A pedagogical grammar is a modern approach in linguistics

Linguistics

Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....

 intended to aid in teaching an additional language.

Structure

This method of teaching is divided into the descriptive: grammatical analysis, and the prescriptive: the articulation of a set of rules. Following an analysis of the context in which it is to be used, one grammatical form or arrangement of words will be determined to be the most appropriate. Pedagogical grammars typically require rules that are definite, coherent, non-technical, cumulative and heuristic. As the rules themselves accumulate, an axiomatic system

Axiomatic system

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A mathematical theory consists of an axiomatic system and all its derived theorems...

is formed between the two languages that should then enable a native speaker of the first to learn the second.