The interrelationships among concept image, identification and situation of complex numbers for grade 12 Lebanese students

Abstract

The purpose of this research study is to (1) investigate Lebanese students’ concept image of complex numbers, (2) examine the impact of the situation in which a complex number is used on students’ concept image of complex numbers and (3) examine the impact of students’ concept image on their identification of complex numbers. A mixed design was used in this study. A qualitative data analysis of 93 Lebanese students’ response to the open-ended concept image questionnaire and the semi-structured complex number justification test was done. The responses to the identification test provided the qualitative data. Analysis of the results revealed that the five situations differ significantly in their distributions of concept image, and the students’ concept image of complex numbers is moderately associated to the situation. Second, the situation in which complex numbers are used impacts the students’ evoked concept image. The impact of the situation on the formation of students’ concept image of complex numbers tends to be affected by the social aspects of constructivism, particularly textbook discourse, as reflected by the definition of complex numbers. Third, the total identification means score differed significantly between the students’ five concept image categories of complex numbers in the identification situation. Moreover, the students with the conceptual view as their concept image had the highest total identification mean score. Finally, when identifying examples of complex numbers, the students rely on their concept image and not their concept definition. The students who rely on the formal definition to construct their concept image might score better in their identification of complex numbers.