CHANGING PGCE STUDENTS’ MATHEMATICAL UNDERSTANDING THROUGH A COMMUNITY OF INQUIRY INTO PROBLEM SOLVING

References

• Alexander , R. J. 2000 . Culture and Pedagogy: International comparisons in primary education , Oxford : Blackwell Publishers .
   Google Scholar
• Ball , D. L. 1990 . Breaking with experience in learning to teach mathematics: The role of a preservice methods course . For the Learning of Mathematics , 10 ( 2 ) : 10 – 16 .
   Google Scholar
• Boaler , J. 2002a . The development of disciplinary relationships: Knowledge, practice and identity in mathematics classrooms . For the Learning of Mathematics , 22 ( 1 ) : 42 – 47 .
   Google Scholar
• Boaler , J. 2002b . Experiencing School Mathematics: Traditional and reform approaches to teaching and their impact on student learning , London : Erlbaum .
   Google Scholar
• Boaler , J. & Staples , M. (in press) Creating mathematical futures through an equitable teaching approach: The case of Railside school , Teachers’ College Record .
   Google Scholar
• Brown , M. 1999 . “ Swings of the pendulum ” . In Issues in Teaching Numeracy in Primary Schools , Edited by: Thompson , I. Buckingham : Open University Press .
   Google Scholar
• Brown , M. , Askew , M. , Millett , A. and Rhodes , V. 2003 . The key role of educational research in the development and evaluation of the National Numeracy Strategy . British Educational Research Journal , 29 ( 5 ) : 655 – 672 .
   Web of Science ®Google Scholar
• Burton , L. 1999 . The practices of mathematicians: What do they tell us about coming to know mathematics? . Educational Studies in Mathematics , 37 ( 2 ) : 121 – 143 .
   Google Scholar
• Burton , L. 2001 . Research mathematicians as learners-and what mathematics education can learn from them . British Educational Research Journal , 27 ( 5 ) : 589 – 600 .
   Web of Science ®Google Scholar
• Crawford , K. and Adler , J. 1996 . “ Teachers as researchers in mathematics education ” . In International Handbook of Mathematics Education , Edited by: Bishop , A. J. , Clements , K. , Keitel , C. , Kilpatrick , J. and Laborde , C. Dordrecht : Kluwer Academic Press .
   Google Scholar
• Crespo , S. 2003 . Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices . Educational Studies in Mathematics , 52 ( 3 ) : 243 – 270 .
   Google Scholar
• Davis , P. and Hersh , R. 1983 . The Mathematical Experience , Harmondsworth : Penguin Books .
   Google Scholar
• Department for Education and Skills ( 2006 ) Renewing the primary framework for mathematics. Guidance paper: Using and applying mathematics . Available online at: http://www.standards.dfes.gov.uk/primaryframeworks/mathematics/Papers/resources/ (accessed 20th March 2007) .
   Google Scholar
• Earl , L. , Watson , N. , Levin , B. , Leithwood , K. , Fullan , M. & Torrence , N. ( 2003 ) Watching and Learning: Final report of the external evaluation of England's national literacy and numeracy strategies ( London : DfES Publications ).
   Google Scholar
• Entwistle , N. J. 1997 . “ Contrasting perspectives on learning ” . In The Experience of Learning: Implications for teaching and studying in higher education , Edited by: Marton , F. , Hounsell , D. and Entwistle , N. Edinburgh : Scottish Academic Press .
   Google Scholar
• Hammersley , M. and Atkinson , P. 1995 . Ethnography: Principles in practice , 2nd edn , London : Routledge .
   Google Scholar
• Hardman , F. , Smith , F. , Mroz , M. & Wall , K. ( 2003 ) Interactive whole class teaching in the national literacy and numeracy strategies , paper presented at the British Educational Research Association Annual Conference, Edinburgh , 11-13 September , 2003 .
   Google Scholar
• Hersh , R. 1998 . What is Mathematics, Really? , London : Vintage .
   Google Scholar
• Jaworski , B. 2003 . Research practice into/influencing mathematics teaching and learning development: Towards a theoretical framework based on co-learning partnerships . Educational Studies in Mathematics , 54 ( 2-3 ) : 249 – 282 .
   Google Scholar
• Jaworski , B. ( 2004a ) Grappling with complexity: Co-learning in inquiry communities in mathematics teaching development , in: Johnson Hoines M. & Fuglestad A. B. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen, Bergen University College, 17-32 .
