Scientific Essay from the year 2018 in the subject Pedagogy - Higher Education, grade: 9, , course: Mathematics (Hons), language: English, abstract: The aim of the article is to discuss an approach to teaching that generally a mathematics teacher follows in higher educational institutions of graduate and postgraduate students and of research scholars. It has been observed that all subjects including mathematics follow the same roots to develop. They all consist of three parts: assumptions, properties and applications, which brought them under the same umbrella of definition. In teaching too they follow the same steps to be explained to the students in order. Although there is no single best method available, an attempt has been made to propound one of the best idealistic method and a realistic inductive method. The article concluded with a short note that realistic inductive method is sufficient for graduate and postgraduate students while idealistic method is useful for research oriented students followed by the scope of further research in open problem section.