Concept learning: vector space, under the mental structures approach

Abstract

Objective: To evaluate the learning of the concept of vector space in students of industrial engineering and systems under the mental structures approach. Methodology: The research is quantitative, prospective and exploratory. The study sample included 75 students of the Faculty of Industrial, Systems and Computing Engineering. The instrument used was a multiple-choice six-item questionnaire and an open problem taken from previous partial exams. Results: The evidence indicates that 16% showed difficulties in giving priority to operations, 25% do not adequately use secondorder logic to discern properties and axioms, 15% use schemas and relational diagrams to relate sets, binary operations and axioms. In addition, 24% use the sequence: analogy, construction and abstraction; as a way of constructing the vector space mathematical object. Finally, it was identified that 20% of the students don't have idea about the existence of arithmetic structures, they can't learn new ideas related to binary operations without leaving aside the old ideas of operations with real numbers. Conclusions: It was identified that 80% of the students conceive the concept of vector space as implicit visions and explicit statements that take shape when the didactic processes that involve analogy, construction and abstraction are traced. Where, second order logic and symbols are the means for external representations and constant manipulations of the signified and the signifier. The 20% of the students are in a stage of mental maturation, they resist leaving their paradigm of numerical arithmetic structures and as a consequence, the representational construction process of vector space is in a reconstruction stage in relation to the reference models.