Children's Developing Understanding of Place Value: Semiotic Aspects

Valeras, Maria; Becker, Joe

doi:10.1207/s1532690xci1502_4

Cited by 30 publications

(25 citation statements)

References 16 publications

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“…Thinking of multidigit numbers as groups of tens and units translates into later place-value knowledge, which is critical for more complex arithmetic operations (e.g., 27 + 14). Varelas and Becker (1997) found that the percentage of children who both traded correctly and correctly identified digits in the tens place on a written arithmetic task increased from 56% to 77% to 98% between second and fourth grades. Comprehension of base-10 structure suggests a deeper understanding of how numbers relate to each other and how numbers can be incremented by intervals greater than one, such as tens and hundreds.…”

Section: Base-10 and Place-value Understandingmentioning

confidence: 95%

“…A multitude of studies have found that place value is a difficult concept for young children (Carpenter, Franke, Jacobs, Fennema, & Empson, 1998;Cauley, 1988;Cobb & Wheatley, 1988;Fuson, 1986Fuson, , 1988Fuson, , 1992Fuson & Briars, 1990;Ginsburg, 1989;Kamii, 1986;Miura & Okamoto, 1989;Resnick & Omanson, 1987;Ross, 1989Ross, , 1990Varelas & Becker, 1997). It takes several years for children to develop an understanding of the base-10 system and place-value notation.…”

Section: Base-10 and Place-value Understandingmentioning

confidence: 99%

“…The age at which children accurately use 10 blocks and unit blocks to represent two-digit numerals seems to depend, in part, on their instructional experiences (Fuson & Briars, 1990;Fuson, Smith, & Lo Cicero, 1997;Hiebert & Wearne, 1992;Miura et al, 1993;Varelas & Becker, 1997). For example, Saxton and Towse (1998) found that a practice trial in which the experimenter demonstrated how to use 10 blocks and unit blocks to represent double-digit numbers had a substantial positive effect on the extent to which young children used both 10 blocks and unit blocks to represent double-digit numbers.…”

Section: Base-10 and Place-value Understandingmentioning

confidence: 99%

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Longitudinal Comparison of Montessori versus Non-Montessori Students’ Place-Value and Arithmetic Knowledge

Laski

Vasilyeva

Schiffman³

2016

JoMR

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Abstract. Understanding of base 10 and place value are important foundational math concepts that are associated with higher use of decomposition strategies and higher accuracy on addition problems (Laski, Ermakova, & Vasilyeva, 2014;Fuson, 1990;Fuson & Briars, 1990; National Research Council, 2001). The current study examined base-10 knowledge, place value, and arithmetic accuracy and strategy use among children in early elementary school from Montessori and non-Montessori schools. Children (N = 150) were initially tested in either kindergarten or first grade. We followed up with a subgroup of the sample (n = 53) two years later, when the children were in second and third grades. Although Montessori curriculum puts a large emphasis on the base-10 structure of number, we found that children from Montessori schools showed an advantage on correct use of base-10 canonical representation in kindergarten but not in first grade. Moreover, no program differences were seen in place-value understanding in second and third grades. Although Montessori children used different strategies to obtain answers to addition problems in second and third grades as compared with non-Montessori children, no program differences in addition accuracy were found at any grade level. Educational implications are discussed.

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Section: Base-10 and Place-value Understandingmentioning

confidence: 95%

Section: Base-10 and Place-value Understandingmentioning

confidence: 99%

Section: Base-10 and Place-value Understandingmentioning

confidence: 99%

See 1 more Smart Citation

Longitudinal Comparison of Montessori versus Non-Montessori Students’ Place-Value and Arithmetic Knowledge

Laski

Vasilyeva

Schiffman³

2016

JoMR

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“…The early knowledge that prepares students to learn cannot just be about quantitative properties, it also needs to be about symbolic representations. Quantitative perceptions and their symbolic representations have different functions and each needs development (Varelas & Becker, 1997). Brain research, for example, indicates activation in different brain regions when people estimate quantities versus when they symbolically compute specific values (Dehaene, 2000).…”

