# Turning ideas into modeling problems

Book chapter

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

Authors | Galbraith, Peter L., Stillman, Gloria and Brown, Jill P. |
---|---|

Abstract | We show how the nucleus of an idea can be developed into modeling problems for secondary school using principles for problem design enunciated in Galbraith (2007). Once the germ has been developed for a task, the idea can be extended as necessary into related problems closer to the personal experience of the adolescents in secondary school. The issues and contexts secondary students choose to investigate, and the questions that they pose when given free reign or minimal constraints, are illustrated from an Australian modeling challenge. Finally, using these contexts as starting points, it is suggested such situations can be developed to engage students in important teaching issues involving necessary constituents of the modeling process. |

Keywords | assessment; competency/competencies; didactic modeling; emergent modeling; ICTMA; mathematical literacies; mathematical modeling; motivation; scaffold |

Page range | 133 - 144 |

Year | 2010 |

Publisher | Springer |

Place of publication | New York |

ISBN | 9781441905604 |

Digital Object Identifier (DOI) | https://doi.org/10.1007/978-1-4419-0561-1_11 |

Research Group | School of Education |

Publisher's version | File Access Level Controlled |

https://acuresearchbank.acu.edu.au/item/8q14y/turning-ideas-into-modeling-problems

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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.

##### 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

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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

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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

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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

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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

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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

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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

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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

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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.

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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.

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

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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##### 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

##### 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.).*Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual conference of the Mathematics Education Research Group of Australasia..*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.).*Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual conference of the Mathematics Education Research Group of Australasia..*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