337
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

University students’ retention of derivative concepts 14 months after the course: influence of ‘met-befores’ and ‘met-afters’

&
Pages 749-764 | Received 22 Dec 2010, Published online: 06 Mar 2012

References

  • Chinnappan , M , Dinham , S , Herrington , A and Scott , D . Year 12 students and higher mathematics: Emerging issues, AARE 2007 International Education Research Conference, 2007
  • Helfgott , M . Five guidelines in the teaching of first-year calculus, Proceedings of the 10th International Congress of Mathematical Education, Copenhagen, Denmark, 2004
  • Morgan , AT . 1990 . A study of difficulties experienced with mathematics students in higher education . Int. J. Math. Educ. Sci. Technol. , 21 ( 6 ) : 975 – 988 .
  • Guzman , M , Hodgson , B , Robert , A and Villani , V . 1998 . Difficulties in the passage from secondary to tertiary education . Doc. Math., ICM , 3 : 747 – 762 .
  • Maull , W and Berry , J . 2000 . A questionnaire to elicit concept images of engineering students . Int. J. Math. Educ. Sci. Technol. , 31 ( 6 ) : 899 – 917 .
  • Bingolbali , E , Monaghan , J and Roper , T . 2007 . Engineering students’ conceptions of the derivative and some implications for their mathematical education . Int. J. Math. Educ. Sci. Technol. , 38 ( 6 ) : 763 – 777 .
  • Lj. Jukić and B. Dahl, The retention of key derivative concepts by university students on calculus courses at a Croatian and Danish university, Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Brazil, Belo Horizonte, PME 2010, Vol. 3, pp. 137–144
  • Lj. Jukić and B. Dahl, What affects retention of core calculus concepts among university students? A study of different teaching approaches in Croatia and Denmark, Proceedings of the 7th Congress of the European Society for Research in Mathematics Education, Poland, Rzeszów, CERME 2011, pp. 2033–2042
  • Lj. Jukić, Teaching and learning outcomes in undergraduate calculus courses for students of technical and science studies in Croatia and Denmark, Ph.D. diss., Department of Mathematics, University of Zagreb, Croatia, 2011
  • Brückler , FM . and Lj. Jukić, How science students understand, remember and use mathematics, The Book of Abstracts of the 4th International Conference Research in Didactics of the Sciences, Poland, Krakow, 2010
  • Hiebert , J and Lefevre , P . 1986 . “ Conceptual and procedural knowledge in mathematics: an introductory analysis ” . In Conceptual and Procedural Knowledge: The Case of Mathematics , Edited by: Hiebert , J . Vol. 22 , 1 – 36 . Hillsdale, NJ : Lawrence Erlbaum Mathematics .
  • Star , JR . 2005 . Re-conceptualizing procedural knowledge . J. Res. Math. Educ. , 36 ( 5 ) : 127 – 155 .
  • Haapasalo , L and Kadijevich , Dj . 2000 . Two types of mathematical knowledge and their relation . J. Für Math.-Didakt. , 21 ( 2 ) : 139 – 157 .
  • Tall , D . 2006 . A theory of mathematical growth through embodiment, symbolism and proof . Ann. Didact. Sci. Cognitives, IREM Strasbourg, , 11 : 195 – 215 .
  • Nogueira de Lima , R and Tall , D . 2008 . Procedural embodiment and magic in linear equations . Educ. Stud. Math. , 67 ( 1 ) : 3 – 18 .
  • McGowen , M and Tall , D . 2010 . Metaphor or met-before? The effects of previous experience on the practice and theory of learning mathematics . J. Math. Behav. , 29 : 169 – 179 .
  • Sousa , DA . 2000 . How the Brain Learns , Thousand Oaks , CA : Corwin Press .
  • Garner , B and Garner , L . 2001 . Retention of concepts and skills in traditional and reformed applied calculus . Math. Educ. Res. J. , 13 ( 3 ) : 165 – 184 .
  • Allen , K , Kwon , ON and Rasmussen , C . 2005 . Students’ retention of mathematical knowledge and skills in differential equations . School Sci. Math. , 16 ( 2 ) : 227 – 239 .
  • Engelbrecht , J , Harding , A and Du Preez , J . 2007 . Long-term retention of basic mathematical knowledge and skills with engineering students . Eur. J. Eng. Educ. , 32 ( 6 ) : 735 – 744 .
  • Robson , C . 2002 . Real World Research: A Resource for Social Scientists and Practitioner-Researchers , Hoboken , NJ : Wiley-Blackwell .
  • Schofield , JW . 1990 . “ Increasing the generalizability of qualitative research ” . In Qualitative Inquiry in Education , Edited by: Eisner , EW and Peshkin , A . 201 – 232 . New York : Teachers College .
  • Kvale , S . 1996 . InterViews: An Introduction to Qualitative Research Interviewing , London : Sage .
  • Killen , R . 2007 . Effective Teaching Strategies: Lessons from Research and Practice , Melbourne : Thomson Social Science Press .
  • Engelbrecht , J , Bergsten , C and Kågesten , O . 2009 . Undergraduate students' preference for procedural to conceptual solutions to mathematical problems . Int. J. Math. Educ. Sci. Technol. , 40 ( 7 ) : 927 – 940 .
  • British Educational Research Association (BERA), Revised Ethical Guidelines for Ethical Research (2004). Available at http://www.bera.ac.uk/files/guidelines/ethica1.pdf
  • Hammersley , M . 1998 . Reading Ethnographic Research – A Critical Guide , London : Longman .
  • Asiala , M , Cottrill , J , Dubinsky , E and Schwingendorf , K . 1997 . The development of students’ graphical understanding of the derivative . J. Math. Behav. , 16 ( 4 ) : 399 – 431 .
  • Zandieh , M and Knapp , J . 2006 . Exploring the role of metonymy in mathematical understanding and reasoning: The concept of derivative as an example . J. Math. Behav. , 25 ( 1 ) : 1 – 17 .
  • Viholainen , A . Prospective mathematics teachers’ informal and formal reasoning about the concepts of derivative and differentiability, Ph.D. diss., Report No. 115, Department of Mathematics and Statistics, University of Jyväskylä, Finland, 2008
  • Weber , K and Alcock , L . 2004 . Semantic and syntactic proof productions . Educ. Stud. Math. , 56 : 209 – 234 .
  • Jukić , D and Scitovski , R . 2000 . Matematika I , Osijek : Gradska Tiskara .
  • Lima , RNogueira de and Tall , D . 2006 . The concept of equation: what have students met before? , Prague, Czech Republic : Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education . Vol. 4, pp. 233–241

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.