The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis "..." in the real…

Our previous studies provide some evidence of between-language effects on arithmetic performance in 2-year-olds. French-speaking children were especially biased by the use of the word "un" as a cardinal value and as an article in the singular/plural opposition (1 vs. the set 2, 3, ...). Here we evaluated the ability of a new action-based…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

THIS PUBLICATION OUTLINES SOME OF THE TERMINAL BEHAVIORAL OBJECTIVES OF THE ELEMENTARY MATHEMATICS INSTRUCTIONAL PROGRAM. INSTRUCTIONAL OBJECTIVES WHICH SPECIFY EXPLICITLY WHAT SKILLS PUPILS HAVE MASTERED ARE INDICATED FOR MANY OF THE TOPICS OF MATHEMATICS. FOR EACH OBJECTIVE, AT LEAST ONE EXAMPLE IS GIVEN TO CLARIFY THE BEHAVIORAL CRITERION WHICH…

This study was concerned with the development of a consistent and reliable arithmetic achievement test to assess the arithmetic ability of educable mentally retarded youngsters ranging in age from thirteen through sixteen. The instrument so constructed is intended to be administered individually, and it requires the subject to do little reading or…

This curriculum project in general mathematics was planned with two specific objectives--(1) to study the existing curricula, textbooks, and teaching methods in mathematics in higher secondary schools of various states, and (2) to develop a new curriculum in mathematics in light of the objectives of teaching the subject and to try out the…

This is a report of an experiment performed to evaluate the effects of the teaching of non-decimal numeration systems in grades four and six. Eighteen classes consisting of 430 students comprised the sample. The students were divided into four randomly assigned treatment groups for each level. Tests were given before a teaching session of five to…