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The paper aims at clarifying the pedagogical relevance of an algebraic-oriented perspective in the foundation of a structural and formalized approach in contemporary computational musicology. After briefly discussing the historical emergence of the concept of algebraic structure in systematic musicology, we present some pedagogical aspects of our MathTools environment within OpenMusic graphical programming language. This environment makes use of some standard elementary algebraic structures and it enables the music theorist to visualize musical properties in a geometric way by also expressing their underlying combinatorial character. This could have a strong implication in the way at teaching mathematical music theory as we will suggest by discussing some tiling problems in computer-aided composition.