TY - JOUR
T1 - The transition from comparison of finite to the comparison of infinite sets
T2 - Teaching prospective teachers
AU - Tsamir, Pessia
PY - 1999
Y1 - 1999
N2 - Research in mathematics education indicates that in the transition from given systems to wider ones prospective teachers tend to attribute all the properties that hold for the former also to the latter. In particular, it has been found that, in the context of Cantorian Set Theory, prospective teachers have been found to erroneously attribute properties of finite sets to infinite ones - using different methods to compare the number of elements in infinite sets. These methods which are acceptable for finite sets, lead to contradictions with infinite ones. This paper describes a course in Cantorian Set Theory that relates to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. The findings clearly indicate that when comparing the number of elements in infinite sets the prospective teachers who took the course were more successful and were also more consistent in their use of a single method than those who studied the traditional, formally-based Cantorian Set Theory course.
AB - Research in mathematics education indicates that in the transition from given systems to wider ones prospective teachers tend to attribute all the properties that hold for the former also to the latter. In particular, it has been found that, in the context of Cantorian Set Theory, prospective teachers have been found to erroneously attribute properties of finite sets to infinite ones - using different methods to compare the number of elements in infinite sets. These methods which are acceptable for finite sets, lead to contradictions with infinite ones. This paper describes a course in Cantorian Set Theory that relates to prospective secondary mathematics teachers' tendencies to overgeneralize from finite to infinite sets. The findings clearly indicate that when comparing the number of elements in infinite sets the prospective teachers who took the course were more successful and were also more consistent in their use of a single method than those who studied the traditional, formally-based Cantorian Set Theory course.
UR - http://www.scopus.com/inward/record.url?scp=0010033385&partnerID=8YFLogxK
U2 - 10.1007/978-94-017-1584-3_10
DO - 10.1007/978-94-017-1584-3_10
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AN - SCOPUS:0010033385
SN - 0013-1954
VL - 38
SP - 209
EP - 234
JO - Educational Studies in Mathematics
JF - Educational Studies in Mathematics
IS - 1-3
ER -