This paper reports an empirical study of students’ classification of sequences before
and after meeting explicit definitions of ‘increasing’ and ‘decreasing’. In doing so, it
explores 1) students’ interpretations of the definitions and 2) the appropriateness of
this apparently straightforward context for teaching students about the status of
mathematical definitions. In particular, it demonstrates that students’ spontaneous
conceptions in this context can be inconsistent with definitions, and it explores the
extent to which exposure to formal definitions influences these conceptions. The
results show an interesting pattern of modified classifications, which demonstrates
increased consistency with the definitions but shows problems with some pivotal
examples.
History
School
Science
Department
Mathematics Education Centre
Citation
ALCOCK, L. and SIMPSON, A., 2009. The role of definitions in example classification. IN: Tzekaki,M., Kaldrimidou, M. and Haralambos, S. (eds). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education, PME 33, 19-24 July 2009, Thessaloniki, Greece : in Search For Theories in Mathematics Education. Thessaloniki, Greece : International Group for the Psychology of Mathematics Education, pp. 33-40