Arriving at the starting point? Exploring a teacher's use of circular reasoning in a mathematics classroom

References

• Adler , J. , Pournara , C. , Taylor , D. , Thorne , B. and Moletsane , G. 2009 . Mathematics and science teacher education in South Africa: A review of research, policy and practice in times of change . African Journal of Research in MST Education, Special Issue , 2009 : 28 – 46 .
   Google Scholar
• Author . 2006 . South African grade 9 mathematics teachers, professional expertise: A situative perspective . Curtin University of Technology , Perth , , Australia .
   Google Scholar
• Author . 2011 . South African rural teachers' reflections on their problems of practice; taking modest steps in professional development . Mathematics Education Research Journal , 23 2 .
   Google Scholar
• Ball , D.L. , Thames , M. H. and Phelps , G. 2008 . Content Knowledge for Teaching. What Makes It Special? . Journal of Teacher Education , 59 ( 5 ) : 389 – 407 .
   Web of Science ®Google Scholar
• Ball , D.L. and Bass , L. 2000 . “ Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics ” . In Multiple perspectives on the teaching and learning of mathematics , Edited by: Boaler , J. 83 – 104 . Westport , CT : Ablex .
   Google Scholar
• Bloch , G. 2009 . The Toxic Mix , Tafelberg : Cape Town .
   Google Scholar
• Brodie , K. 2004 . Re-thinking teachers’ mathematical knowledge: Afocus on thinking practices . Perspectives in Education , 22 ( 1 ) : 65 – 80 .
   Web of Science ®Google Scholar
• Brodie , K. 2010 . Teaching Mathematical Reasoning in Secondary School Classrooms , New York : Springer .
   Google Scholar
• Centre for Development and Entreprise . 2011 . Value in the classroom . The quantity and quality of South Africa's teachers, CDE in Depth, 11 .
   Google Scholar
• Cobb , P. , Yackel , E. and Wood , T. 1993 . “ Discourse, mathematical thinking, and curriculum practice ” . In Contexts for learning: Socio-cultural dynamics in children's development , Edited by: Forman , E. , Minick , N. and Stone , C. 91 – 119 . Oxford : Oxford University Press .
   Google Scholar
• Cockburn , A.D. 2011 . Working with less successful teachers . Paper presented at the 35th conference of the International Group for the Psychology of Mathematics Education .
   Google Scholar
• Davis , B. 1997 . Listening for differences: An Evolving conception of Mathematics Teaching . Journal for Research in Mathematics Education , 28 ( 3 ) : 355 – 376 .
   Web of Science ®Google Scholar
• Dubinsky , E. 1991 . “ Reflective Abstraction in Advanced Mathematical Thinking ” . In Advanced Mathematical Thinking , Edited by: Tall , D. 95 – 123 . Kluwer : The Netherlands .
   Google Scholar
• Dubinsky , E. 2010 . Personal Communication , Durban , January 2010 .
   Google Scholar
• Howie , S. 2001 . Mathematics and Science Performance in Grade 8 in South Africa 1998/1999 , Pretoria : Human Sciences Research Council .
   Google Scholar
• Howie , S. 2004 . A national assessment in mathematics within an international comparative assessment . Perspectives in Education , 22 ( 2 ) : 149 – 162 .
   Web of Science ®Google Scholar
• Hugo , W. J. M. , Wedekind , V. Wilson , D. 2010 . The state of education in KwaZulu-Natal: A report to the Provincial Treasury , Pietermaritzburg : KZN Provincial Treasury .
   Google Scholar
• Kriek , J. and Grayson , D. 2009 . A Holistic Professional Development model for South African Physical Science teachers . South African Journal of Education , 29 : 185 – 203 .
   Web of Science ®Google Scholar
• Maoto , S. and Wallace , J. 2006 . What does it mean to teach Mathematics for understanding? When to tell and when to listen . African Journal of Research in SMT education , 10 ( 1 ) : 59 – 70 .
