One hundred students, 25 each in grades 2, 4, 6, and 8, were individually interviewed. A cylindrical beaker with five equidistant levels marked on it was presented first, and a pear-shaped separation funnel was also presented. The funnel had a "faucet" at the bottom that allowed water to start and stop running into the beaker. The interviewer…

Based on Piaget's theory of logico-mathematical knowledge, 126 students in grades 2-5 were asked 6 questions about elapsed time. The main reason found for difficulty with elapsed time is children's inability to coordinate hierarchical units (hours and minutes). The educational implications drawn are that students must be encouraged to think about…

This book describes and develops an innovative program of teaching arithmetic in the early elementary grades. The educational strategies employed are based on Jean Piaget's constructivist scientific ideas of how children develop logico-mathematical thinking. The book is written in collaboration with a classroom teacher and premised on the…

Fifty 1-to 3-year-olds were asked to imitate: (1) the rolling of a cylinder down an incline and (2) the making of an incline with a board and a block. Their incorrect imitations and progress were videotaped and analyzed, and interpreted in light of Piaget's theory about the elaboration of logico-mathematical relationships in an interrelated way.…

Shares the results of a study in which 204 first grade students were interviewed. Interprets the findings in light of Piaget's emphasis on abstraction. Concludes that children represent ideas at their respective levels of abstraction. (Author/ASK)

Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)

Equivalent fractions are usually introduced in fourth grade and reviewed repeatedly in the subsequent grades as the four arithmetical operations are taught. In spite of this repeated instruction, the results are disappointing. This paper reviews some data from previous research documenting the difficulty of equivalent fractions, explains this…

Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

Views education as vital in reducing violence. Emphasizes Piaget's view of the aim of education--moral and intellectual autonomy--as the way to teach children to resolve conflicts without resorting to violence. Discusses what Piaget means by autonomy, the changes it entails in classroom practices, and how these changes are likely to reduce…

In individual interviews, 220 students in grades 4, 6, 8, and 9 were given one task, and 72 eighth graders were given three tasks to answer two questions: (a) Is a square the unit of measurement for an area for students in grades 4-8? and (b) Does a square have a space-covering characteristic for students in grade 8? The answers to both questions…

Guided by Piaget's constructivist theory on how children learn, this book explores an innovative approach to teaching physical knowledge in preschool. Part 1 differentiates between "science education" and "physical-knowledge" activities, noting that physical-knowledge activities involve primarily movements of objects and changes in objects. This…

Maintains that young children learn to think when they act on objects, thus developing what Piaget refers to as physical and logico-mathematical knowledge. Teachers can encourage thinking/mental action by creating situations that are personally meaningful to the children, by providing decision-making opportunities, and by providing opportunities…

Presents evidence from data on how well five first-grade classes did without any formal instruction showing that if children's numerical reasoning is strong, then formal instruction of missing addends is unnecessary. Explains the findings in light of Piaget's constructivism and discusses educational implications. (ASK)

Presents a method of teaching two-column addition which the authors argue is based on Piaget's theory and fosters the children's own natural thinking. The method does not use objects such as straws bundled or base-ten blocks. (PK)

Investigates children's difficulty in understanding (numerical) place value. A counting and estimating task, based on Piaget's number theory, was devised to determine if children in grades one through five evidenced this construction. (Author/BB)