Starting with Woodworth and Thorndike's classical experiment published in 1901, major periods in mathematics education throughout 20th century and on into the current century are reviewed in terms of competing epistemological and psychological paradigms that were operating within as well as across the major periods. The periods were marked by…

Leslie Steffe, among the foremost mathematics education researchers in the world, has had a profound influence on three generations of researchers. In 2006, he received the first-ever Senior Scholar Award from the AERA Special Interest Group: Research in Mathematics for the excellence and seminal nature of his work. Steffe shares his thoughts…

This study was concerned with the effects of selected experiences on the ability of preschool children to use conservation of length and conservation of length relations. The experiences involved the equivalence relation "the same length as" and the two order relations "shorter than" and "longer than." The subjects were 51 four and five year old…

Examined were differential performances among categories of first graders when solving arithmetical workd problems of eight types under two distinct conditions. The categories were based on various types of quantitative comparisons which children are known to make. Several statistically significant results were obtained involving differences…

This study was designed to test the effects of a sequence of 12 lessons on the ability of kindergarten and first-grade children to recognize and conserve numerousness. Two pretests were administered to the children in each grade level, the Lorge-Thorndike Intelligence Test (nonverbal) and a test of numerousness. One post-test, the test of…

Four levels of quantitative comparisons based on Piagetian task analysis and three IQ levels were used to partition a population of 341 first grade children. Each child was then tested on a set of addition facts and a set of addition problems which varied according to the use of aids or transformation. (JG)

The goal of this study was to investigate improvement in the usage of equivalence and order relations under specified instructional conditions. Forty-eight upper middle class kindergarten children were given a 14-session pretreatment designed to define two equivalence and four order relations of length and matching, followed by tests of…

The author defends the teaching of thinking strategies. (MK)

Six seven-year-old children were interviewed to investigate the quality of their solutions to whole-number tasks. Detailed analyses are provided of interviews with a girl who displayed an operative counting scheme (numerical extension) and a boy with a figurative counting scheme (intuitive extension). (MNS)

Theory and research concerning the development of spatial concepts by young children are discussed. Results of Martin and Kidder are compared with those of Piaget. (SD)

This essay considers recent research on classification as related to the study of mathematics in the early grades. The first section deals with the bases and types of classification used by children in free sorting activities. The next section specifically relates to elementary school mathematics. Experiments and theory on class inclusion,…

This report presents the results of a teaching experiment which investigated (1) the role of mathematical experiences on the development of counting, addition, subtraction, mental arithmetic, classification, and other arithmetical topics and (2) the role of quantitative comparisons and class inclusion as readiness variables for learning the…

Six tests were constructed, four on a pictorial level and two on a symbolic level, to measure the performance of fourth-, fifth-, and sixth-grade children, in three different ability groups, on problems concerning ratios or fractions. Two variables were of interest in the four tests on a pictorial level: (a) "equal" ratio situations vs.…

Research findings related to children's concepts of length, area, volume, weight and time are reviewed. Implications for instruction in measurement of these qualities are discussed. (SD)