Characteristics of 5th Graders' Logical Development Through Learning Division with Decimals

Okazaki, Masakazu; Koyama, Masataka

doi:10.1007/s10649-005-8123-0

Cited by 14 publications

(13 citation statements)

References 17 publications

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“…This explanation supports Okazaki and Kaoyama's (2005) research which highlighted the difficulties of 5th grade children in learning division with decimals.…”

Section: Attitude Scalessupporting

confidence: 87%

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Bragg¹

2007

Math Ed Res J

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Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This paper reports on the methodological dilemma of resultant conflicting attitudinal data related to game-playing. Concerns arising from the divergence in the results are raised in this paper. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.Mathematical games are popular with teachers as alternatives to more traditional forms of repetitive practice, for many parts of the mathematics curriculum, and especially for arithmetical computation. The research literature, as well as popular commercial publishing, supports the idea that games can fire children's interest and motivation because students enjoy competition, challenge, and fun (Bragg, 2003;Bright, Harvey, & Wheeler, 1985;Ernest, 1986;Gough, 1999;Owens, 2005).This research began by assuming that a novel pedagogical approach, such as game-playing, might have a positive effect on students' classroom engagement and attitudes towards mathematics. What is reported here is based on a larger study which explored games as a pedagogical approach to enhance mathematical learning (see . Games were examined in that larger study for their potential to promote mathematical learning, but that aspect is not reported in this paper. Surprisingly, triangulation of the data revealed conflicting attitudinal responses from the students about games. These attitudinal data were collected via Likert scales and student interviews. This paper focuses on the methodological difficulty of interpreting conflicting results and raises some possible explanations as to the contradictory nature of these data. Background and Theoretical FrameworkAttitudes

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“…This explanation supports Okazaki and Kaoyama's (2005) research which highlighted the difficulties of 5th grade children in learning division with decimals.…”

Section: Attitude Scalessupporting

confidence: 87%

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Bragg¹

2007

Math Ed Res J

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“…En contraste con el planteamiento anterior, Okazaki (2003) afirma que en el aprendizaje de las operaciones con números decimales, los estudiantes tienden a privilegiar los procedimientos algorítmicos asociados a dichas operaciones, permaneciendo relegadas las elaboraciones del pensamiento, las que requieren ser fortalecidas a través de una enseñanza pertinente.…”

Section: Los Números Decimales Sus Operaciones Y Las Dificultades Counclassified

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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“…In an analysis of mathematics textbooks, Sun (2011) illustrated that partitive division extends beyond whole numbers as divisors to tasks with any rational number divisor. Similarly, Okazaki and Koyama (2005) cite Vergnaud (1983) to offer that partitive division can be conceived as finding the unit value (quantity per one unit), whether or not divisors are whole numbers. Cengiz and Rathouz (2011) assert that learners may be unsure about how to handle a quantity shared with a number of groups that is not a whole number; they include problem situations with fractions as divisors as examples of partitive division tasks.…”

Section: Partitive Divisionmentioning

confidence: 99%

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

Jansen

Hohensee

2015

J Math Teacher Educ

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The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient) and flexible (i.e., capable of differentiating between opportunities to partition or iterate (or both) when solving a partitive division task; aware that partitioning or iterating (or both) could be associated with the operation of division, as appropriate). Seventeen PSTs participated in task-based interviews prior to instruction in a mathematics content course for teachers. These PSTs demonstrated disconnected conceptions of partitive division with fractions when they incorrectly translated between representations and either inconsistently or did not express awareness that the purpose of the task was to generate a unit rate. These PSTs demonstrated rigid conceptions of partitive division with fractions such that they did not express awareness that the process of iterating could be associated with the operation of division, even when they obtained a correct answer by iterating. Results extend prior research by looking beyond PSTs' performance on tasks to elaborate upon PSTs' conceptions of the operation of partitive division. This study contributes new insights into PSTs' conceptions that can be used by mathematics teacher educators to inform the design of future instructional interventions.

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Characteristics of 5th Graders' Logical Development Through Learning Division with Decimals

Cited by 14 publications

References 17 publications

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

Students’ conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma

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

Examining and elaborating upon the nature of elementary prospective teachers’ conceptions of partitive division with fractions

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