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.…

The aim of this study was to show that the superiority of corrected-for-guessing scores over number right scores as true score estimates depends on the ability of examinees to recognize situations where they can eliminate one or more alternatives as incorrect and to omit items where they would only be guessing randomly. Previous investigations…

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)

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

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)

This paper describes how a target group of seven students in a combined fourth and fifth grade mathematics class used structured representations to solve fraction problems situated within various realistic contexts. Emphasis is given to the ways in which students' thinking about rational number concepts influences and is influenced by the…

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

Two studies are reported that explore the effectiveness of instruction in promoting students' conceptual understanding of the average concept using a leveling model and an open-ended problem-solving approach. One teacher and her 46 sixth-grade students participated in the first study. One year later, the second study was conducted with the same…

Using data from 135 sixth-, seventh-, and eighth-graders between 11 and 15 years old attending a middle school in a suburban Southwest Ohio school district, two hypothesized models of the factor structures for the Coopersmith Self-Esteem Inventory were tested. One model represents the original Coopersmith factor structure, and the other model is…