“If you can count to ten you can count to infinity really”: fostering conceptual mathematical thinking in the first year of primary school

References

• Askew , M. , Brown , M. , Rhodes , V. , William , D. and Johnson , D. 1997 . Effective teachers of numeracy , London : King's College London .
   Google Scholar
• Brown , M. , Askew , M. , Baker , D. , Denvir , H. and Millett , A. 1998 . Is the National Numeracy Strategy research-based? . British Journal of Educational Studies , 46 ( 4 ) : 362 – 385 .
   Web of Science ®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 – 667 .
   Web of Science ®Google Scholar
• Cobb , P. and Yackel , E. 1996 . Constructivist, emergent, and sociocultural perspectives in the context of developmental research . Educational Psychologist , 31 : 175 – 190 .
   Web of Science ®Google Scholar
• Cobb , P. Yackel , E. . 1998 . Analysing the mathematical learning of the classroom community: The case of statistical data analysis . In Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education A. Olivier and K. Newstead , 1 : 33 – 48 . Stellenbosch, SA : University of Stellenbosch .
   Google Scholar
• Cobb , P. and Yackel , E. 1999 . Individual and collective mathematical development: The case of statistical data analysis . Mathematical Thinking and Learning , 1 ( 1 ) : 5 – 43 .
   Google Scholar
• DfEE . 1999 . Framework for teaching mathematics from reception to Year 6 . London : Department for Education and Employment .
   Google Scholar
• Harel , G. and Sowder , L. 2005 . Advanced mathematical thinking at any age: Its nature and its development . Mathematical Thinking and Learning , 7 ( 1 ) : 27 – 50 .
   Google Scholar
• Haylock , D. and Cockburn , A.D. 2003 . Understanding mathematics in the lower primary years , London : Paul Chapman Publishing .
   Google Scholar
• Hiebert , J. and Carpenter , T.P. 1992 . “ Learning and teaching with understanding ” . In Handbook of research in mathematics teaching and learning , Edited by: Grouws , D. 65 – 97 . New York : McMillan .
   Google Scholar
• Iannone , P. , and A. D. Cockburn . 2006 . Fostering conceptual mathematical thinking in the early years: A case study . In Proceedings of the 30th Annual Conference of the International Group for Psychology in Mathematics Education J. Novotna , H. Moraova , M. Kratka and N. Stehlikova , 3 : 329 – 336 . Prague, , Czech Republic : Charles University
   Google Scholar
• Jaworski , B. 2002 . Sensitivity and challenge in university mathematics tutorial teaching . Educational Studies in Mathematics , 51 : 71 – 94 .
   Google Scholar
• Kazemi , E. and Stipek , D. 2001 . Promoting conceptual thinking in four upper-elementary mathematics classrooms . The Elementary School Journal , 102 : 59 – 80 .
   Web of Science ®Google Scholar
• Krutetskii , V. A. 1976 . The psychology of mathematical abilities in school children . Chicago : University of Chicago Press [trans. J. Teller; ed. J. Kilpatrick and I. Wirszup] .
   Google Scholar
• Lyle , J. 2003 . Stimulated recall: A report on its issues in naturalistic research . British Educational Research Journal , 29 ( 6 ) : 861 – 878 .
   Web of Science ®Google Scholar
• van Oers , B. 2001 . Educational forms of initiation in mathematical culture . Educational Studies in Mathematics , 46 : 59 – 85 .
   Google Scholar
• Ogden , L. 2000 . Collaborative tasks, collaborative children: An analysis of reciprocity during peer interaction at Key Stage 1 . British Education Research Journal , 26 ( 2 ) : 211 – 225 .
   Web of Science ®Google Scholar
• Pepin , B. 1999 . Epistemologies, beliefs and conceptions of mathematics teaching and learning: The theory, and what is manifested in mathematics teachers’ work in England, France and Germany . TNTEE Publications 2(1). http://tntee.umu.se/
   Google Scholar
• Raymond , A.M. 1997 . Inconsistency between a beginning elementary school teacher's mathematics beliefs and teaching practice . Journal for Research in Mathematics Education , 28 ( 5 ) : 550 – 576 .
   Web of Science ®Google Scholar
• Saldana , J. 2005 . Codeweaving: An introductory qualitative data analytic method . Paper presented at the Annual Meeting of the American Educational Research Association Conference, April 11–15, in Montreal, Canada .
   Google Scholar
• Sfard , A. 2000 . On reform movement and the limits of mathematical discourse . Mathematical Thinking and Learning , 2 ( 3 ) : 157 – 189 .
   Google Scholar
• Stake , R.E. 2005 . “ Qualitative case studies ” . In The Sage handbook of qualitative research, third edition , Edited by: Denzin , N. and Lincoln , Y. 443 – 466 . London : Sage Publications .
   Google Scholar
• Thompson , A.G. 1984 . The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice . Educational Studies in Mathematics , 15 : 105 – 127 .
   Google Scholar
• Watson , A. and De Geest , E. 2001 . Low attainers exhibiting higher-order mathematical thinking . Support for Learning , 16 ( 4 ) : 179 – 183 .
   Google Scholar
• Watson , A. and De Geest , E. 2005 . Principled teaching for deep progress: Improving mathematical learning beyond methods and materials . Educational Studies in Mathematics , 58 : 209 – 234 .
   Google Scholar
• White , B. 2000 . Pre-service teachers’ epistemology viewed through perspectives on problematic classroom situations . Journal of Education for Teaching , 26 ( 3 ) : 279 – 305 .
   Google Scholar
• Williams , G. 2004 . The nature of spontaneity in high quality mathematics learning experiences . In Proceedings of the 28th Annual Conference of the International Group for Psychology in Mathematics Education M. J. Høines and A. B. Fuglestad , 4 : 433 – 440 . Bergen, , Norway : Bergen University College .
   Google Scholar
• Wood , T. , Williams , G. and McNeal , B. 2006 . Children's mathematical thinking in different classroom cultures . Journal for Research in Mathematics Education , 37 ( 3 ) : 222 – 255 .
   Web of Science ®Google Scholar