh (Ed.). New Zealand: Mathematics Education Research Group of Australasia. pp. 250 - 257##### Learning and improving MKT through teaching and professional development mechanisms

Stillman, Gloria Ann. (2018). Learning and improving MKT through teaching and professional development mechanisms. In In Y. Li and R. Huang (Ed.).*How Chinese acquire and improve mathematics knowledge for teaching*pp. 263 - 274 Brill. https://doi.org/10.1163/9789463512367

##### Empirical research on teaching and learning of mathematical modelling:a survey on the current state-of-the-art

Schukajlow, S., Kaiser, Gabriele and Stillman, Gloria. (2018). Empirical research on teaching and learning of mathematical modelling:a survey on the current state-of-the-art.*ZDM: The International Journal on Mathematics Education.*50(43132), pp. 5 - 18. https://doi.org/10.1007/s11858-018-0933-5

##### 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.

##### 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

##### 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 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

##### 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

##### 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.

##### 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

##### 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.

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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

##### 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.##### 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

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

##### 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