Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises…

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also…

When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this…

This study investigated the relationships between children's home literacy environments and their early hypotheses about printed words in the year prior to entering school. There were 147 children (70 girls and 77 boys: mean age 57 months, range = 47-66 months, standard deviation = 4.5 months) in the study. Results showed that the children had…

In the Slovenian National Mathematics Curriculum the probability contents are first mentioned in the ninth grade of elementary school (at the age of 14), yet they are introduced informally, only in some first triad textbook sets. The researchers disagree as to the age of children at which they are able to deal with certain probability contents. In…

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and…

Two studies trace children's acquisition of counting as a means to extract, compare, and reproduce number from arrays of objects. Study 1 examined 3-, 4-, and 7-year-olds' use of counting to compare and reproduce arrays numerically. In study 2, nine of the 3-year-olds from the study 1 were retested after 12 and 18 months. (Author/JMB)

In a replication study, children 3 and 4 years old were given verbal rule training in order to probe the importance of identity, reversibility, and compensation explanations in training number and length concepts. Among the results, as before, identity was found to be the most significant factor in conservation acquisition. (Author/RH)

In this study children between the ages of 3 and 6 years were each presented with six number problems in which length and density were varied according to the proposed composition rules. (Authors)

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

Available from: British Medical Journal, 1172 Commonwealth Avenue, Boston, Massachusetts 02134. In order to determine whether Central Nervous System irradiation effects intellectual abilities, 28 children in remission at least 2 years after completing chemotherapy for acute lymphoblastic leukemia were assessed on standardized psychological tests…

Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…

In order to describe developments in children's conceptions of numbers and numerical relations, judgments of similarities between numbers were solicited from adults and from children in kindergarten and grades 3 and 6. A nonmetric multidimensional scaling analysis suggested that children gradually become sensitive to an expanding set of numerical…

Piaget's organismic-developmental theory of intelligence was investigated in this study to determine the effectiveness of training middle class 3 and 4 year olds on two logico-mathematical structures: classification and seriation. Twenty-four children were divided into two main age groups (mean ages: 3 years 8 months; 4 years 5 months). Within…