This paper is an attempt of the author to answer the question ``What is the psycho-linguistic basis of teaching Mathematics in English to non-native speakers?" The idea presented is based on Piaget's Theory of Cognitive Development and Chomsky's Extended Standard Theory (Transformational Syntax). The core of the author's idea is the proposal that there exists a connection between Piagetian operations and operational schemes, on one hand, and Chomsky's Deep Structures from which the sentences describing these operations have been derived, on the other. Two SAT coaching courses have been explored and much literary evidence found in support of this idea. As many as possible examples taken from these books have been included to help teacher's practice. At the end, the author expresses his conviction that this approach can be most generally applied to the formation of a psycho-linguistic basis of using English for specific purposes.