Understanding secondary–tertiary transition in mathematics

References

• Barnard , D . 2003 . The transition to mathematics at university: Students’ views . New Zealand J. Math. , 32 ( supplementary issue ) : 1 – 8 .
   Google Scholar
• Crawford , K , Gordon , S , Nicholas , J and Posser , M . 1994 . Conceptions of mathematics and how it is learned: The perspectives of students entering university . Learn. Instruct. , 4 : 331 – 345 .
   Google Scholar
• Crawford , K , Gordon , S , Nicholas , J and Posser , M . 1998 . Qualitatively different experiences of learning mathematics at university . Learn. Instruction , 8 : 455 – 468 .
   Web of Science ®Google Scholar
• Guzman, M. de, Hodgson B., Robert, A., and Villani, V., Difficulties in passage from secondary to tertiary education, in Proceedings of the International Congress of Mathematicians, Berlin, 1998, Vol III: Invited Lectures, pp. 747–762
   Google Scholar
• Gruenwald , N , Klymchuk , S and Jovanoski , Z . 2004 . Reducing the gap between the school and university mathematics: university lecturers' perspective . New Zealand Math. Mag. , 41 ( 3 ) : 12 – 24 .
   Google Scholar
• McInnes , C , James , R and Hartley , R . 2000 . Trends in the First Year Experience in Australian Universities , Canberra : AGDS .
   Google Scholar
• Schoenfeld , AH . 1994 . What do we know about mathematics curricula? . J. Math. Behav. , 13 ( 1 ) : 55 – 80 .
   Google Scholar
• Tall , DO . 1992 . “ The transition to advanced mathematical thinking: Functions, limits, infinity and proof ” . In Handbook of Research on Mathematics teaching and Learning , Edited by: Grouws , DA . 495 – 511 . New York : Macmillan .
   Google Scholar
• Tall , D . 1997 . “ From school to university: The effects of learning styles in the transition from elementary to advanced mathematical thinking ” . In Proceedings of The Seventh Annual Australasian Bridging Network Mathematics Conference , Edited by: Thomas , MOJ . 9 – 26 . Auckland, , New Zealand : University of Auckland .
   Google Scholar
• Wood , L . 2001 . “ The secondary–tertiary interface ” . In The Teaching and Learning Mathematics at University Level: An ICMI Study , Edited by: Holton , DA . 87 – 98 . Netherlands : Kluwer Academic Publishers .
   Google Scholar
• Leach , E . 1973 . “ Some anthropological observations on number, time and common-sense ” . In Developments in Mathematical Education, in Proceedings of the Second International Congress on Mathematical Education , Edited by: Howson , AG . Cambridge : Cambridge University Press .
   Google Scholar
• Wood , L . 2004 . University mathematics teaching and learning, MERGA Review of Research in Australia 2000–2003 , 219 – 242 . Flaxton : Post Pressed .
   Google Scholar
• Persens , J . 2003 . “ Foundation programmes in mathematics: Any wisdom gained? ” . In Remarkable Delta: 03 Communications , International Delta Steering Group, eds. Auckland : University of Auckland .
   Google Scholar
• Varsavsky , C . 2001 . Towards a relevant mathematics and statistics curriculum for first year students . QM J. South African Math. Soc. , Sup 1 : 141 – 147 .
   Google Scholar
• Clark , M and Lovric , M . 2008 . Suggestion for a theoretical model for secondary–tertiary transition in mathematics . Math. Educ. Res. J. , 20 ( 2 ) : 25 – 37 .
   Google Scholar
• Gennep , AVan . 1960 . The Rites of Passage (Transl.) , 1960 Chicago : The University of Chicago Press . (original work published 1908)
   Google Scholar
• Piaget , J . 1985 . The Equilibrium of Cognitive Structures , Cambridge, MA : Harvard University Press .
   Google Scholar
• Tall , DO . 1991a . “ The psychology of advanced mathematical thinking ” . In Advanced Mathematical Thinking , Edited by: Tall , DO . 3 – 21 . Holland : Kluwer .
   Google Scholar
• Tall , DO . 1991b . “ Reflections ” . In Advanced Mathematical Thinking , Edited by: Tall , DO . 251 – 259 . Holland : Kluwer .
   Google Scholar
• Tall , DO . 1995 . “ Mathematical growth in elementary and advanced mathematical thinking ” . In Proceedings of PME-19 , Edited by: Meira , L and Carraher , D . Vol. 1 , 61 – 75 . Brasil : Recife .
   Google Scholar
• Ward , C , Bochner , S and Furnham , A . 2001 . The Psychology of Culture Shock , Hove, East Sussex : Routhledge .
   Google Scholar
• Davis , J . 2001 . Conceptual change, in Emerging Perspectives on Learning, Teaching, and Technology Edited by: Orey , M . 2001. Available at www.coe.uga.edu/epltt/ConceptualChange.htm
   Google Scholar
• Biza , I , Souyoul , A and Zachariades , T . 17–21 February 2005 . Conceptual change in advanced mathematical thinking , Discussion paper 17–21 February , Spain : Fourth Congress of ERME, Sant Feliu de Guíxols .
   Google Scholar
• London Mathematical Society, Institute of Mathematics and its Applications, Royal Statistical Society, 1995. Tackling The Mathematics Problem. Available at http://www.lms.ac.uk/policy/tackling/report.html. Last visited: 4 February 2009
   Google Scholar
• Turner , VW . 1969 . The Ritual Process: Structure and Anti-Structure , Chicago : Aldine Publishing Company .
