Structural-mathematical thinking and its development in teaching Mathematics

Abstract

The paper highlights the content and components of structural-mathematical thinking, substantiates its classification basis and establishes typological characteristics. In the conceptual-categorical section of the present study, structural-mathematical thinking is introduced as a form of theoretical thinking that embodies the specifics of mathematical comprehension of reality. The content as well as structural and functional characteristics of the phenomenon under study represent the content and components of the mathematical structure. Hence, the adherence to the deductive nature of Mathematics was ensured in the study, also emphasizing the phenomenological characteristic of structural-mathematical thinking regarded as the ability to reflect reality in accordance with the content components of the mathematical structure. Taking into account the theoretical advances, using the system approach and the modeling method, a model of developmental-conceptual teaching of Mathematics was elaborated. By considering the theoretical advancements and applying both a systemic approach and modeling method, a model for instructing Mathematics in a developmental-conceptual approach was elaborated, which represents a problem-based approach and develops students’ structural-mathematical thinking. The crux of teaching Mathematics through a developmental and conceptual approach lies in creating a framework that addresses the three-fold challenge of problem-solving ↔ competency-building ↔ problem-solving proficiency. Taking into account the addressed issue, the paper elicits the outcomes of a pilot study how structural-mathematical thinking is manifested by the would-be teachers of Mathematics. Furthermore, the efficacy of the authors’ approach to its enhancement is experimentally validated.