Develops a division algorithm in terms of familiar manipulations of concrete objects and presents it with a series of questions for diagnosis of students' understanding of the algorithm in terms of the concrete model utilized. Also offers general guidelines for using concrete illustrations to explain algorithms and other mathematical principles.…

In a large-scale field experiment aimed at improving spelling instruction in Dutch schools, the effectiveness of a newly developed algorithmic teaching method was compared with the conventionally and commonly used analogy approach. The analogy group showed comparatively little progress in learning results. (Seventy-five test items are appended).…

Investigated the continuous fraction concepts of (n=59) students in grades four, five, and six. Students were confident and accurate when performing sharing tasks, but were much less successful on continuous quantity tasks involving formal fraction language and symbol manipulation fraction tasks. (14 references) (Author/MKR)

A 14-year-old Brazilian boy in the fourth grade was given 170 problems orally, each asking for the sum of 2 2-digit numbers. Responses indicated he had invented his own algorithm for addition, similar to the school one, based largely on his experiences with money. (Contains 13 references.) (JAF)

Studied the ability of logical test design (LTD) to predict student performance in reading Roman numerals for 211 sixth graders in Mexico City tested on Roman numeral items varying on LTD-related and non-LTD-related variables. The LTD-related variable item iterativity was found to be the best predictor of item difficulty. (SLD)

Computational strategies and estimating abilities of 466 Japanese students were tested and interviews with a subsample of that group were used to compare with a theoretical model based on a sample from the United States. Results of the comparison of computational and estimating abilities are presented. (CW)