TY - JOUR
T1 - The basis step in the construction of the principle of mathematical induction based on APOS theory
AU - García-Martínez, Isabel
AU - Parraguez, Marcela
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - Using APOS theory as the framework along with a case study from a perspective within the methodological design of APOS theory, this study presents a cognitive model of the Principle of Mathematical Induction (PMI) in higher education. Based on evidence from university classrooms and the result of an initial measurement, the genetic decomposition designed by Dubinsky and Lewin for this concept was reformulated, introducing and defining the basis step in the PMI as a mental process. Using this reformulated genetic decomposition, the productions of four university students are analysed in order to support or refute the constructions it proposes. The results show that the reformulated genetic decomposition is viable and that the inclusion of the basis step as a mental process was seen in the cognitive model of the PMI shown by the students. The instruments used provide activities for a teaching sequence for the PMI at university level.
AB - Using APOS theory as the framework along with a case study from a perspective within the methodological design of APOS theory, this study presents a cognitive model of the Principle of Mathematical Induction (PMI) in higher education. Based on evidence from university classrooms and the result of an initial measurement, the genetic decomposition designed by Dubinsky and Lewin for this concept was reformulated, introducing and defining the basis step in the PMI as a mental process. Using this reformulated genetic decomposition, the productions of four university students are analysed in order to support or refute the constructions it proposes. The results show that the reformulated genetic decomposition is viable and that the inclusion of the basis step as a mental process was seen in the cognitive model of the PMI shown by the students. The instruments used provide activities for a teaching sequence for the PMI at university level.
KW - APOS
KW - Genetic decomposition
KW - Principle of mathematical induction
KW - University education
UR - http://www.scopus.com/inward/record.url?scp=85018437979&partnerID=8YFLogxK
U2 - 10.1016/j.jmathb.2017.04.001
DO - 10.1016/j.jmathb.2017.04.001
M3 - Article
AN - SCOPUS:85018437979
VL - 46
SP - 128
EP - 143
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
SN - 0732-3123
ER -