Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 269-281). Available also in a digital version from Dissertation Abstracts.

Children’s counting strategies, such as counting from one or by groups of tens, reflect how much they understand the place-value structure of numbers. In a novel task for assessing place-value concept, namely the strategic counting task, children were asked to count small squares, which were arranged with or without correspondence to the base-ten number structure. The counting strategies of kindergarteners and first graders revealed that children developed from perceiving number as an undivided entity to seeing it as a collection of independent groups of tens, indicating a trend of increasing place-value understanding. First graders’ strategic counting task scores at the end of fall semester predicted their mathematical achievement at the end of spring semester, over and above age, intelligence, and measures of simple counting, number representation, place-value understanding, and arithmetic calculation. Based on item analysis, a brief version containing only five items was developed for more user-friendly classroom administration. First graders’ scores in the brief version uniquely predicted their mathematical achievement even at the end of second grade. Growth curve modeling revealed that children who were low mathematics achievers at the end of second grade had already shown poor performance in the brief version in early first grade and remained lagging behind their peers over the 18 months. Early poor understanding of place-value concept, then, seems to persist to upper grade and impede mathematical development. Implications for early support to children with difficulties in place-value concept were discussed. / published_or_final_version / Psychology / Doctoral / Doctor of Philosophy

The purpose of this study was to find some remedy to frustrations engendered when children fall to grasp the essential principle of place value after several attempts at reteaching. It was hypothesized that these children must have failed to acquire understanding of some numerical principle(s) prerequisite to understanding the place value aspect of the numeration system. Four plausible prerequisite principles were identified (1) synthesis of ordinal and cardinal properties of the numeration system, (2) both the addition and subtraction operations, (3) understanding of counting by groups, and (4) understanding of exchange equivalences such as one ten for ten ones, etc. It was hypothesized that understanding of analog clock reading was also dependent upon understanding of the same four prerequisite principles. By conducting four pilot studies, six interview protocol instruments were developed to measure levels of understanding for the four prerequisite principles and the place value and clock reading criterion principles. Three levels of understanding: no understanding, transitional understanding, and competence were designated to correspond with Plagetian stages in the development of a new operation. Forty-eight children, twenty with second grade completed and twenty-eight with third grade completed, were tested on all six instruments. Hypotheses tested were: (1) if the four identified prerequisite principles are necessary to understanding of place value, then subjects will demonstrate a level of understanding on the place value measure no higher than their lowest level of understanding achieved on the four prerequisite measures; and (2) if the four identified prerequisite . principles are necessary to understanding of clock reading, then subjects will demonstrate a level of understanding on the clock reading measure no higher than their lowest level of understanding achieved on . the four prerequisite measures. The findings were that both hypotheses were supported at the .01 probability level. Analysis of the research design and examiner observations suggested possible explanations for anomalous aspects of the obtained data. Limitations, directions for further research, and implications for teachers were also discussed. / Ph. D.

This investigation examined Chinese children's development of place-value numeration concepts from ages 3 through 9, compared the development of place-value understanding of these Chinese children with that of American and Genevan children whose performances had been described in the literature, and examined the influence of adult assistance during Chinese children's performances on some of the place-value tasks.

The purpose of this study was to examine my own practice of teaching place value and the influence virtual manipulatives had, in addition to physical manipulatives, on place value understanding of my second grade students. I wanted to see how adding a base-ten computer applet might better meet the needs of all learners while also meeting the needs of today’s technological classroom. Through this study, I found that both physical and virtual manipulatives helped students acquire place value concepts. I found that virtual manipulatives had features that engaged students in a way that increased their mathematical language, increased students’ ability to represent more conceptual understanding of composing and decomposing numbers, and express enthusiasm towards mathematics. A pretest and posttest revealed that students’ academic performance increased. While research on virtual manipulatives and mathematical achievement is fairly recent, this study offers insight to other classroom teachers and the research community.