Developing a task design and implementation framework for fostering mathematical modelling competencies

Journal article


Geiger, Vince, Galbraith, Peter, Niss, Mogens and Delzoppo, Catherine. (2022). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics. 109(2), pp. 313-336. https://doi.org/10.1007/s10649-021-10039-y
AuthorsGeiger, Vince, Galbraith, Peter, Niss, Mogens and Delzoppo, Catherine
Abstract

In this article, we describe the generation of a Design and Implementation Framework for Mathematical Modelling Tasks (DIFMT) through a researcher-teacher collaboration. The purpose of the framework is to support holistic approaches to instructional modelling competency. This framework is underpinned by principles drawn from theory and praxis which are informed by the anticipatory capabilities that teachers require for the design and effective implementation of quality modelling tasks in secondary classrooms. A draft DIFMT was developed from a synthesis of research literature and was refined through an iterative process of task development, implementation and observation, reflection through teacher/student interviews, and revision of the framework. Each iteration made use of the most recent refinement of the co-constructed DIFMT, building theory while simultaneously addressing a problem in educational practice, consistent with a design-based methodology. Thus, the DIMFT developed organically throughout the project. While initial modelling exemplars were researcher-designed, the locus of responsibility moved to teachers as the project progressed. The DIFMT consists of two major components—principles for modelling task design and pedagogical architecture—each of which is structured around dimensions that include elaborations which detail the knowledge required for modelling as well as teacher and student capabilities.

Keywordsmathematical modelling; competencies; competency; task design; task implementation; framework
Year2022
JournalEducational Studies in Mathematics
Journal citation109 (2), pp. 313-336
PublisherSpringer
ISSN0013-1954
Digital Object Identifier (DOI)https://doi.org/10.1007/s10649-021-10039-y
Scopus EID2-s2.0-85105216186
Research or scholarlyResearch
Page range313-336
FunderAustralian Research Council
Publisher's version
License
All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online23 Apr 2021
Publication process dates
Accepted07 Feb 2021
Deposited25 May 2022
ARC Funded ResearchThis output has been funded, wholly or partially, under the Australian Research Council Act 2001
Grant IDARC/DP170101555
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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
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
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
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
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
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: an international journal of mathematics education. 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
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
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