After evaluating a proposal by Jon Star (2005) that mathematics educators reconceptualize the construct of procedural knowledge, we offer an alternative reconceptualization based on an extension and amalgamation of his and other conceptualizations of procedural knowledge and conceptual knowledge. We then propose some implications for research…

This study evaluated the efficacy of a preschool mathematics program based on a comprehensive model of developing research-based software and print curricula. Building Blocks, funded by the National Science Foundation, is a curriculum development project focused on creating research-based, technology-enhanced mathematics materials for pre-K…

Ordering theory was used in two studies to empirically determine hierarchies of developmental precedence for Piaget's 16 logical combinations. In study 1, subjects (N=94) responded to statements about odd and even numbers; in study 2, 30 subjects responded to statements about line segments. Results are reported and discussed. (Author/JN)

Five preservice teachers' perceived sources of teaching decisions were studied as they proceeded through a secondary mathematics education methods course and through student teaching. Sources cited most often included methods course content, school textbooks, suggestions made during teaching episodes in the methods course, past teachers'…

Describes the van Hiele levels of reasoning in geometry according to responses to clinical interview tasks concerning triangles and quadrilaterals. Subjects were 13 students from grades 1 through 12 plus a university mathematics major. Students' behavior on tasks was consistent with the van Hiele original general description of the levels.…

Data were collected on mathematics achievement, spatial visualization ability, student attitudes, sex, parent attitudes, and student career interests of 1982 seventh- and eighth-grade students from 13 midwestern junior high schools. Parent attitudes and student career interests were significant predictors of mathematics achievement over and above…

Investigated long-term retention of mathematical concepts in a Keller plan course conducted without a final examination as compared to a conventional lecture course with a final examination. Results indicate greater long-term retention of concepts for students taking a traditional lecture course with final examination rather than the Keller plan…

Over 600 pupils in grades five, seven, and nine in Italian schools were asked to choose the operation needed to solve 26 multiplication and division word problems. The findings seemed to confirm the impact of the repeated addition model on multiplication and of the partitive model on division. (MNS)

Fourth-grade students' understanding of the order and equivalence of fractions was investigated in an 18-week teaching experiment. Three related characteristics of thinking are hypothesized to be related to success of such tasks, involving flexibility and reasoning that becomes increasingly independent of specific concrete embodiments. (MNS)

Fifty Brazilian children aged seven-13 were individually given addition and subtraction exercises. Counting was the preferred procedure, with use of school-taught algorithms limited. Some children decomposed numbers into tens and units and then worked at both levels. They rarely referred to previous results when doing related exercises. (MNS)

Students from six fourth-grade classes were paired and randomly assigned to computer or worksheet treatments on multiplication and division. Those using computer-based drill-and-practice programs made greater gains on some tests of basic facts, but had no higher retention of algorithms. (MNS)

This study: (1) documented the spontaneous derived facts strategies (DGSs) that second-grade children (N=23) used; (2) investigated how training in use of DFSs influenced the solution strategies children used to solve addition and subtraction problems; and (3) examined the role of DFSs in the transition to recall of number facts. (JN)

Examined the potential of using repeated rate-of-response measures to identify students exhibiting difficulties in arithmetic. Second-grade students (N=30) were followed over two years. Pearson product-moment correlations were computed to determine the ability of rate-of-response measures to predict arithmetic achievement. Results indicate that…

Forty-eight students with no previous exposure to probability or statistics read one of three textbooks that varied in emphasis placed on rote and conceptual learning of basic elementary probability concepts. Findings, among others, show students who read textbooks emphasizing conceptual learning tended to be less sensitive to surface features.…

Determined whether 11 third-grade children, differing in cognitive processing capacity, solve addition and subtraction word problems differently. Results, among others, show that children who differ in cognitive processing capacity also differ in strategies they use to solve the same verbal problems and differ in their success in finding correct…