Transitional points in constructing the preimage concept in linear algebra

• Published in: International journal of mathematical education in science and technology Vol. 53; no. 5; pp. 1170 - 1189
• Main Authors: Oktaç, Asuman, Vázquez Padilla, Rita, Ramírez Sandoval, Osiel, Villabona Millán, Diana
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 28.05.2022; Taylor & Francis Ltd
• Subjects: Calculus; Context; Foreign Countries; Guidelines; Higher education institutions; Intervention; Introductory Courses; Learning; levels in APOS theory; Linear algebra; linear transformation; Linear transformations; Mathematical Concepts; Mathematics education; Mathematics Instruction; mental mechanisms; Mental structures; Mexicans; preimage; Schemata (Cognition); Task Analysis; Teaching Methods; Undergraduate Students; Mexico
• ISSN: 0020-739X; 1464-5211
• DOI: 10.1080/0020739X.2021.1968523

From an APOS (Action-Process-Object-Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the learning of the concept of linear transformation in general, and the notion of preimage in particular. A questionnaire was designed and applied to 31 students from three different higher education institutions in Mexico, who were enrolled in an introductory linear algebra course. For the first time, transitional points known as levels are explicitly identified in the aforementioned context and empirical evidence is presented. Some difficulties resulting from the intervention of constructions related to the function concept are also pointed out. Discussion about the characteristics of levels in the APOS framework provides a theoretical contribution to the field.