Children's Symbolic Representation of Addition and Subtraction Word Problems

1990 ◽  
Vol 21 (2) ◽  
pp. 123-131
Author(s):  
Harriett C. Bebout
Keyword(s):  
Word Problems ◽  
First Graders ◽  
Symbolic Representation ◽  
Problem Types ◽  
Addition And Subtraction ◽  
Types Of Change ◽  
Informal Strategies

Forty-five first graders were categorized into three levels according to their informal strategies for solving addition and subtraction word problems. They were taught to write canonical and noncanonical open number sentences to symbolically represent the structure of eight types of Change and Combine word problems. Their performances on the posttest indicated that children at each level were successful in learning to symbolically represent and solve the instructed problem types.

Representation of Addition and Subtraction Word Problems

1988 ◽  
Vol 19 (4) ◽  
pp. 345-357 ◽  
Author(s):  
Thomas P. Carpenter ◽  
James M. Moser ◽  
Harriett C. Bebout
Keyword(s):  
Young Children ◽  
Word Problems ◽  
First Graders ◽  
Standard Form ◽  
Second Graders ◽  
Simple Addition ◽  
Mathematical Symbolism ◽  
Addition And Subtraction ◽  
Informal Strategies

This study investigated children's ability to write number sentences for simple addition and subtraction word problems. First graders taught to represent problems with open number sentences (e.g., 5 + □ = 8) represented a variety of problems with number sentences that directly modeled the action in the problems. First graders taught to represent all problems with number sentences in standard form (a + b = □, a − b = □) were limited in the problems they could represent. Second graders could represent problems directly with open number sentences or transform them to number sentences in standard form. The results, consistent with research on solutions using modeling and counting strategies, suggest that open number sentences may provide mathematical symbolism that allows young children to build upon informal strategies for representing and solving simple word problems.

The Effect of Semantic Structure on First Graders' Strategies for Solving Addition and Subtraction Word Problems

1987 ◽  
Vol 18 (5) ◽  
pp. 363-381 ◽  
Author(s):  
Erik De Corte ◽  
Lieven Verschaffel
Keyword(s):  
Word Problems ◽  
First Graders ◽  
Semantic Structure ◽  
Problem Structure ◽  
Related Research ◽  
Solution Strategies ◽  
Simple Addition ◽  
School Year ◽  
Longitudinal Investigation ◽  
Addition And Subtraction

In a longitudinal investigation, data were collected on the problem representations and solution strategies of 30 first graders who were given a series of simple addition and subtraction word problems (Verschaffel, 1984). The children were interviewed three times during the school year, and data obtained on their solution strategies and on the influence of problem structure on the strategies. The results complement those of recent related research, especially the work of Carpenter and Moser (1982, 1984). More precisely, the influence of problem structure on children's solution strategies appears even more extensive and decisive than that described by previous researchers.

scholarly journals Parsing Algebraic Word Problems into Equations

2015 ◽  
Vol 3 ◽  
pp. 585-597 ◽  
Author(s):  
Rik Koncel-Kedziorski ◽  
Hannaneh Hajishirzi ◽  
Ashish Sabharwal ◽  
Oren Etzioni ◽  
Siena Dumas Ang
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Word Problems ◽  
Single Equation ◽  
Manual Annotation ◽  
Arithmetic Operations ◽  
Discriminative Models ◽  
Small Set ◽  
Addition And Subtraction

This paper formalizes the problem of solving multi-sentence algebraic word problems as that of generating and scoring equation trees. We use integer linear programming to generate equation trees and score their likelihood by learning local and global discriminative models. These models are trained on a small set of word problems and their answers, without any manual annotation, in order to choose the equation that best matches the problem text. We refer to the overall system as Alges.We compare Alges with previous work and show that it covers the full gamut of arithmetic operations whereas Hosseini et al. (2014) only handle addition and subtraction. In addition, Alges overcomes the brittleness of the Kushman et al. (2014) approach on single-equation problems, yielding a 15% to 50% reduction in error.

scholarly journals The Degree of Abstraction in Solving Addition and Subtraction Problems

2007 ◽  
Vol 10 (2) ◽  
pp. 285-293 ◽  
Author(s):  
Vicente Bermejo ◽  
Juan José Díaz
Keyword(s):  
Developmental Stage ◽  
Primary Education ◽  
First Graders ◽  
Fourth Grade ◽  
First Grade ◽  
Second Graders ◽  
School Grade ◽  
Levels Of Abstraction ◽  
Direct Modeling ◽  
Addition And Subtraction

In this study, the incidence of the degree of abstraction in solving addition and subtraction problems with the unknown in the first term and in the result is analyzed. Ninety-six students from first grade to fourth grade in Primary Education (24 students per grade) solved arithmetic problems with objects, drawings, algorithms, and verbal problems. The participants were interviewed individually and all sessions were video-taped. The results indicate a different developmental pattern in achievement for each school grade depending on the levels of abstraction. The influence of the level of abstraction was significant, especially in first graders, and even more so in second graders, that is, at the developmental stage in which they start to learn these arithmetic tasks. Direct modeling strategies are observed more frequently at the concrete and pictorial level, counting strategies occur at all levels of abstraction, whereas numerical fact strategies are found at higher levels of abstraction.

CLASSROOM ACTIVITIES FOR ABLE STUDENTS: In Kindergarten, First and Second Grades

1981 ◽  
Vol 28 (6) ◽  
pp. 48-54
Author(s):  
Edward C. Rathmell ◽  
Larry P. Leutzinger
Keyword(s):  
Word Problems ◽  
Major Part ◽  
Learning Experiences ◽  
Primary Grades ◽  
Primary Teachers ◽  
Instructional Time ◽  
Classroom Activities ◽  
Addition And Subtraction ◽  
Subtraction Facts

A major part of the instructional time devoted to mathematics in the primary grades involves helping children learn to count, read and write numerals, memorize basic addition and subtraction facts, add and subtract twodigit numbers, tell time, count money, and solve word problems. Since many able students already know or quickly learn these topics, primary teachers are faced with the problem of providing appropriate learning experiences for these children while the remainder of the class is learning them.

Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

1990 ◽  
Vol 21 (3) ◽  
pp. 180-206 ◽  
Author(s):  
Karen C. Fuson ◽  
Diane J. Briars
Keyword(s):  
School District ◽  
First Graders ◽  
Second Graders ◽  
Teaching Approach ◽  
Second Grade ◽  
Place Value ◽  
Urban School District ◽  
Value System ◽  
Number Words ◽  
Addition And Subtraction

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from five to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N=169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N=75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N=783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N=707) completing subtraction work learned at least four-digit subtraction.

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