A semantic analysis of addition and subtraction word problems in arithmetic

Nesher, Pearla; Katriel, Tamar

doi:10.1007/bf00385925

Cited by 37 publications

(32 citation statements)

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“…However, our findings are consistent with recent evidence that multiplication and division are represented separately (e.g., Campbell, 1999) and with evidence on the relative difficulty of problem solving when using the different operations. For example, there is strong empirical evidence that shows that solving subtraction word problems is more difficult than solving addition problems, regardless of problem type (Nesher, 1982). Likewise, problem solving with division is more difficult than with multiplication, even for students in the eighth grade and above (Reese, Miller, Mazzeo, & Dossey, 1997).…”

Section: Discussionmentioning

confidence: 99%

The representations of the arithmetic operations include functional relationships

2001

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Current theories of mathematical problem solving propose that people select a mathematical operation as the solution to a problem on the basis of a structure mapping between their problem representation and the representation of the mathematical operations. The structure-mapping hypothesis requires that the problem and the mathematical representations contain analogous relations. Past research has demonstrated that the problem representation consists of functional relationships, or principles. The present study tested whether people represent analogous principles for each arithmetic operation (i.e., addition, subtraction, multiplication, and division). For each operation, college (Experiments 1 and 2) and 8th grade (Experiment 2) participants were asked to rate the degree to which a set of completed problems was a good attempt at the operation. The pattern of presented answers either violated one of four principles or did not violate any principles. The distance of the presented answers from the correct answers was independently manipulated. Consistent with the hypothesis that people represent the principles, (1) violations of the principles were rated as poorer attempts at the operation, (2) operations that are learned first (e.g., addition) had more extensive principle representations than did operations learned later (multiplication), and (3) principles that are more frequently in evidence developed more quickly. In Experiment 3, college participants rated the degree to which statements were indicative of each operation. The statements were either consistent or inconsistent with one of two principles. The participants' ratings showed that operations with longer developmental histories had strong principle representations. The implications for a structure-mapping approach to mathematical problem solving are discussed.

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Section: Discussionmentioning

confidence: 99%

The representations of the arithmetic operations include functional relationships

2001

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“…This notion, that too much situational detail can impair abstract understanding and therefore transfer, is prevalent among math educators who design highly generic word problems with few salient details to distract students (Kintsch & Greeno, 1985;Nesher & Katriel, 1977). Most word problems contain only minimal information about situations, in part to help students align situations with underlying mathematical structures (Bassok, 2001).…”

Section: Pedagogical Implicationsmentioning

confidence: 99%

The transfer of abstract principles governing complex adaptive systems

Goldstone

Sakamoto

2003

Cognitive Psychology

250

217

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“…Esto lo planteamos, apegándonos a los procesos atribuidos a la resolución de problemas matemáticos por Nesher (1982Nesher ( , 1992, Vergnaud (1982), Carpenter, Fennema y Romberg (1993), Kieren (1993), Valdemoros y Ruiz (2008), Deliyanni et al (2009), entre muchos investigadores de la aritmética que han desarrollado este recurso.…”

Section: El Problema De Investigaciónunclassified

“…Esto lo planteamos, apegándonos a los procesos atribuidos a la resolución de problemas matemáticos por Nesher (1982Nesher ( , 1992 Al situar a los números decimales en el terreno de la escuela primaria de adultos, estamos enfatizando el carácter elemental de su desarrollo cognitivo inicial y la correspondiente relevancia de su investigación. …”

Section: Introductionunclassified

El Caso de Francisca y el Sentido Otorgado a los Números Decimales

Valdemoros-Álvarez

Ruiz-Ledesma

2017

Bolema

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ResumenEn una investigación cualitativa realizada en una escuela primaria nocturna de la Ciudad de México, desarrollamos este estudio de caso referido a una joven de 19 años, incorporada al quinto grado de esa institución y dependiente de una papelería. Ella resolvió problemas que involucraban el uso de los números decimales y sus operaciones fundamentales. Francisca fue seleccionada a partir de la aplicación de un cuestionario en el que la joven evidenció un desempeño globalmente adecuado, aunque no exento de errores. En el seguimiento del caso de Francisca fueron utilizados dos instrumentos metodológicos: el cuestionario y la entrevista; la última y algunos de sus diálogos fueron el soporte fundamental de este estudio. Nuestra pregunta general de investigación fue: ¿cómo asigna sentido a los números decimales el adulto, cuando resuelve problemas referidos a tales números? Francisca los significó a partir de las situaciones familiares asociadas a sus experiencias de vida y de trabajo; en la resolución de problemas, les asignó sentido al establecer equivalencias entre tales números y los naturales, en primera instancia, aunque también los vinculó con las fracciones. Al idear problemas, la joven privilegió el uso del dinero y de ciertas medidas de longitud expresadas en el sistema métrico decimal. Algunas dificultades de Francisca se mostraron en las interpretaciones posicionales de las cifras decimales y de la notación del punto decimal. Ella exhibió unos pocos errores de lectura, escritura y operacionales ligados a ciertas nociones posicionales inestables. Palabras AbstractIn a qualitative research carried out in a night elementary school in Mexico City, we performed the case study of a young woman of 19 years of age and fifth grade student at the school, who is a stationery's employee. She solved problems, which involved the use of decimal numbers and their basic operations. Francisca chose from a questionnaire in which she evidenced an adequate overall performance although not without errors. Two followup instruments were used in Francisca's case: questionnaire and interview; the latter and some of its dialogs were the fundamental support of this research. Our general research question was: how does the adult assign sense to decimal numbers in the resolution of problems with those numbers? Francisca signified such numbers through familiar situations of life and working experiences. In problem solving, she assigned decimal numbers establishing equivalence between those numbers and mainly natural numbers, while she linked secondly decimal en muchos sujetos que tienden a apoyarse sólo en la poderosa algoritmia de los decimales) y el punto de partida de la ulterior construcción de conceptos referidos a tales números (de estos últimos objetos de estudio no nos ocupamos en la presente investigación).En el proceso semántico de producción de sentido concedemos especial atención a las dificultades cognitivas vinculadas a la resolución de tales problemas (en tanto indicadoras de algunos nodos semánticos primordiales) ...

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A semantic analysis of addition and subtraction word problems in arithmetic

Cited by 37 publications

References 13 publications

The representations of the arithmetic operations include functional relationships

The representations of the arithmetic operations include functional relationships

The transfer of abstract principles governing complex adaptive systems

El Caso de Francisca y el Sentido Otorgado a los Números Decimales

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