Addition Word Problems Research Articles

Influence of Irrelevant Information in Addition Word Problems on Problem Solving

The purpose of this study was to investigate the problem-solving performance of learning disabled students and their peers. Irrelevant linguistic and numerical information embedded within addition word problems was presented to matched groups of subjects. Whereas irrelevant numerical information negatively affected pupil performance, irrelevant linguistic information did not affect performance. Learning disabled students exhibited lower accuracy levels and problem-solving rates than grade-age peers. Implications of these findings are discussed in terms of students' problem-solving processes as well as educational programming for learning disabled pupils.

An Analysis of Addition and Subtraction Word Problems in American and Soviet Elementary Mathematics Textbooks

Current theories of how elementary school children solve addition and subtraction word problems have emphasized semantic characteristics of the problems as the major factor influencing ease of solution. The present study assesses the potential impact the instructional environment (textbooks, in particular) might have on the relative difficulty of different types of addition and subtraction word problems by comparing the presentation of word problems in four American textbook series with the corresponding presentation in one Soviet textbook series. In general, the four American text series were found to resemble each other but to differ markedly from the Soviet text series. Several important findings emerged: (a) Distribution of word problems across the various problem types was extremely uneven in the American texts, with two thirds of all problems being of only three simple one-step problem types. The Soviet problems were distributed over many types, including more complex two-step problems; (b) most of ...

Teaching Children to Add by Counting-On With One-Handed Finger Patterns

Three experiments report classroom instruction derived from cognitive research and focused on moving children across two developmental transitions: from counting-all to counting-on with entities present for the second addend and from the latter to counting-on as a number-word sequence solution procedure to solve symbolic single-digit addition problems. For the second transition, a new particularly efficient method of keeping track of number words counted-on was taught: counting-on with one-handed finger patterns. Classroom teachers were able to teach both kinds of transitions to most first and second graders, even to first graders below average in mathematics. Many first graders spontaneously transferred counting-on with finger patterns to the solution of addition word problems; some required instruction to do so. Most children were readily able to extend counting-on with finger patterns to counting up with finger patterns for subtraction. Counting-on with finger patterns was procedurally efficient enough to be used in instruction in multi digit addition problems; second graders successfully learned to use counting-on with finger patterns to add 10-digit numbers. Teaching these transitions to children permitted them to learn addition and subtraction topics from 1 to 4 years earlier than is usual in American schools.

Brief Report: Cognitive Functioning and Performance on Addition and Subtraction Word Problems

The question addressed in this paper is, Do children in the third grade who differ in cognitive-processing capacity solve addition and subtraction word problems differently? Information from a more extensive study (Romberg & Collis, 1983) was used to examine this question.

Cognitive Functioning and Performance on Addition and Subtraction Word Problems

The question addressed in this paper is, Do children in the third grade who differ in cognitive-processing capacity solve addition and subtraction word problems differently? Information from a more extensive study (Romberg & Collis, 1983) was used to examine this question. The question was initially raised in the Coordinated Studies in Mathematics Project at the Wisconsin Center for Education Research (Romberg, Carpenter, & Moser, 1978). That longitudinal project studied the development of strategies children use to solve verbal addition and subtraction problems that differ in their semantic structure (see Carpenter & Moser, 1984, for a summary of that work). The project was related to a host of international studies being conducted on the influence of semantic structure of word problems on performance and the use of strategies (see Carpenter, Moser, & Romberg, 1982). In this study the cognitive-processing capacity of children was related to the strategies they use to solve word problems. Cognitive-processing theories are based on the idea that mental functions can be characterized by the way information is stored, accessed, and operated on. Mental functions are discussed in terms of an intake register through which information from the environment enters the system, a working or short-term memory (M-space) in which the actual processing occurs, and a long-term memory in which knowledge is stored. For this study, measures of M-space and quantitative processing were combined to determine cognitive functioning. The working memory's growing capacity to process information appears as a fundamental characteristic of cognitive development in a number of theories (Bruner, 1966; Case, 1978a; Flavell, 1971). Young children are quite limited in their ability to deal with all the information demands of complex

Children’s Thinking in Arithmetic Word Problem Solving

AbstractChildren’s arithmetic problem solving was studied in the context of addition and subtraction word problems, half of each kind requiring carrying or borrowing. Response latency and error data indicated that subtraction was uniformly more difficult than addition and that carrying or borrowing introduced extra difficulty as well. Analysis of the kinds of errors children made was conducted in terms of the important distinction between systematic rule-based errors, “bugs,” and nonsystematic calculation or working memory errors, termed “slips.” The subjects’ verbal reports were also analyzed, revealing a rich variety of strategies used in solving the problems. Aside from using the taught algorithm for two-digit additions or subtractions, subjects demonstrated many “invented” strategies, many of them tailored to the nature of the problem being solved. The understanding of children’s word problem solutions in terms of flexible strategy use and the realization that many errors have a lawful, systematic bas...

The Acquisition of Addition and Subtraction Concepts in Grades One through Three

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problemsolving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.

The Acquisition of Addition and Subtraction Concepts in Grades One through Three

Children's solutions to simple addition and subtraction word problems were studied in a 3-year longitudinal study that followed 88 children from Grades 1 through 3. The children were able to solve the problems using a variety of modeling and counting strategies even before they received formal instruction in arithmetic. The invented strategies continued to be used after several years of formal instruction. Four levels of problem-solving ability were found. At the first level, children could solve problems only by externally modeling them with physical objects. Modeling strategies were gradually replaced with more sophisticated counting strategies. The results of the study are at variance with important aspects of models of children's performance proposed by Briars and Larkin and by Riley, Greeno, and Heller.

Untersuchungen zum Lösen eingekleideter Aufgaben

The purpose of this study was (a) to examine the addition and subtraction procedures used by kindergarten- and first-grade-children on orally presented problems, (b) to reexamine the research in several countries on different categories of addition and subtraction word problems, and (c) to compare the attitude of children K — 6 to word problems in mathematics.

The effect of instruction on children's solutions of addition and subtraction word problems

This study investigated the effect of initial instruction on the processes children use to solve addition and subtraction word problems. Prior to instruction and following a two-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different addition and subtraction situations. Prior to instruction, the children's solution processes directly modeled the action or relationships described in the problem. Following instruction, they generally used a separating strategy for all subtraction problems. Although they could solve the problems, few children could coordinate their solutions with the arithmetic sentence they wrote to represent the problem.

A semantic analysis of addition and subtraction word problems in arithmetic

A semantic analysis of addition and subtraction word problems in arithmetic