Using mathematics as evidence supporting critical reasoning and enquiry in primary science classrooms

Journal article

Geiger, Vince. (2019). Using mathematics as evidence supporting critical reasoning and enquiry in primary science classrooms. ZDM. 51(6), pp. 929 - 940. https://doi.org/10.1007/s11858-019-01068-2
AuthorsGeiger, Vince
Abstract

In this article I describe an approach to task design and implementation that addresses the broad capabilities common to 21st Century Skills and the STEM education agenda. Principles of task design and implementation were co-constructed by ten teachers and a single researcher during a longitudinal study that took place over 3 years. A vignette that draws on observation data from a Year 1 class and a post-lesson teacher interview is used to illustrate the possibilities that exist for mathematics to support critical reasoning and enquiry in primary science. The article concludes with a reflection on the role of teachers in designing and implementing tasks aimed at promoting effective STEM teaching and learning.

KeywordsSTEM; 21st century skills; mathematics education; numeracy; mathematical literacy; science education; critical reasoning
Year2019
JournalZDM
Journal citation51 (6), pp. 929 - 940
PublisherSpringer Nature
ISSN1863-9690
Digital Object Identifier (DOI)https://doi.org/10.1007/s11858-019-01068-2
Scopus EID2-s2.0-85068111977
Page range929 - 940
Research GroupInstitute for Learning Sciences and Teacher Education (ILSTE)
Publisher's version
File Access Level
Controlled
Grant IDARC/DP170101555
ARC/DE150100269
Place of publicationGermany
EditorsK. Maaß, M. Doorman and V. Geiger and M. Goos
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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.
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.
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.
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
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
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.
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
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
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. 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