This document is an English-language abstract (approximately 1500 words) of a new approach to the teaching of mathematics in Mexican elementary schools. Three aspects of mathematical reform are discussed: (1) syllabus content; (2) teaching methods; and (3) the question of introducing the pupil to modern mathematics at the earliest possible stage in his education. The principle of introducing the student to modern mathematics at an early stage has stood the test of experience, as pioneered by Jerome Bruner and Jean Piaget. The project is considered experimental and progressive in nature, and its results should be applied gradually. The second part of the document gives a stage by stage account of the research project. During the second stage, training was given to the team of teachers assigned to the project. The success of the experiment was due to the close cooperation of both technical and administrative authorities and the teachers. The students' work book proved to be an effective learning aid, and their interest was simulated. Tests had to be devised for objective evaluation. (Author/GDB)