Number Sentences: Linking Addition and Subtraction Word Problems and Symbols

1991 ◽  
Vol 22 (4) ◽  
pp. 266-280
Author(s):  
Deborah A. Carey
Keyword(s):  
Word Problems ◽  
First Grade ◽  
Semantic Structure ◽  
Large Numbers ◽  
Addition And Subtraction

Twenty-four first-grade children were asked to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Responses were qualitatively different across five clusters of children. Clusters were characterized by the degree of flexibility in accepting alternative number sentences for word problems. Children in all clusters could write and select open number sentences, such as a+□ =b and □ −a=b, that matched the semantic structure of problems for word problems with small and large numbers. Only the more advanced children could identify standard number sentences, a+b=□ and a−b=□, as appropriate representations for all addition and subtraction word problems. Flexibility in selecting alternative number sentences was related to number size, suggesting that knowledge of number relationships plays a role in the development of a general understanding of part-whole relationships.

Young Children Are Good Problem Solvers

1982 ◽  
Vol 30 (3) ◽  
pp. 24-26
Author(s):  
James M. Moser ◽  
Thomas P. Carpenter
Keyword(s):  
Problem Solving ◽  
Young Children ◽  
Word Problems ◽  
First Grade ◽  
Educational Progress ◽  
National Assessment ◽  
Comparison Problem ◽  
Addition And Subtraction ◽  
Problem Solvers ◽  
Good Problem

Do you think many first-grade children could solve this comparison problem? Joe won 6 prizes at the fair. His sister Connie won 9 prizes. How many more prizes did Connie win than Joe? Most curricular programs apparently assume that word problems are difficult for children of all ages, and that children must master symbolic addition and subtraction operations before they will be able to solve even simple word problems. Recent National Assessment of Educational Progress (NAEP) results (Carpenter et al. 1980) also give some credence to the belief that children are poor at problem solving. We believe. however, that young children are good problem solvers.

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.

Teachers' Pedagogical Content Knowledge of Students' Problem Solving in Elementary Arithmetic

1988 ◽  
Vol 19 (5) ◽  
pp. 385-401
Author(s):  
Thomas P. Carpenter ◽  
Elizabeth Fennema ◽  
Penelope L. Peterson ◽  
Deborah A. Carey
Keyword(s):  
Student Achievement ◽  
Problem Solving ◽  
Pedagogical Content Knowledge ◽  
Content Knowledge ◽  
Word Problems ◽  
First Grade ◽  
Problem Difficulty ◽  
Pedagogical Content ◽  
Addition And Subtraction

This study investigated 40 first-grade teachers' pedagogical content knowledge of children's solutions of addition and subtraction word problems. Most teachers could identify many of the critical distinctions between problems and the primary strategies that children used to solve different kinds of problems. But this knowledge generally was not organized into a coherent network that related distinctions between problems, children's solutions, and problem difficulty. The teachers' knowledge of whether their own students could solve different problems was significantly correlated with student achievement.

scholarly journals Analysis of Word Problems in Primary Education Mathematics Textbooks in Spain

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2123
Author(s):  
Raúl Tárraga-Mínguez ◽  
Julio Tarín-Ibáñez ◽  
Irene Lacruz-Pérez
Keyword(s):  
Primary Education ◽  
Word Problems ◽  
Educational Institution ◽  
Educational Practice ◽  
Low Complexity ◽  
Semantic Structure ◽  
Mathematics Textbooks ◽  
Situational Contexts ◽  
Official Curriculum ◽  
Teaching Learning

A textbook constitutes the hegemonic material of the educational institution. It acts as a mediator between the official curriculum and the educational practice. Given its potential influence in the classroom, this study analyzes the treatment of word problems included in the mathematics textbooks published by the publishing houses with the greatest diffusion in Spain at every primary education grade. Three variables were analyzed: their semantic structure, their degree of challenge, and their situational context. The results indicate that most of the problems included in textbooks are characterized by low complexity and variability regarding their semantic structure. They are also characterized by a limited degree of challenge and by being presented in highly standardized situational contexts. Likewise, it is found that there is no evolution in the treatment of these problems with respect to previous studies carried out in the Spanish context. Therefore, it is concluded that the mathematics textbooks currently used in schools are not effective tools to address the process of teaching-learning problem solving.

Becoming an Adult Member in a Community of Learners

2001 ◽  
Author(s):  
Eugene Matusov
Keyword(s):  
Classroom Interaction ◽  
Teaching Experience ◽  
First Grade ◽  
Second Grade ◽  
Paper Strip ◽  
Strip Line ◽  
Classroom Structure ◽  
School Year ◽  
Design Activities ◽  
Addition And Subtraction

I thought it would be relatively easy for me, with my six-year background of high school teaching and tutoring of math and physics, to co-op in the OC classroom with my first-grade son. I was both right and wrong. Indeed, my teaching experience and professional knowledge as a graduate student in child psychology helped me design activities suitable for first- and second-grade children. However, in terms of philosophy of teaching and organization of learning activities, my experience with traditional schooling was more harmful than helpful. My previous experience prepared me for delivering a lesson to a whole class or an individual. I was used to controlling children’s talk, which was supposed to be addressed only to me, and my students had learned early on in their schooling that they could talk legitimately only to the teacher and only when it was allowed by the teacher. The teacher was supposed to be the director, conductor, and main participant in classroom interaction. In the OC, I was shocked to discover that this traditional format of instruction was actively discouraged by teachers, co-opers, and children. This kind of teaching was not supported by the children in their interactions or by the classroom structure, with its small-group organization, children’s choice of groups, and nonsimultaneous rotation of the children from group to group. However, I did not know how to teach any other way. At the beginning of the school year I planned an activity that I called Magic Computer. It was designed to teach the reversibility of addition and subtraction as well as reading and computational skills, and it had worked beautifully with first- and second-graders in the past. The activity involved moving a paper strip that carried “computer commands” (“Think of a number. Add five to it. Take two away from it,” and so on) through an envelope with a window, to see one command at a time. The commands were designed so that addition and subtraction compensated for each other; therefore, the last message was “You have got your initial number!” The children’s job was to discover addition and subtraction combinations that cancel each other out and write them down on the paper strip, line by line.

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.

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