   Google Scholar
• Jaworski , B. 2004b . “ Insiders and outsiders in mathematics teaching development: The design and study of classroom activity ” . In Research in Mathematics Education, 6 , Edited by: McNamara , O and Barwell , R. London : BSRLM .
   Google Scholar
• Jaworski , B. 2005 . Learning communities in mathematics: Creating an inquiry community between teachers and didacticians . Research in Mathematics Education , 7 : 101 – 119 .
   Google Scholar
• Lakatos , I. 1976 . Proofs and Refutations. The logic of mathematical discovery , Cambridge : Cambridge University Press .
   Google Scholar
• Lampert , M. 1990 . When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching . American Educational Research Journal , 27 ( 1 ) : 29 – 63 .
   Web of Science ®Google Scholar
• Lave , J. and Wenger , E. 1991 . Situated Learning: Legitimate peripheral participation , Cambridge : Cambridge University Press .
   Google Scholar
• Lodge , O. 1905 . Easy Mathematics. Arithmetic , London : Macmillan .
   Google Scholar
• Mason , J. 1999 . Learning and Doing Mathematics , 2nd edn , York : QED .
   Google Scholar
• Mason , J. 2002 . Researching your own practice. The discipline of noticing , London : Routledge Falmer .
   Google Scholar
• Mason , J. , Burton , L. and Stacey , K. 1984 . Thinking mathematically , Harlow : Addison Wells .
   Google Scholar
• National Council of Teachers of Mathematics (NCTM) ( 2000 ) Principles and Standards for School Mathematics ( Reston, VA : National Council of Teachers of Mathematics ).
   Google Scholar
• Nickson , M. 2003 . A Review of BSRLM Research 1995-2002 , London : British Society for Research into Learning Mathematics .
   Google Scholar
• Pólya , G. 1945 . How to Solve it , Princeton : Princeton University Press .
   Google Scholar
• Pratt , N. 2006 . Interactive teaching in numeracy lessons: What do children have to say? . Cambridge Journal of Education , 36 ( 2 ) : 221 – 236 .
   Google Scholar
• Pratt , N. and Kelly , P. 2007 . Mapping mathematical communities: Classrooms, research communities and masterclasses . For the Learning of Mathematics , 27 ( 2 ) : 34 – 39 .
   Google Scholar
• Schoenfeld , A. H. 1985 . Mathematical Problem Solving , New York : Academic Press .
   Google Scholar
• Schoenfeld , A. H. 1987 . Pólya, problem solving, and education . Mathematics Magazine , 60 ( 5 ) : 283 – 291 .
   Google Scholar
• Schoenfeld , A. H. 1996 . In fostering communities of inquiry, must it matter that the teacher knows “The answer”? . For the Learning of Mathematics , 16 ( 3 ) : 11 – 16 .
   Google Scholar
• Schoenfeld , A. H. 2004 . Multiple learning communities: Students, teachers, instructional designers, and researchers . Journal of Curriculum Studies , 36 ( 2 ) : 237
   Web of Science ®Google Scholar
• Sfard , A. 1998 . On two metaphors for learning and the dangers of choosing just one . Educational Researcher , 27 ( 2 ) : 4 – 13 .
   Google Scholar
• Sfard , A. , Nesher , P. , Streefland , L. , Cobb , P. and Mason , J. 1998 . Learning mathematics through conversation: Is it as good as they say? . For the Learning of Mathematics , 18 ( 1 ) : 44 – 51 .
   Google Scholar
• Sherin , M. G. , Mendez , E. P. and Louis , D. A. 2004 . A discipline apart: The challenges of fostering a community of learners in a mathematics classroom . Journal of Curriculum Studies , 36 ( 2 ) : 207 – 232 .
   Web of Science ®Google Scholar
• Treffers , A. and Beishuizen , M. 1999 . “ Realistic mathematics education in the Netherlands ” . In Issues in Teaching Numeracy in Primary Schools , Edited by: Thompson , I. 27 – 38 . Buckingham : Open University Press .
   Google Scholar
• Wells , G. 1999 . Dialogic Inquiry: Towards a sociocultural practice and theory of education , Cambridge : Cambridge University Press .
   Google Scholar
• Wenger , E. 1998 . Communities of Practice: Learning, meaning and identity , Cambridge : Cambridge University Press .
   Google Scholar
• Woods , P. and Pratt , N. 2006 . PGCE students’ professional change through experiences of problem solving . Proceedings of the British Society for Research into Learning Mathematics , 26 ( 3 ) : 71 – 76 .
   Google Scholar