PIAGET HAS PROPOSED THAT THE CONCEPT OF NUMBER IS PREDICATED ON THE CONCEPT OF CONSERVATION OF SUBSTANCE--THAT IS, THE CONCEPT THAT THE AMOUNT OR NUMBER REMAINS THE SAME DESPITE SPATIAL REARRANGEMENTS. BECAUSE OF THE CURRENT EMPHASIS ON REVISION OF MATHEMATICS CURRICULUM AND OF THE APPARENT VALUE OF NUMBER TRAINING TO PRESCHOOL DISADVANTAGED…

This study investigates the relationship between Ghanaian children's acquisition of conservation and their age, parental profession and schooling or lack of schooling. Subjects were 120 females, 40 in each of three age groups (6-7, 8-9 and 10-11 years). Half of the subjects in each group had parents in traditional African professions such as…

Studies concerned with the synchronous emergence prediction of Piaget's structures-of-the-whole principle are discussed in conjunction with three groups of concrete-operational skills: (1) transitivity/conservation/class inclusion; (2) double classification/double seriation; and (3) ordinal, cardinal, and natural number concepts. Findings show…

This paper reviews some of the cognitive and linguistic functions which develop during the period of concrete operational thought (ages 4-9) as defined in Piaget's developmental theory. Discussion centers on the formation of classes and relations and the development of the language associated with these operations. Also discussed are conservation…

This paper proposes a method for teaching number applying the conservation theory of Piaget in the classroom. It is suggested that number facts cannot be taught by social transmission, since there is a fundamental distinction between logico-mathematical and social knowledge. Conservation cannot be taught to non-conservers, but there are ways to…

This book examines the Piagetian periods of concrete operations and formal operations from both educational and psychological points of view. The twin purposes are to interpret these levels and the transition between them in terms of implications for mathematics curriculum and teaching, and to derive psychological implications from experiences in…

This study examined differential performances among groups (categories) of first grade children when solving eight different types of arithmetical word problems under two distinct experimental conditions. The categories of children were actually 4 ability groups: (1) low quantitative comparison scores and low IQ (Lorge-Thorndike IQ Test), (2) low…

Four experiments (involving a total of 158 children) demonstrated observationally-induced learning effects on multidimensional conservation tasks using brief, single session training. First grade samples of middle class Anglo-American, and economically disadvantaged Mexican-American children displayed gains in vicariously-induced conservation as…

Two factor analyses were conducted on data obtained from measurements of the reasoning, moral judgment, and moral conduct of 75 retarded and 75 normal subjects ranging in age from 6 to 18 years. One factor analysis sought to determine relationships between the reasoning variables and standard measures of intelligence and achievement. A second…

The effects of modeling and corrective feedback on the conservation of equalities and inequalities were studied with items spanning three stimulus dimensions (length, number, and two-dimensional space). Observation of a model, correction training (joining positive feedback with verbal rule provision), and the combination of observation and…

Eighteen students, 8 to 15 years of age, from six classes in the School for Language and Hearing Impaired Children in New York City, learned mathematical concepts of conservation, grouping, ordering, and a spatial orientation through procedures developed for teaching and evaluating cognitive achievement of painting and drawing tasks. The students…

This study investigated: (1) the level of thinking of the Iteso Primary School children in Uganda; and (2) whether abilities involved in the Piagetian tasks of conservation, classification, and seriation develop at the same rate. The subjects, ages 6 to 13 (the period of the 7-year African primary school) were interviewed in their own language and…

Mental ages for normals' and for retardates' achievement on 21 Piagetian measures of reasoning are presented in this exploratory longitudinal study. Before standardization data can be provided, a study which involves a more extended sample is necessary. It is, however, suggested that: (1) Normals' (IQ 90-110) transition from concrete to formal…

This paper outlines the syntactic structures which represent a stage in the cognitive development of children, and focusses on an aspect of cognitive development known as conservation. The cognitive components of conservation are presented as the primordial base for the set of syntactic structures which map or mirror them. Piaget proposed four…

Forty-three preschoolers learned the concept of one-to-one correspondence by matched discovery, expository, or observational learning. The groups did not differ on short-term recall and near transfer, but the discovery group excelled on far transfer and delayed recall. The effect of guided discovery on broader learning outcomes was also discussed.…