The author cites research from students' misconceptions of decimal notation that indicates that many students treat decimals as another whole number to the right of the decimal point. This "whole number thinking" leads some students to believe, in the context of comparing decimals, that "longer is larger" (for example, 0.45 is…

The applicability of the identical elements (IE) model of arithmetic fact retrieval (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) to cued recall from episodic (image and sentence) memory was explored in 3 transfer experiments. In agreement with results from arithmetic, speedup following even minimal practice recalling a missing word from an…

The way in which two teachers, Elizabeth and Carolyn, posed problems to develop their own conceptual understanding of division of fractions in terms that would also be meaningful for their students is described. Carolyn and Elizabeth's approach is to pose several problems of various degrees of difficulty and complexity for each aspect of the…

The purpose of this study was to examine preservice mathematics teachers' knowledge about common (mis)conceptions and difficulties of elementary students. In addition, it was aimed to investigate preservice teachers' knowledge about the possible sources of these misconception/difficulties, and their suggested strategies to overcome those…

The present study examines private speech and strategy-use patterns for solving simple number fact problems in addition. The progressive differentiation by grade between children's levels of private speech internalization--including silence--was investigated and related to children's developmental patterns for subcategories of strategy-use…

This article reports the results of a questionnaire applied to secondary school students (n=35) to explore efficiency in the resolution of equations in the domain of whole numbers and the spontaneous responses to problems leading to negative solutions. The most significant results obtained with the questionnaire are the lack of knowledge of the…

Relating natural language to mathematical language is an important component of elementary mathematics education. This paper describes new steps toward a computerized database of addition and subtraction word problems that could provide teachers and students with access to critical natural language terms and expressions for mathematical…

This book aims to present helpful, practical ideas and suggestions for mathematics teaching. Focus is on how teaching can be developed in a Rudolf Steiner (Waldorf) School and includes treatment of mathematical topics applicable to the 7-14 age group. Suggestions for curriculum and examples for children to work on are presented with a very wide…

This six month study investigated the similarities and differences between 137 fourth graders' understanding of and reasoning about multiplication, division, and proportion tasks. All students were administered a pretest mid-year and a posttest at the end of year. A sample of 18 students was interviewed individually on tasks involving reasoning…

This study assessed estimation skills on both static and transformation (conservation) tasks on numerosities ranging from 3 to 16, and included addition and subtraction trials to control for response bias. A total of 148 four- and five-year-old children estimated the number of balls of yarn sewn on elastic straps, and participated in 1 addition, 1…

The impact of summer vacation on the reading and arithmetic skills of 166 learning disabled pupils (6 to 11 years old) was examined. Ss included pupils in resource programs or special classes. Analysis of scores on the Wide Range Achievement Test (reading and arithmetic subtests) before and after summer vacation revealed significant differences in…

Authors analyzed the merits of focusing on the three R's and how each of those skills compared with the other as a priority for student development. (RK)

An experimental test battery (the Johnson O'Connor Research Foundation battery) designed to measure numerical facility was administered to 1,451 subjects at 12 testing centers across the United States over a 5-month period. Five work samples were included: (1) arithmetic; (2) counting backwards; (3) number reasoning; (4) rule learning; and (5)…

As part of a curriculum development project for gifted students, seventh and tenth grades (N=323) were tested with the Structure of Intellect Learning Abilities Test (SOI-LA) to compare students' scores with norms already collected, investigate differences between the sexes, identify specific types of tasks to promote achievement, and to determine…

Described in the context of a computer simulation are highlights of a program of research focusing on the storage of mathematics problem solving information in young children's memory and the development of such knowledge structures in older children. Specifically discussed are the problem size effect, the network nature of the memory…