A concept for quantitative comparison of mathematical and natural language and its possible effect on learning

Starting with the question whether there is a connection between the mathematical capabilities of a person and his or her mother tongue, we introduce a new modeling approach to quantitatively compare natural languages with mathematical language. The question arises from educational assessment studies that indicate such a relation. Texts written in natural languages can be deconstructed into a dependence graph, in simple cases a dependence tree. The same kind of deconstruction is also possible for mathematical texts. This gives an idea of how to quantitatively compare mathematical and natural language. To that end, we develop algorithms to define the distance between graphs. In this paper, we restrict the structure to trees. In order to measure the distance between trees, we use algorithms based on previous work measuring the distance of neurons using the constrained tree edit distance. Once a distance matrix has been computed, this matrix can be used to perform a cluster analysis.