Using error analysis and individual interviews, the problem-solving actions of first and second graders were analyzed. Shortcomings of children's knowledge and solution strategies were seen to be overcome by instruction. A control group, with usual arithmetic instruction, and an experimental group were established and the hypothesized…

This study illustrates a process for selecting a preferred model in the validation of hierarchical learning scales. The test performance of 100 8-to 11-year-old children on subtraction tasks involving variations in borrowing are examined. Goodman's response scaling technique is illustrated. (Author/GDC)

The problem was to determine the relationship between performance on Piagetian class inclusion tasks and on missing-addend computation and verbal problem tasks for first-Grade students, and to describe the methods used by the children in solving both the missing-addend and the verbal problem tasks. From 168 first-grade students who received a…

The paragraph unit that constitutes an addition or subtraction word problem text is discussed and the logical conditions such problems must fulfill are formulated. An attempt is then made to formulate the semantic conditions which will define well-formed addition and subtraction texts. (MN)

Specific instruction in different contexts provide needed background for solving addition and subtraction problems. The categories of problems and relative difficulties are presented, followed by an explanation of a successful instructional sequence. (MNS)

Children, 9-11 years old, solved subtraction problems in the form of M-N=..., then gave a verbal report on the thought processes used, analysis of which utilized a model based on analyses of reaction times, and resulted in a more detailed process model. (AN)

Analyzed conceptual and linguistic complexities of matching situation word problems. Found a four-level progression in conceptualizing and solving these problems: Relational ("who had more/less" but not "how much more/less"); Language Cue (equalizing or compare language); Understand Matching Situations (difference between two…

Solution processes for simple arithmetic word problems are examined in three dimensions: the order of mention, the identity of the unknown, and the type of verb. The influence of mathematical and linguistic factors in these processes are discussed. (BJG)

The purpose of this study was to ascertain whether children in grade 3 who differ in cognitive processing capacity add and subtract differently. The researchers drew upon information from three sources: individual results from a battery of 14 tests, an objective-referenced achievement test measuring a variety of arithmetic skills related to…

The study concerns the performances of first grade children in solving problems involving subtraction situations and the relationship of these performances to levels of conservation of numerousness and to I.Q. groups. The subjects were grouped into levels of conservation by a pretest administered prior to the main test of problem solving in…

Suggestions for improving problem-solving skills of first-grade students are made after the results of five studies of addition and subtraction story problems are presented. (JT)

This guide contains classroom-tested problems designed to introduce and reinforce mathematical concepts in a quick, "fun" way. Activities emphasize the logic and reasoning skills needed to build a strong foundation in mathematics. The problems are thinking activities and require only elementary level mathematics skills. Activities are…

Presented is an example of how a child adopted an incorrect method for solution to arithmetic sentences. Methods for detecting and correcting this behavior are discussed. (JP)

Problems focusing on number theory that can make good use of the calculator in discovering and proving simple theorems are proposed. The focus is on the properties of subtracting the smaller of a three digit number and its mirror number from the larger in a process that leads to zero. (MP)