   Google Scholar
• Appleby , J and Cox , W . 2002 . “ The transition to higher education ” . In Effective Learning & Teaching in Mathematics and Its Applications , Edited by: Kahn , P and Kyle , J . 3 – 19 . Sterling, VA : Stylus Publishing Inc. .
   Google Scholar
• Oates , G , Paterson , J , Reilly , I and Statham , M . 2005 . Effective tutorial programmes in tertiary mathematics . Int. J. Math. Educ. Sci. Technol. 7 , 36 : 731 – 739 .
   Google Scholar
• Lovric, M, Learning How To Teach And Learn Mathematics–‘Teaching Mathematics’ Course At McMaster University, in Proceedings of the 1st Africa Regional Congress of the International Commission on Mathematical Instruction (ICMI), 22–25 June 2005, University of the Witwatersrand, Johannesburg, 2005
   Google Scholar
• Lovric , M and Trim , K . 2001 . Teaching mathematics course–Teaching experience for undergraduate students . Positive Pedagogy 2 , 1 Available at: http://www.mcmaster.ca/cll/posped/pastissues/volume.1.no.2/teaching.mathematics.htm
   Google Scholar
• Hofstede , G . 1983 . “ Dimensions of national cultures in fifty countries and three regions ” . In Expiscations in Cross-Cultural Psychology , Edited by: Deregowski , J , Dzuirawiec , S and Annis , C . 335 – 355 . The Netherlands : Swets&Zeitlinger .
   Google Scholar
• Kotsopoulos , D . 2008 . Beyond teachers’ sight lines: Using video modeling to examine peer discourse . Mathematics Teacher , 101 ( 6 ) : 468 – 472 .
   Google Scholar
• Alcock , L and Simpson , A . 2002 . Definitions: Dealing with categories mathematically . Learn. Math. , 2 : 28 – 34 . 22, (July 2002)
   Google Scholar
• Maddern , E . 1990 . What is it that fifteen year olds need? Notes on developing initiations appropriate to our times . Adventure Educ. , 17 ( 1 ) : 29 – 32 .
   Google Scholar
• Kajander , A and Lovric , M . 2009 . Mathematics textbooks and their potential role in supporting misconceptions . Int. J. Math. Educ. Sci. Technol. , 40 ( 2 ) : 173 – 181 .
   Google Scholar
• Howson , G . 1989 . Maths Problem: Can More Pupils Reach Higher Standards? Policy Studies No. 102 , London : Centre for Policy Studies .
   Google Scholar
• Cooper , H , Nye , B , Charlton , K , Lindsay , J and Greenhouse , S . 1996 . The effects of summer vacation on achievement test scores: A narrative and meta-analytic review . Rev. Educ. Res. , 66 ( 3 ) : 227 – 268 . (1996)
   Web of Science ®Google Scholar
• Johns Hopkins University, School of Education, National Center for Summer Learning. Available at: http://www.summerlearning.org/index.php. Last visited: 5 February 2009
   Google Scholar
• Easter , W . 1990 . Ensuring Minorities’ Success in Mathematics, Engineering and Science: The MESA Program . Carnegie Quarterly, , XXXV ( 1990 ) : 1 – 7 .
   Google Scholar
• Cohen , D . 1978 . Maths in the sun . New Scientist , 3 August
   Google Scholar
• Chandler , S . 1997 . A-level mathematics examinations as a fair assessment of the needs of students post-GCSE intermediate and higher tiers . Teach. Math. Appl. , 16 ( 4 ) : 157 – 159 .
   Google Scholar
• Cox , W . 2000 . Predicting the mathematical preparedness of first year undergraduates for teaching and learning purposes . Int. J. Math. Educ. Sci. Technol. , 31 ( 2 ) : 227 – 248 .
   Google Scholar
• L. Rylands, Performance of students with weak mathematics in first year mathematics and science, preprint (2009), submitted to International Journal of Mathematics Educations in Science and Technology
   Google Scholar
• E. Hoover, Undergraduates study much less than professors expect, survey of student ‘engagement’ says, The Chronicle of Higher Education (2004), November 15
   Google Scholar
• Quadling , D . 1979 . Mathematics Education at Upper Secondary School, College and University Transition, New Trends in Mathematics Teaching , Vol. IV , Paris : UNESCO .
   Google Scholar
• Clark , M . 1995 . “ Raising achievement in mathematics for pacific island students in New Zealand ” . In Regional Collaboration in Mathematics Education , Edited by: Hunting , R , Fitzsimons , G , Clarkson , P and Bishop , A . 201 – 210 . Melbourne : Monash University .
   Google Scholar
• M. Prensky, Digital Natives, Digital Immigrants, On the Horizon, NCB University Press, Vol. 9, No. 5, 2001, October
   Google Scholar
• J.M. Young-Loveridge, Number Skills in Junior Classrooms, SET 2 (1998) Item 16. NZCER, Wellington, 1998
   Google Scholar
• Timperley , H , McNaughton , S , Howie , L and Robinson , V . 2003 . Transitioning children from early childhood education to school: Teacher beliefs and transition practices . Aust. J. Early Child. , 28 ( 2 ) : 32 – 38 .
   Google Scholar
• Sherley , B . 2006 . Personal communication ,
   Google Scholar
• Averill , R . 2001 . Just by aiming at middle , MSc Thesis Wellington : Victoria University .
   Google Scholar