Cas-enabled technologies as ‘agents provocateurs’ in teaching and learning mathematical modelling in secondary school classrooms

This paper draws on a one year study of three secondary school classrooms to examine the nature of student-student-technology interaction when working in partnership with computer algebra systems (CAS) on mathematical modelling tasks and the classroom affordances and constraints that influence such interaction. The analysis of these data indicates that CAS enabled technologies have a role to play as provocateurs of productive student-student-teacher interaction in both small group and whole class settings. Our research indicates that technologies that incorporate CAS capabilities have the potential to mediate collaborative approaches to mathematical enquiry within life-related mathematical tasks.

[1]  Merrilyn Goos,et al.  Teaching Mathematics in New Times, Proceedings of the 21st Annual Conference of the Mathematics Education Research Group of Australasia (MERGA) , 1998 .

[2]  Merrilyn Goos,et al.  Computers, multimedia, and the Internet in mathematics education , 2004 .

[3]  P. Ramsden Mathematica In Education: Old Wine In NewBottles Or A Whole New Vineyard? , 1970 .

[4]  Merrilyn Goos,et al.  Classroom voices: Technology enriched interactions in a community of mathematical practice , 2000 .

[5]  Training,et al.  Discipline review of teacher education in mathematics and science , 1989 .

[6]  A. Schoenfeld Cognitive Science and Mathematics Education , 1987 .

[7]  Paul Drijvers,et al.  Learning Algebra in a Computer Algebra Environment. , 2004 .

[8]  R. Pea Beyond Amplification : Using the Computer to Reorganize Mental Functioning , 1985 .

[9]  Peter Galbraith,et al.  Modelling and Applications in Mathematics Education , 2007 .

[10]  Ken Houston,et al.  Mathematical modelling in education and culture , 2003 .

[11]  Merrilyn Goos,et al.  Perspectives on technology mediated learning in secondary school mathematics classrooms , 2003 .

[12]  Barry Kissane The algebraic calculator and mathematics education , 1999 .

[13]  Robert B. Burns,et al.  Introduction to Research Methods , 2015, Research Methods for Political Science.

[14]  Carmel M. Diezmann,et al.  Exceptional students in mathematics , 2004 .

[15]  M. Goos,et al.  Reshaping teacher and student roles in technology-enriched classrooms , 2000 .

[16]  Merrilyn Goos,et al.  TECHNOLOGY, MATHEMATICS, AND PEOPLE: INTERACTIONS IN A COMMUNITY OF PRACTICE , 1999 .

[17]  Jere Confrey,et al.  A Theory of Mathematical Modelling in Technological Settings , 2007 .

[18]  J. Fey,et al.  Effects of Standards-Based Mathematics Education: A Study of the Core-plus Mathematics Project Algebra and Functions Strand , 2000 .

[19]  Merrilyn Goos,et al.  Navigating Currents and Charting Directions. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (31st, Brisbane, Queensland, Australia, June 28-July 1, 2008). Volumes 1 and 2. , 2008 .

[20]  Merrilyn Goos,et al.  Technology Enriched Classrooms: Some Implications for Teaching Applications and Modelling , 2003 .

[21]  R. Stake Qualitative Case Studies. , 2005 .

[22]  Luc Trouche,et al.  Instrumental Genesis, Individual and Social Aspects , 2005 .

[23]  Barry Kissane,et al.  The algebra curriculum and personal technology: Exploring the links , 2001 .

[24]  B. Perry,et al.  Research in mathematics education in Australasia 2008-2011 , 2004 .

[25]  Vince Geiger,et al.  Technology, Communication, and Collaboration: Re-thinking Communities of Inquiry, Learning and Practice , 2009 .

[26]  N. Denzin,et al.  The Sage handbook of qualitative research, 3rd ed. , 2005 .

[27]  Werner Blum,et al.  Modelling and Applications in Mathematics Education : the 14th ICMI Study , 2007 .

[28]  Luc Trouche,et al.  The didactical challenge of symbolic calculators : turning a computational device into a mathematical instrument , 2005 .

[29]  Michal Yerushalmy Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra , 2000 .

[30]  Merrilyn Goos,et al.  CAS Enabled Devices as Provocative Agents in the Process of Mathematical Modelling , 2008 .

[31]  Thomas P. Dick,et al.  Teachers' perceptions of the impact of graphing calculators in the mathematics classroom , 1997 .

[32]  H. Doerr,et al.  You have printed the following article : Creating Meaning for and with the Graphing Calculator , 2008 .

[33]  Clive Kanes Teaching Mathematics in New Times , 1998 .

[34]  Azita Manouchehri,et al.  Using interactive algebra software to support a discourse community , 2004 .