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…

This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area…

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…

Displays that by themselves always elicited chance judgment of number were shown to three- to four-year-olds and six- to seven-year-olds. The first display was transformed into the second, and so on. Results indicated that three- to four-year-olds do not understand conservation of number because judgements of successive displays were independent…

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)

The major objective of this study was to investigate differential performances among 5-year-old children when using transitivity of matching relations. Instruments were constructed to measure the subjects' (1) knowledge of matching relations, (2) ability to conserve the relations, and (3) proficiency in making inferences using the transitive…

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

One major purpose of this investigation was to determine and compare the effects of three different perceptual situations (screening, neutral, and conflict) on kindergarten and first grade children's ability to use the transitive property of the equivalence relation "same length as" and the two order relations "longer than" and…

Thirty mildly retarded children (mean age 9 years) participated in a study in which 24 of the children were trained to a prespecified criterion on one of three logical operations tasks involving length: identity conservation, equivalence conservation, or transitivity. (Author)

A central component in the young child's construction of a number system is an understanding of correspondence. Although current research demonstrates that preschool children use correspondence in a variety of tasks, the nature of the relationship between the use of correspondence action patterns and the use of correspondence as a quantifier is…

Research supported by National Science Foundation grant GE-3 to the University of Minnesota.

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)

An exploratory study involving three days of brief instruction in a process-by-attribute approach. Significant performance gains were recorded. (MM)