The main purpose of this study is focused upon a comparison study between the curriculum and teaching materials of mathematics education of the 1 st-to-6th-grade elementary schools in USA and those in the ROC. From the study, the researcher wishes to find out the differences concerned and the feature and progress of this aspect in USA so as to adept them as a valuable reference for us in the ROC. The information presented in this study is the "Mathematics Objective" published by Boston Public Elementary School Systems. After a comparison study, several conclusions and suggestions are made as follows: 1. Concerning the method of stating the outline of the content, USA adopts "behavioral objectives", which is still, absent in Taiwan, and therefore worthy to be noted as a future direction. 2. Their "problem solving" is identically our 'utilized problem' or 'word problem'. However, our word problem is quite problem-centered, 'but theirs extends to the field of daily lives. Such a method is surely a matter worthy of attention. 3. The Curriculum Objectives in USA are divided into "priority objectives" and "objec-tives". The former allows a common study for all students while the latter allows individual study for the fast-learning students. This is much needed in our country. 4. The heading of categories of the objectives in USA are as Numeration, Computation, Fraction, Decimal and Percentage, Estimation, Geometry and Measurement in the spiral pattern for development. If we are to improve our teaching materials and methods, the spiral curriculum pattern seems to be most likely feasible.