Examples from some area tasks indicate that misconceptions about linear measurement can be carried over to area measurement; children will occasionally count points rather than length units or area units. (MP)

Some of the literature related to preschool mathematical experiences and their effect on the development of how the child perceives the relationships of mathematics is reviewed. (MP)

Advance organizers may fail to promote learning even though they are approximately related to the main learning experience and internally meaningful and logical. If they are to optimize the likelihood that new materials will be readily and properly subsumed, they must also be constructed to conform to the cognitive preparedness and scholastic…

A presentation of learning experiences involving materials is recommended which reflects the sequence of the developmental stages. This sequence is concrete, concrete-abstract, pictorial-abstract, and abstract. Instructional examples at each level are presented. (JP)

This research study shows that it is possible to advance the use of proportional reasoning of many secondary school students by means of a well-designed teaching program. (MP)

A total of 450 seventh and eighth graders responded to six tasks requiring proportional reasoning and representing different degrees of concreteness. Results showed that more students answered questions correctly when concrete aspects existed, and that about one-fourth of the group was unpredictable in applying proportional reasoning at the formal…

Preservice teachers administered Piagetian tasks to elementary students. On the whole data collected compared favorably with the findings of Renner (EJ 044 727) in showing that students achieved conservation of substance (liquids and solids), length, area, and weight at later ages than stated by Piaget. No significant sex differences were found.…

Reports the results of a study that indicate that junior and senior high school science students are penalized (by receiving lower grades) for not being able to think at the formal operational level. Outlines some methods that may be used to facilitate growth in cognitive development of students. (JR)

Reviews the nature of the spiral approach in the teaching of mathematics and illustrates its use with an example of teaching place value by presenting eight different expressions of this concept. The spiral approach involves building an idea, concept or an algorithm at different times in different manners. (PR)

This discussion is primarily designed to increase teachers' awareness of Piaget's theory of cognitive development and implications for mathematics in the middle school. It is hoped such awareness will compel instructors to adopt strategies that help pupils gain more from mathematical experiences, by providing impetus for innovation and…

Describes a study, involving 120 first grade children, which supports the hypothesis that the rate of attainment of conservation skills is significantly enhanced by experiences made possible by the first grade program of SCIS. Describes the six conservation tasks used for pre-tests and post-tests: number, liquid amount, solid amount, length,…

Some possible uses of math lab materials and activities that are natural and appropriate to the development of process skills are explored through a discussion of a geoboard activity. (MP)

In the experiment discussed, three modes of presenting materials to second grade students were compared. Data analysis showed that the abstract mode was less successful than the others, but there was no clear difference between the manipulative and pictorial modes. (SD)

The mathematics laboratory is described as being not just the use of concrete teaching aids but involving a new philosophy of how children learn and the teacher's role in the facilitation of learning. (CP)

The teacher of mathematics or science must be aware of the concepts, facts, and generalizations of his field, of psychological principles of learning, and of teaching methods. Methods appropriate to the teaching of concepts differ from methods for teaching generalizations. (SD)