   Google Scholar
• Mason , J. 1989 . Mathematical Abstraction as the result of a shift of attention . For the learning of Mathematics , 9 ( 2 ) : 2 – 8 .
   Google Scholar
• Mji , A. and Makgato , M. 2006 . Factors associated with high school learners’ poor performance: a spotlight on mathematics and physical science . South African Journal of Education , 26 ( 2 ) : 253 – 266 .
   Web of Science ®Google Scholar
• Peressini , D. , Borko , H. , Romagnano , L. , Knuth , E. and Willis , C. 2004 . A Conceptual framework for learning to teach secondary Mathematics: A situative perspective . Educational Studies in Mathematics , 56 ( 1 ) : 67 – 96 .
   Google Scholar
• Polkinghorne , D.E. 1995 . “ Narrative configuration in qualitative analysis ” . In Life history as narrative , Edited by: Hatch , J. A. and Wisniewski , R. 5 – 23 . London : Falmer .
   Google Scholar
• Prawat , R.S. 1989 . Teaching for understanding: Three key attributes . Teaching and Teacher Education , 5 ( 4 ) : 315 – 328 .
   Web of Science ®Google Scholar
• Rakumako , A. and Laugksch , R. 2010 . Demographic profile and perceived INSET needs of secondary mathematics teachers in Limpopo province . South African Journal of Education , 30 : 139 – 152 .
   Web of Science ®Google Scholar
• Reddy , V. 2006 . Mathematics and Science Achievement at South African Schools in TIMMSS 2003 , Cape Town : Human Sciences Research Council .
   Google Scholar
• Santi , G. 2011 . Objectification and semiotic function . Educational Studies in Mathematics , 77 : 285 – 311 .
   Web of Science ®Google Scholar
• Sfard , A. 2008 . Thinking as Communicating , New York : Cambridge University Press .
   Google Scholar
• Sfard , A. 1991 . On the dual nature of Mathematical conceptions: Reflections on processes and objects as different sides of the same coin . Educational Studies in Mathematics , 22 : 1 – 36 .
   Google Scholar
• Sfard , A. 1992 . “ Operational Origins of mathematical objects and the quandary of reification- the case of a function ” . In The concept of function , Edited by: Dubinsky , E. and Harel , G. 59 – 71 . DC : Mathematical Association America: Washington .
   Google Scholar
• Shulman , L.S. 1986 . Those who understand: knowledge growth in teaching . Educational Researcher , 15 ( 2 ) : 4 – 14 .
   Google Scholar
• Spaull , N. 2011 . A preliminary analysis of SACMEQ III South Africa , Stellenbosch : University of Stellenbosch .
   Google Scholar
• Soudien , C. 2007 . The “A” factor: Coming to terms with the question of legacy in South African education . International Journal of Educational Development , 27 : 182 – 193 .
   Web of Science ®Google Scholar
• Stake , R.E. 2008 . “ Qualitative Case studies ” . In Strategies of Qualitative Inquiry , Edited by: Denzin , N. K. and Lincoln , Y. S. 119 – 150 . Thousand Oaks : California .
   Google Scholar
• Steinbring , H. 1998 . Elements of epistemological knowledge for mathematics teachers . Journal of Mathematics Teacher Education , 1 ( 2 ) : 157 – 189 .
   Google Scholar
• Taylor , N. and Vinjevold , P. 1999 . Getting learning right. Report of the President's Education Initiative Research Project , Witwatersrand , , South Africa : Joint Education Trust .
   Google Scholar
• Volmink , J. 2010 . Results of Some Critical Subjects in the National Senior Certificate Examination . Paper presented at the UKZN Teaching and Learning Conference .
   Google Scholar
• Wu , H. 2005 . Must content dictate pedagogy in mathematics education? Talk given at California State University , USA .
   Google Scholar
• Yin , R. K. 2009 . Case study research: Design and methods , Beverley Hills , CA : Sage .
   Google Scholar