The child's ability to identify numerousness as a property of a set, distinct from all the other properties of that set, may be a prerequisite to conservation of numerousness of sets. To test this theory, 11 lessons designed to develop the ability to identify properties of objects and of sets of objects and to represent length and numerousness…

Students were pretested, then 27 first graders were trained using a highly verbal procedure emphasizing class addition activities. On posttests, trained subjects significantly improved their class inclusion and number conservation scores, but no effects were found for substance conservation or transitivity. (DT)

This study tested 148 preschoolers between the ages of 48 and 72 months on a Piagetian number conservation task. Children's judgment accuracy, estimation, and response latency were measured. Children were also questioned about the number conservation principle. A four-step developmental sequence was hypothesized: (1) nonconservation; (2) correct…

Forty kindergarten children at the Stephen Bull School in Racine, Wisconsin were tested to determine the effects of a sequence of 12 experimental lessons on the ability of kindergarten children to recognize and conserve numerousness. Subjects were 40-low-to-middle socioeconomic level children divided into treatment and control groups. A specially…

The study attempted to trace the relationship between facility with cardinal-ordinal aspects of number; attention to dimensions of number, length, and density; and the presence and absence of number conservation. On the basis of performances on the standard test for number conservation, 25 nonconserving kindergarteners, 34 conserving…

Study tests four predictions derived from Piaget's cognitive theory. (CB)

A combination of readiness and body-part training was the most effective in producing number conservation with external objects. (Authors)

Critics assert that Piaget's tests seriously underestimate operational thinking by failing to consider experimenter and presentation variables. This experiment studied the impact of these social influences on number conservation performance. Subjects viewed videotapes in which the task was presented by an adult or by puppets. Presentation mode…

A group of 161 kindergarten and first grade children were instructed in mathematics using exercises in linear measurement to increase understanding of unit-quantity relations. A comparison group made up from two adjacent and comparable middle-class schools was taught mathematics without intervention into the mathematics content. Treatment and…

The study concerns the performances of first grade children in solving problems involving subtraction situations and the relationship of these performances to levels of conservation of numerousness and to I.Q. groups. The subjects were grouped into levels of conservation by a pretest administered prior to the main test of problem solving in…

The objective of this study was an attempt to clarify the nature of number conservation with number conservation tasks using variations in length, area, and volume. According to Piagetian theory, conservation is attained successively for number, length, area, and, finally, volume. It was hypothesized that success on the number conservation tasks…

The main problem of this study was to attempt to determine the source of adults' nonconservation error as well as to explain young children's apparent success. Subjects were 188 children from elementary school, high school, and college. (Author/MP)

Results are discussed in terms of why children of the same age fail to conserve number in the standard conservation task and how complex number concepts might develop. (Author)

An investigation was conducted with 200 first-grade students to determine whether language is a major factor in conservation of number experiments. It was concluded that language was not a major factor. (RP)