A progression in first-grade children’s thinking about variable and variable notation in functional relationships

Blanton, Maria; Brizuela, Bárbara M.; Gardiner, Angela Murphy; Sawrey, Katharine; Newman-Owens, Ashley

doi:10.1007/s10649-016-9745-0

Cited by 50 publications

(44 citation statements)

References 23 publications

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“…Students represent the result of generalization verbally and symbolically. It is according to a previous study was found that students in first grade can learn to think in sophisticated ways about variable quantities and variable notation (Blanton et al 2017). Students show correspondence verbal rule in this study by generalizing pattern correspondence.…”

Section: Discussionsupporting

confidence: 66%

“…Recursive to correspondence symbolic rule used by students to find "formal generalization" (Amit & Neria, 2008). The previous study showed the representation of generalization varying quantities in a different way; there are by a verbal, table, graph, or symbolic (Blanton et al 2017;Blanton & Kaput, 2004, 2005Warren et al 2006). This study showed that elementary students represent generalization in two ways that are verbally and symbolically.…”

Section: Discussionmentioning

confidence: 99%

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Elementary students’ functional thinking: From recursive to correspondence

Syawahid

Purwanto

Sukoriyanto

et al. 2020

Journal for the Education of Gifted Young Scientists

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This study aims to identify elementary students' functional thinking processes in solving pattern problems. Previous studies showed that elementary students' functional thinking still often experience errors in solving pattern problems. The study of the functional thinking process in solving pattern problems is a fundamental key as a solution to find out the strengths and weaknesses of elementary school students, so that they are better prepared in generalizing relationships, representing and analyzing function behavior in advanced algebra classes. This study used a descriptive qualitative approach with a case study method. Participants of study was sixty-five elementary students who had not yet received generalization patterns material. The instruments were tasks and interview guidelines. Based on the task results, students who had correct answers were chosen using purposive sampling to be given an in-depth interview. The finding indicated that elementary students are able to think functionally in different ways. Students' functional thinking begins with recursive thinking in the pre-finding formula in the entry stage. Students find the formula by corresponding thinking in the attack stage. Finally, students use the formula to get inverse in the review stage.

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Section: Discussionsupporting

confidence: 66%

Section: Discussionmentioning

confidence: 99%

Elementary students’ functional thinking: From recursive to correspondence

Syawahid

Purwanto

Sukoriyanto

et al. 2020

Journal for the Education of Gifted Young Scientists

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“…Las cuestiones que son de nuestro interés han sido investigadas previamente a través de estudios longitudinales que se han centrado en el aprendizaje a lo largo del tiempo y utilizan progresiones y trayectorias de aprendizaje como herramientas para comprender y representar el desarrollo de la comprensión de los estudiantes (Stephens et al, 2017). Por ejemplo, Blanton y colaboradores han propuesto trayectorias hipotéticas sobre la generalización (Blanton et al, 2015) y sobre la apropiación de la notación de la variable (Blanton et al, 2017). A diferencia de estos estudios, este trabajo busca aportar al estudio de la generalización a partir de un seguimiento detallado del proceso efectuado por cada estudiante en una sola sesión de clases.…”

Section: Pna 15(3)unclassified

“…Atendemos así a una línea de investigación abierta señalada por Kaput (2009) y complementamos investigaciones previas sobre el desarrollo de pensamiento algebraico desde los primeros cursos que describen cómo los estudiantes logran establecer la relación entre las variables y expresarlas de diversas formas por medio de representaciones convencionales tales como tablas, notación algebraica o gráficos (e.g. Ayala-Altamirano y Molina, 2020;Blanton et al, 2017;Ureña et al, 2019).…”

Section: Pna 15(3)unclassified

El Proceso de generalización y la generalización en acto. Un estudio de casos

Ayala-Altamirano

Molina

2021

pna

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A partir de un análisis microgenético del proceso de generalización de tres estudiantes de cuarto de primaria, se describe cómo construyen, dan sentido y expresan una relación funcional en un contexto de resolución de problemas. Los resultados contribuyen a la comprensión y reflexión sobre la integración del enfoque funcional en las aulas de primaria. Se distinguen diferentes grados de sofisticación en el proceso de generalización según los medios semióticos empleados. Uno de los estudiantes expresa de forma explícita la generalización mientras que en los otros dos casos queda implícita en las acciones de los estudiantes sugiriendo una incipiente conciencia sobre lo indeterminado o presencia de la analiticidad.

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“…Recently, research on early algebra has gained increased interest [1]- [6]. Some of the main initial ideas behind the early algebra movement were to determine: (a) whether elementary students can really start learning algebra [7] and (b) if the initial exposure to basic algebraic concepts can alleviate the very difficulties that adolescents face in algebra in secondary education [8].…”

Section: Introductionmentioning

confidence: 99%

The Use of Bring Your Own Device-based Learning to Measure Student Algebraic Thinking Ability

Rudyanto

Marsigit

Wangid

et al. 2019

Int. J. Emerg. Technol. Learn.

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Many students have algebraic difficulties in learning. This is proven by the fact that students having dif-ficulty facing algebraic elective courses in the 7th semester, where they lack the ability to solve algebraic problems called algebraic thinking skills. This study focuses on finding out the judgment of experts about the use of BYOD-based mathematics knowledge to measure students' algebraic completion skills. This research applied 3 tests in the control class and treatment class with the reliability of Cronbach to see an increase in the use of BYOD-based learning. Thus, there is an increase in the use of BYOD-based learning to measure students' algebraic thinking abilities.

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A progression in first-grade children’s thinking about variable and variable notation in functional relationships

Cited by 50 publications

References 23 publications

Elementary students’ functional thinking: From recursive to correspondence

Elementary students’ functional thinking: From recursive to correspondence

El Proceso de generalización y la generalización en acto. Un estudio de casos

The Use of Bring Your Own Device-based Learning to Measure Student Algebraic Thinking Ability

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