A relationship was postulated between the experienced difficulty of patterns and the amount of disorientation of their reproduction. It was proposed that the underlying factor, in the comparison of Africans to Europeans, might be the development of the concept of horizontality, which reduces dependence on the perceptual pull of the prevailing…

The development of abstract mathematical thinking is an essential part of mathematics and the geometry is regarded as a suitable domain to serve this purpose. As different technologies such as computers and graphing calculators are widely being used, curriculum developers on geometry should take these technologies into consideration. Several…

Although mathematics deals with generalizations relating abstract ideas, very little attention has been given in the mathematics education literature to the role of abstraction and generalization in the development of mathematical knowledge. In this paper, the meanings of "abstraction" and "generalization" are first explored by…

Nearly a quarter of a century ago, John G. Nicholls proposed the four developmental levels of motivational reasoning that focused upon the roles that ability and effort play in academic success. These levels theoretically begin at early childhood and end at adolescence. This report attempts to validate the developmental and predictive nature of…

Activities designed for primary children to develop the geographic concepts of spatial arrangement and location, as well as to build basic map skills, are outlined. (Author/KM)

This paper analyzes common practice and the difficulties children encounter and outlines an entre to mathematics learning which may make the child's task easier. (Author)

The relationship between verbal reasoning ability on the one hand and sex, social class, family size, and ordinal position in the family on the other were examined for a representative sample of 11-year-old Irish children. (Authors)

Article describes an experiment to deterimine how to promote cognitive growth in terms of classroom mathematics learning. (MM)

Two selection and nine evaluation hypothesis testing tasks varying systematically with respect to causality, response alternatives, and context continuity were administered to two samples of adults (N=35; N=32). It was to determine effects of these variables and the degree to which subjects reasoned with material conditional, biconditional,…

A test was given to 322 secondary students to develop a profile of mathematical ability based on four components: computation, pattern recognition, logical reasoning, and symbolic manipulation. These profiles were compared to mathematics test scores; the results verified hypotheses about individual differences in mental processes and knowledge…

Extends earlier studies investigating possible relationships between student aptitudes and different modes of mathematical instruction. In the study, college students were exposed to either a verbal-pictorial-numeric treatment or a verbal-symbolic-numeric treatment in quadratic inequalities. Interactions between instructional treatment and…

Explored deductive inference processes in concept learning in four age groups. Results confirm findings of age differences in concept problem solving, with likelihood of solving the problem lower in older adults. However, solvers of all ages made the same correct inferences. (Author/JAC)

Until recently, norms of experimental reasoning have lacked systematic theoretical development. Thus, it has been easy for psychologists like Tversky and Kahneman to misclassify certain human reasoning processes as being Pascalian and invalid, rather than as being Baconian and valid. (CP)