TY - JOUR
T1 - Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis
AU - Biza, Irene
AU - Christou, Constantinos
AU - Zachariades, Theodossios
PY - 2008/3/1
Y1 - 2008/3/1
N2 - The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis.
AB - The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students’ responses, we describe students’ thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis.
KW - tangent line
KW - concept image
KW - Analysis
U2 - 10.1080/14794800801916457
DO - 10.1080/14794800801916457
M3 - Article
VL - 10
SP - 53
EP - 70
JO - Research in Mathematics Education
JF - Research in Mathematics Education
SN - 1479-4802
IS - 1
ER -