Children's Symbolic Representation of Addition and Subtraction Word Problems

Bebout, Harriett C.

doi:10.2307/749139

Cited by 13 publications

(6 citation statements)

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“…Several studies have been conducted concerning the use of number sentences for solving addition and subtraction word problems, either by asking pupils to write a number sentence corresponding to a given problem (Bebout, 1990; Carey, 1991; Carpenter, Moser & Bebout, 1988), or by asking them to choose from among several number sentences the one that they would write for the problem (Carey, 1991). Indeed, several correct number sentences were observed for the resolution of the same problem (Bebout, 1990; Brissiaud, 1994; Carey, 1991; Carpenter et al ., 1988). Pupils who find the right numerical solution, 39, to the MA‐problem S [3 + □ = 42] might, for instance, write 3 + 39 = 42, which is the number sentence that directly models the problem, but they might use some arithmetic knowledge and write 39 + 3 = 42 (use of commutativity) or 42 – 3 = 39 (use of subtraction).…”

Section: Methodsmentioning

confidence: 99%

“…Indeed, children are often required to identify as quickly as possible the operation to solve a word problem (Verschaffel & De Corte, 1997). For example, ‘7 + 5 = 12’ is a number sentence corresponding to the use of a situation strategy for a problem such as S [7 + □ = 12], and the pressure towards the use of the standard number sentence (12 – 7 = 5) may generate failures (Bebout, 1990; Carey, 1991; Carpenter, Moser & Bebout, 1988). For a problem such as D q [ = 30], the risk is even higher because a number sentence that directly models the problem is ‘10 + 10 + 10 = 30’.…”

Section: Methodsmentioning

confidence: 99%

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Arithmetic word problem solving: a Situation Strategy First framework

Brissiaud

Sander²

2009

Developmental Science

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Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing the numerical solution is the representation of the problem modified so that the relevant arithmetic knowledge might be used. Three experiments were conducted with Year 3 and Year 4 children. Subtraction, multiplication and division problems were created in two versions involving the same wording but different numerical values. The first version could be mentally solved with a Situation strategy (Si version) and the second with a Mental Arithmetic strategy (MA version). Results show that Si-problems are easier than MA-problems even after instruction, and, when children were asked to report their strategy by writing a number sentence, equations that directly model the situation were predominant for Si-problems but not for MA ones. Implications of the Situation Strategy First framework regarding the relation between conceptual and procedural knowledge and the development of arithmetic knowledge are discussed.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Arithmetic word problem solving: a Situation Strategy First framework

Brissiaud

Sander²

2009

Developmental Science

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“…Other authors have reported the same finding (Bebout, 1990;Bermejo et al, 1998;De Corte & Verschaffel, 1987), observing that children were more successful solving problems of change with the unknown in the result.…”

Section: Analysis Of Results and Discussionmentioning

confidence: 53%

“…However, this level decreases when the unknown is located in the second term, and even more so when in the first term (Bebout, 1990;Bermejo, 1990;Carpenter, Hiebert, & Moser, 1981De Corte & Verschaffel, 1987).…”

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confidence: 98%

The Degree of Abstraction in Solving Addition and Subtraction Problems

Bermejo

Díaz

2007

Span. J. Psychol.

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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. Keywords: abstraction level, arithmetic problems, strategies, mathematical developmentEn este estudio se analiza la incidencia del grado de abstracción en la resolución de problemas de suma y resta con la incógnita en el primer término y en el resultado. Noventa y seis alumnos de primero a cuarto curso de Educación Primaria (24 escolares por curso) resuelven tareas aritméticas con objetos, dibujos, algoritmos y verbales. Los participantes se entrevistaron de manera individual y se registraron en vídeo todas las sesiones. Los resultados indican un patrón evolutivo diferente en el rendimiento para cada curso escolar según los niveles de abstracción. Resulta significativa la influencia del nivel de abstracción sobre todo en primero y más aún en segundo curso, es decir, en el momento evolutivo en que se inicia el aprendizaje de estas tareas aritméticas. Las estrategias modelado directo se manifiestan más en el nivel concreto y pictórico, las estrategias conteo ocurren en todos los niveles de abstracción, mientras que las estrategias hechos numéricos se encuentran en los niveles de mayor abstracción. Palabras clave: nivel de abstracción, problemas aritméticos, estrategias, desarrollo matemático

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“…The students' thinking about simple arithmetic problems has been widely researched (Bebout, 1990;Carpenter, Moser & Romberg, 1982;Carpenter, Ansell, Franke, Fennema, & Weisbeck, 1993;Christou & Philippou, 1998;De Corte & Verschaffel, 1993;Fuson & Briars, 1990;Kamii, Lewis & Kirkland, 2001;Nesher, Greeno, & Riley, 1982;Siegler & Booth, 2004;Vergnaud, 1982). Moreover, researchers have stressed that the students' ability to successfully cope with one-strep arithmetic word problems is affected by various factors, including the wording of the problems and the way information is presented, the students' familiarity with mathematical language, their ability to execute an operation and their short-term memory (Geary, 1994;López, 2014;Reed, 1999;Riley, Greeno & Heller, 1983;Stern, 1993).…”

Section: Mathematical Thinking In One-step Addition and Subtraction Wmentioning

confidence: 99%