Recent Trends in Mathematics Curriculum Research Marogt Critchfield Project Solo, University of Pittsburgh 15260 Mathematics curriculum reform in the last 10 years (1964-74) cannot be as neatly characterized as that of the decade which preceded it. The years 1954-64 saw the rise of a 'glamour movement,' the 'new mathematics,' which markedly changed the subject matter of school mathematics. The principal mechanism used to effect these changes was textbook writing. The change was accomplished with unusual swiftness and a good deal of publicity. A number of different research projects were involved, and yet there appears to have been unanimity regarding the changes needed and the topics to be incorporated. It is this period of research which most strongly influences school practice today, and which is subject to the greatest scrutiny. By contrast, the ten years of research 1964-74 have not yet had a widespread influence on actual school practice. Also, the unanimity of the earlier period appears to have dissipated considerably during the second. (I suspect that a deeper analysis of the earlier period might reveal more diversity, as well.) There are a number of developing trends in the period 1964-74; I will discuss three of these, which I consider most important. First, there appears to be a change in the attitude of professional educators toward curriculum research. I consider this to be as important as the development of any new movement. Evidence of this can be seen in a booklet put out by the National Council of Teachers of Mathematics in 1968 . ln contrast to a previous booklet with similar cover design and similar title put out in 1961 , this collection of articles is generally cooler and contains more diverse viewpoints. While calling for still more changes in the curriculum (and for much the same reasons as the earlier book), it does so only after having described the problems as having many different facets. It calls for greater care on the part of school decision makers in choosing from the available curriculum projects. "They should not accept change simply because it is the current fad, nor should they assume it is successful simply because it is new." Some of the most prominent topics of the new math sets, non-decimal number bases, and axiomatics come in for criticism, although no blanket condemnation is expressed: "it will become increasingly necessary, however, for educators to make value judgments as to which topigs must be stressed heavily for which children. Significantly, I think, the pamphlet encourages local district curriculum development, which it felt had gone into a decline with the emergence of large-scale, national curriculum projects. "Some local directors of curriculum apparently have decided that the period of curriculum-making at the school or district level was over and that the challenge now was to select the best program available that had been developed by the 'experts'...the 'best' may consist of a selection of useful topics from several programs." This second booklet spotlights the provocative curriculum suggestions of the Cambridge Conference on School Mathematics (CCSM) at the very front. (CCSM will be the second major trend discussed here.) However, the authors of this pamphlet appear to find many problems that are not helped by CCSM and the controversy it sparked. By 1973, this cooler attitude seems to have 'congealed'. The report of an NSF sponsored conference that summer, made the following statements  : "There is a substantial lack of trust and communication between the mathematics education community in the universities and that in the schools. Efforts need to be instigated to reestablish cooperation." "At the present time, there seems to be no clear consensus with regard to the mathematics which should be taught in K-12 and there is an urgent need for a program which will examine societal needs and delineate the goals of mathematics education with sufficient authority to provide a broadly acceptable base for curriculum development." The second important trend of research activity is what term a continuation and intensification of the spirit of 'new math.' The Cambridge Conference on School Mathematics (CCSM) held its first meeting in June, 1963. It was a brainstorming session, not a textbook writing one, but its recommendations fit into the category of wanting "more and better mathematics" in schools. Further, many of the old 'new math' approaches and topics, if not their current implementation, were re-affirmed in its recommendations. CCSM produced Goals for School Mathematics in 1964  and went on to write two more documents, Goals for Mathematical Education of Elementary Teachers, 1966  and Goals for the Correlation of Elementary Science and Mathematics, 1969 , as well as experimental units embodying their goals. CCSM's goals, although accompanied by warnings that they were tentative and not to be used as a blueprint, were an audacious challenge by intellectuals to the schools and curriculum developers. "...thirteen years of mathematics in grades K to 12 should [give] a level of training comparable to three years of top-level college training today; ... two years of calculus, and one semester each of modern algebra and probability theory,"  "We propose to gain three years through a new organization of the subject matter and the virtual total abandonment of drill for drill's sake ,... "  Some of the other features mentioned in CCSM's 1963 report were: (1) "...the parallel development of geometry and arithmetic (or algebra in later years) from kindergarten on." (2) "...structure of the real number system and the basic ideas of geometry both synthetic and analytic...considerable attention...to inequalities in the earliest grades." (3) "'spiral' curriculum which repeatedly returns to each topic, always expanding it and showing more connections with other topics." (4) "(K-6) should be understandable by virtually all students; it should lead to a level of competence well above that of the general population today."