Algebra as a study of quantitative relationship is one of four conceptions of school algebra which serves as a foundation for the concept of function. However, there is still a lack of attention to this particular relationship, especially in early algebraic reasoning. This study aims to investigate how the aspect of quantitative relationship in…

The first idea that must be understood by the students to learn the concept of concept of conservation of area is recomposing shape. In recomposing shape, the students will see the fact that the shape can be transformed into a different form without adding or losing the part of the shape. So the students could conclude that the area of the shape…

This article describes some aspects of Piaget's Theory of Cognitive Development. It highlights the importance of giving young children specific access to explore conservation in measurement, which will give students invaluable experiences in measurement that in years to come will be regarded as their prior knowledge of the concept. This is…

Reported is a study which measured conservation of length among kindergarten and first-grade subjects using several verbal and nonverbal procedures. The results indicated that conservation of length is not a simple unitary concept, but has empirical gradations. (Author/CT)

Investigated was the feasibility of inducing number conservation through training kindergarten children on reversibility tasks not related to the criterion measure. (JG)

Forty students from the first, second, fourth, and sixth grades (10 from each), equally balanced for sex and representing a middle class SES, were individually administered mathematical tasks of matching, equality, cardination, and measure and Piagetian conservation task of number, length, and surface or area. (NQ)

Four levels of quantitative comparisons based on Piagetian task analysis and three IQ levels were used to partition a population of 341 first grade children. Each child was then tested on a set of addition facts and a set of addition problems which varied according to the use of aids or transformation. (JG)

This study investigated the relationship between conservation of length and impulsive-reflectivity. Kindergarten and first-grade students were administered two conservation of length tasks and an impulsive-reflexive scale. No statistically significant relationship between the two concepts was found. (FL)

The effects of numerical and visual cues, equality or inequality of initial volumes, size of measurement unit, and order of cue presentation on conservation of liquid volumes by first- and second-graders were investigated. Some findings extend, and others contradict, those of Piaget. (SD)

Reported are the results of an investigation of the child's acquisition of the concept of area measure. To measure this acquisition, four axioms were developed to define the concept of area. A task was developed for each axiom to test operational understanding of the axiom. A test of vocabulary and a conservation of area task were administered to…

The purpose was to investigate the influence of variations in conservation form and perceptual modality on the expressed level of understanding of the conservation of weight concept, and to determine if these variations result in significantly different observed rates of concept development. Sampling included 225 children, five to twelve years…

The goal of this study was to investigate improvement in the usage of equivalence and order relations under specified instructional conditions. Forty-eight upper middle class kindergarten children were given a 14-session pretreatment designed to define two equivalence and four order relations of length and matching, followed by tests of…

Tested was a method of learning numeration, addition, and subtraction using measuring operations in place of the more usual counting operations. It is claimed that an approach through "units of measurement" to continuous variables is mathematically more powerful than counting, which leads only to nominal and ordinal variables. Twelve children…

Discussed are the results of interviews with 63 Australian children (interviewed in English) and 62 Nigerian children (62 interviewed in English and 60 interviewed in Yoruba) to determine how they used number concepts in discussing five demonstrations manipulating physical matter. Differences between the two groups are considered. (RH)

Children were grouped according to ability to conserve number and then randomly assigned to training on arithmetic concepts or playing a game. The research hypothesis that there would be an interaction effect between conservation and effect of treatment was not confirmed. (SD)