On the Specification of the Relevant Mathematical Notations
Abstract:
Mathematical notations are a form of graphical language
used to express statements. The language is thought of as formally well
defined and is made of a broad spectrum of symbols. Because of its for-
mality, it is common to consider that mathematical notations (or the
mathematical knowledge) are universal and can be universally under-
stood. This consideration is not correct. We describe examples of nota-
tions which fail to be universal and propose explanations for these fail-
ures. Thus, the following question is natural: How or who should specify
the relevant mathematical notations when planning a content or software
project? We propose approaches to answer this.
The breadth of the spectrum of mathematical symbols, and the dom-
inating handwritten practice, brings another important aspect to this
question: Every mathematician considers himself or herself empowered
to create new notations. We explain why this freedom of invention is
important and sketch implications for the design of educational tools.
Published:
7th International Workshop on Culturally-Aware Tutoring Systems (CATS2024), Recife, Brazil, July 8, 2024, Emmanuel G. Blanchard, Isabela Gasparini, Maria Mercedes. T. Rodrigo (editors)