Section: Inventive Production and The Development Of Early Knowledgementioning

confidence: 99%

Inventing to Prepare for Future Learning: The Hidden Efficiency of Encouraging Original Student Production in Statistics Instruction

Schwartz¹,

Martin²

2004

Cognition and Instruction

554

452

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Activities that promote student invention can appear inefficient, because students do not generate canonical solutions, and therefore the students may perform badly on standard assessments. Two studies on teaching descriptive statistics to 9th-grade students examined whether invention activities may prepare students to learn. Study 1 found that invention activities, when coupled with subsequent learning resources like lectures, led to strong gains in procedural skills, insight into formulas, and abilities to evaluate data from an argument. Additionally, an embedded assessment experiment crossed the factors of instructional method by type of transfer test, with 1 test including resources for learning and 1 not. A "tell-and-practice" instructional condition led to the same transfer results as an invention condition when there was no learning resource, but the invention condition did better than the tell-and-practice condition when there was a learning resource. This demonstrates the value of invention activities for future learning from resources, and the value of assessments that include opportunities to learn during a test. In Study 2, classroom teachers implemented the instruction and replicated the results. The studies demonstrate that intuitively compelling student-centered activities can be both pedagogically tractable and effective at preparing students to learn.The renowned instructional theorist Robert Gagne built his work on the observation that different forms of instruction are suited to different learning outcomes. For example, he proposed repetition for developing motor skills and reinforcement

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“…El formato arábigo se basa en un sistema posicional en donde el valor de cada dígito está determinado por su posición en la cadena de dígitos y a su vez, cada posición corresponde a un orden. Este orden es definido por la potencia de diez, la cual se incrementa a partir de 0 desde el primer dígito de la derecha y cada vez que el dígito es movido una posición hacia la izquierda (Lerner & Sadovsky, 1994;Miura, Chang, & Okamoto, 1988;Orozco, et ál., 2007;Otálora & Orozco, 2006;Varelas & Becker, 1997).…”

Section: El Sistema De Numeración En Base Diez (Snbd)unclassified

The Numerical transcoding process and The Understanding of place value: A weak empirical and theoretical relationship

Muñoz¹,

Guerrero²,

García³

2015

psdc

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psicología desde el caribe issn 0123-417x (impreso) issn 2011-7485 (on line) Vol. 32, n.° 3, septiembre-diciembre 2015 http://dx.doi.org/10.14482/psdc.32.3.6015 Transcodificación numérica y comprensión del valor de posición: una débil relación teórica y empíricaThe Numerical transcoding process and The Understanding of place value: A weak empirical and theoretical relationshipYiseth Bibiana Muñoz* Diego Fernando Guerrero* José Fernando García* ResumenEsta investigación explora la relación entre la comprensión del valor de posición y el proceso de transcodificación numérica del formato verbal hablado al formato arábigo. Participaron 22 niños del grado primero de primaria de un colegio privado de Cali. Se presentó una tarea de dictado de numerales y tres tareas de comprensión del valor de posición. Se realizó un análisis del logro en función del acierto y el error y un análisis correlacional entre las tareas de valor de posición y la tarea de transcodificación numérica. Adicionalmente, se realizó un análisis de redes de vínculos. Se encontraron diferencias en el desempeño de los niños entre la tarea de dictado y las tareas de comprensión del valor de posición, señalando que no es necesaria la comprensión del valor de posición para la escritura de numerales a partir del dictado. Palabras clave: valor de posición, transcodificación numérica, sistema de numeración.

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Children's Developing Understanding of Place Value: Semiotic Aspects

Cited by 30 publications

References 16 publications

Longitudinal Comparison of Montessori versus Non-Montessori Students’ Place-Value and Arithmetic Knowledge

Longitudinal Comparison of Montessori versus Non-Montessori Students’ Place-Value and Arithmetic Knowledge

Inventing to Prepare for Future Learning: The Hidden Efficiency of Encouraging Original Student Production in Statistics Instruction

The Numerical transcoding process and The Understanding of place value: A weak empirical and theoretical relationship

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