Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

Through the historical analysis of Dienes' works and through the suggestions of activities, the objective of this text is to understand the movement of systematization of knowledge for teaching and to teach classification, ranking, and ordination through the use of logical blocks during the Modern Mathematics Movement (1960-1980), a time of…

The "Building Blocks PreK Math Curriculum" (Clements & Sarama, 2007) was designed to facilitate children's engagement in math and talk about math. Much research investigates the effect of curriculum on classrooms or teacher practices. This study used a mediational model to look at a curriculum's effect on children's achievement gain, operating…

Choosing challenging problems to facilitate student learning of new mathematics is a difficult task so by using open-ended problems with prospective mathematics teachers, the potential solution characteristics were studied. It is shown that considering the conceptual diversity of solutions helps students develop a better sense of different…

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith,…

Describes methods for explaining advances in mathematics teaching to parents. Explains important points to be made, followed by examples of how the Everyday Mathematics program responds to each issue. Examples of points include Teachers as Facilitators, Subject Integration, Focus on Reasoning and Problem Solving, Emphasis on Communication, Meeting…

In this paper we present three cases of instructional design that illustrates both horizontal didactising, the activity of using already established principles to design instruction, and vertical didactising the activity of developing new tools and principles for instructional design. The first case illustrates horizontal didactising by…

The aggregate findings of experiments with modern mathematics for the last 30 years show that there have not been many detrimental effects of "new math" either on achievement or attitude. Instead, the evidence points toward beneficial effects in terms of improvement in overall achievement and attitude. (Author/BW)

The main purpose of the present study was to identify and examine the concerns of primary school teachers in Cyprus in relation to the recent implementation of a new mathematics curriculum and the use of new mathematics textbooks. An adaptation of the Stages of Concern Questionnaire (SoCQ) based on the Concerns-Based Adoption Model (CBAM) was…

Seventh grade students (N=9) from a small rural school in Ridgway, Colorado were exposed to a teacher-developed individualized program in modern math during the 1962-63 school year and again the following year. The students were divided into an average and above group and a below average group; group assignments were determined by IQ scores, the…

Questionnaires administered to 3,500 math teachers explored professional background, learning objectives, classroom organization, teaching techniques, and textbook use. Apparently math teaching has changed little in 15 years; little impact of "new math" was seen. Moreover, teachers considered computational skills and algebraic manipulation as most…

The main objective of this document is to give an outline of the reform movement within mathematics education in the United States from 1951 until the late 1970's. The reform movement is divided into three phases which are distinguished by certain features common to events of the period. The material is divided into the following main chapter…

The purpose of this study was to evaluate the appropriateness and effectiveness of current high school mathematics curricula for students in technical and vocational education programs. Students in 21 Wisconsin high schools were surveyed; administrators and chairmen of mathematics departments in these schools were also interviewed. Results…

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…

Reports on a study of the move away from abstract calculations toward "mathematics in context" among 50 British female secondary school students. Discusses implications of findings in relation to reported female underachievement and disinterest in school mathematics. (CFR)