Algebraic transformation of unary partial algebras II: Single-pushout approach

AbstractThe single-pushout approach to graph transformation is extended to the algebraic transformation of partial many-sorted unary algebras. Such a generalization has been motivated by the need to model the transformation of structures which are richer and more complex than graphs and hypergraphs.The main result presented in this article is an algebraic characterization of the single-pushout transformation in the categories of all conformisms, all closed quomorphisms, and all closed-domain closed quomorphisms of unary partial algebras over a given signature, together with a corresponding operational characterization that may serve as a basis for implementation.Moreover, all three categories are shown to satisfy all of the HLR (high-level replacement) conditions for parallelism, taking as occurrences the total morphisms in each category. Another important result presented in this article is the definition of HLR conditions for amalgamation, which are also satisfied by the categories of partial homomorphisms considered here, taking again the corresponding total morphisms as occurrences

Minimising mathematical anxiety in teaching mathematics and assessing student’s work

This paper builds up a theoretical perspective and supports a possibility of creating a special assessment environment for students, where mathematical knowledge and understanding can be assessed with a reduced number of external psychological factors that may affect such assessment. A concept of a zone with minimal effect of anxiety is introduced and described. Students’ successful work on extending the zone by means of a carefully selected chain of questions, where some questions only are part of a real assessment, allows students to reconsider their attitudes towards mathematics and assist teachers to identify some students’ main learning difficulties as of psychological character. Further suggestions about developing and investigating special assessment environments are outlined and discussed