Transitional points in constructing the preimage concept in linear algebra

Asuman Oktaç ^[4] ; Rita Vázquez Padilla ^[1] ; Osiel Ramírez Sandoval ^[2] ; Diana Villabona Millán ^[3]
1. [1] Universidad Autónoma de la Ciudad de México
  
  Universidad Autónoma de la Ciudad de México
  
  México
2. [2] Universidad Autónoma de Ciudad Juárez
  
  Universidad Autónoma de Ciudad Juárez
  
  México
3. [3] Universidad Industrial de Santander
  
  Universidad Industrial de Santander
  
  Colombia
4. [4] Mexico City
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Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 53, Nº. 5, 2022, págs. 1170-1189
Idioma: inglés
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Resumen
- 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.