This paper provides a general overview of the forces that contributed to the rise and fall of the "new math" movement. It is noted that the movement developed as a response to certain problems in mathematics education; these problems remain to be solved. Some small-scale successes were achieved, from which we can learn. The answer to…

This set of transparencies shows how the manipulation of combinatorial structures in the context of modern combinatorics can easily lead to interesting teaching and learning activities at every level of education from elementary school to university. The transparencies describe: (1) the importance and relations of combinatorics to science and…

The process of change and development of the mathematics curriculum in the United States is reviewed. Fundamental changes of implemented curricula from 1960-1980 are discussed in the light of the considerable efforts at reform during the 1950's and 1960's. Elements of the educational system are mapped out, and reasons for the lack of effective…

The life cycle of "new math" is fertile ground for the study of the diffusion of an innovation. New math arrived in 1958 to save the day for America after the Soviet Union launched Sputnik, the first successful space flight in 1957. In a period of 16 years an entire diffusion cycle was completed throughout the entire educational system…

This paper discusses some findings of research studies developed in Italy on the approach to theoretical knowledge. Two examples are discussed in detail: (1) a classroom discussion concerning the shift from an empirical to a theoretical compass in primary school (fifth grade); and (2) the scheme of a teaching experiment on overcoming conceptual…

In 1964 the island of St. Lucia began the St. Lucia Mathematics Program, a five-year program designed to develop materials and a primary level program of modern mathematics for use in the English-speaking Caribbean territories. Representatives from the ministry of education, the teachers' college, and the University of the West Indies Institute of…

Based on the assumption that each student learns in a unique way, this paper outlines the factors to be considered before selecting the methods of instruction for particular mathematics courses and their students. The advantages and disadvantages of the lecture/textbook and question/answer method, individualized instruction, self-pacing,…