Showing posts from December 19, 2021

A Gap in Mathematics Education

The process of creation of mathematics has the following hierarchically dependent components: Coming up with a concept. Coming up with a question dealing with a relationship between concepts (this includes formulating a hypothesis, as well as finding an example or a counterexample of a concept/phenomenon). Answering a question dealing with a relationship between concepts (this includes proving theorems as well as solving problems without being given the recipe for solution). Applying the answer to a question dealing with a relationship between concepts to answer another such question (this includes solving problems by applying a given recipe for solution). Modern mathematics education (both at the school and at the university levels) focuses mainly on the last two points. What is regarded as a low quality mathematics education would focus only on the last point. For a more whole mathematics education, the first two points must receive as much attention as the last two points do.  It is

Musical Works

Introduction My musical works, which I have started creating in 2014, explore deeper abstract emotions, such as those arising from an intellectual pursuit, that may be connecting oneself with their dream world and touch the essence of existence. The works can be classified in the following categories: Impromptus  and ballades : these works are based on once-off improvisations, which may be edited for fixing accidental notes, adjusting suitable playback tempo, and introducing repetitions/transpositions. The difference between impromptus and ballades lies mainly in the playback length of the musical piece, with ballades being the longer musical works. A ballade is meant to tell a "musical story", while an impromptu paints a "musical picture".  Esprits : these musical pieces are combined with improvised performance of theatrical nature as a visual interpretation of music. Esprits belong to an artform defined by "mindful improvisation" (which I call "espr