Math Fluency: Accuracy Versus Speed in Preoperational and Concrete Operational First and Second Grade Children

Ramos-Christian, Vanessa; Schleser, Robert; Varn, Mary E.

doi:10.1007/s10643-008-0234-7

Cited by 18 publications

(16 citation statements)

References 23 publications

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“…In order to gain a better understanding of the absolute level of conservation ability, children were classified as conservers (at least five of six correct answers) and nonconservers (fewer than five correct answers) according to the procedure described by Ramos-Christian et al (2008). Conservers were considered to have a reliable understanding of conservation principles.…”

Section: Resultsmentioning

confidence: 99%

“…Studies have revealed associations between math skills and various conservation abilities even above IQ (e.g., Campbell & Ramey, 1990; Freyberg, 1966; Shayer, Ginsburg, & Coe, 2007) in elementary school children. Studies indicate that nonconserving children in kindergarten and in the early school years differ significantly from conserving children (Conservation of Substance and Number) in math fluency in single-digit arithmetic (addition, subtraction, multiplication, and division) with respect to their accuracy and speed in solving basic rote calculations (e.g., 2 + 3 = 5; 4 × 5 = 20; 45 / 5 = 9) (Cooper & Schleser, 2006; Ramos-Christian, Schleser, & Varn, 2008). Low conservation abilities contribute to difficulties with measurement (Burgard & Roos, 1991) or open-equation problems (e.g., 4 + __ = 12; Steffe, Spikes, & Hirstein, 1976).…”

Section: Mathematical Ability and Conservation Skillsmentioning

confidence: 99%

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Conservation Abilities, Visuospatial Skills, and Numerosity Processing Speed: Association With Math Achievement and Math Difficulties in Elementary School Children

Lambert

Spinath

2017

J Learn Disabil

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The aim of the present study was to investigate the associations between elementary school children's mathematical achievement and their conservation abilities, visuospatial skills, and numerosity processing speed. We also assessed differences in these abilities between children with different types of learning problems. In Study 1 ( N = 229), we investigated second to fourth graders and in Study 2 ( N = 120), third and fourth graders. Analyses revealed significant contributions of numerosity processing speed and visuospatial skills to math achievement beyond IQ. Conservation abilities were predictive in Study 1 only. Children with math difficulties showed lower visuospatial skills and conservation abilities than children with typical achievement levels and children with reading and/or spelling difficulties, whereas children with combined difficulties explicitly showed low conservation abilities. These findings provide further evidence for the relations between children's math skills and their visuospatial skills, conservation abilities, and processing speed and contribute to the understanding of deficits that are specific to mathematical difficulties.

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Section: Resultsmentioning

confidence: 99%

Section: Mathematical Ability and Conservation Skillsmentioning

confidence: 99%

Conservation Abilities, Visuospatial Skills, and Numerosity Processing Speed: Association With Math Achievement and Math Difficulties in Elementary School Children

Lambert

Spinath

2017

J Learn Disabil

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“…Finally, we wanted to have an index of arithmetic competence, which is a crucial component in math ability. We thus evaluated arithmetic fluency (i.e., the ability to quickly solve arithmetic operations), which is highly critical for efficient arithmetic performance (see for instance, Ramos-Christian, Schleser, & Varn, 2008). To do so, we created a paper-and-pencil test, adapted from the Tempo-Test Rekenen (De Vos, 1992; as in Nys & Content, 2012;Sasanguie et al, 2013).…”

Section: Symbolic Magnitude Comparisonmentioning

confidence: 99%

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

Guillaumé

Gevers

2015

Psychological Research

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Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate.The findings reported in the literature are actually inconsistent; some studies emphasised the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the Coefficient of Variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and nonnumerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.Abstract word count: 243 words.

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“…Nonetheless, concrete-operational thinking represents an important prerequisite of formal thinking (Inhelder and Piaget, 1958;Powell and Kalina, 2009). It is associated with a range of learning outcomes and academic achievement (Jordan and Brownlee, 1981;Hattie, 2009), such as maths fluency and maths achievement (conservation ability; Arlin, 1981;Cooper and Schleser, 2006;Ramos-Christian et al, 2008;Krajewski and Schneider, 2009;Wubbena, 2013;Lambert and Spinath, 2018), as well as reading comprehension and reading achievement (conservation and classification ability; Arlin, 1981;Cartwright, 2002;Colé et al, 2014;Cartwright et al, 2017). At the same time, differences in the ability of concrete-operational thinking become clear, as e.g., students with learning disabilities show lower levels of concrete-operational thinking than their peers (Wember, 1986;Riley, 1989;Fakouri, 1991).…”

Section: Concrete-operational Thinkingmentioning

confidence: 99%

The Association of Strategy Use and Concrete-Operational Thinking in Primary School

Börnert-Ringleb

Wilbert

2018

Front. Educ.

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Concrete-operational thinking depicts an important aspect of cognitive development. A promising approach in promoting these skills is the instruction of strategies. The construction of such instructional programs requires insights into the mental operations involved in problem-solving. In the present paper, we address the question to which extent variations of the effect of isolated and combined mental operations (strategies) on correct solution of concrete-operational concepts can be observed. Therefore, a cross-sectional design was applied. The use of mental operations was measured by thinking-aloud reports from 80 first-and second-graders (N = 80) while solving tasks depicting concrete-operational thinking. Concrete-operational thinking was assessed using the subscales conservation of numbers, classification and sequences of the TEKO. The verbal reports were transcribed and coded with regard to the mental operations applied per task. Data analyses focused on tasks level, resulting in the analyses of N = 240 tasks per subscale. Differences regarding the contribution of isolated and combined mental operations (strategies) to correct solution were observed. Thereby, the results indicate the necessity of selection and integration of appropriate mental operations as strategies. The results offer insights in involved mental operations while solving concrete-operational tasks and depict a contribution to the construction of instructional programs.

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Math Fluency: Accuracy Versus Speed in Preoperational and Concrete Operational First and Second Grade Children

Cited by 18 publications

References 23 publications

Conservation Abilities, Visuospatial Skills, and Numerosity Processing Speed: Association With Math Achievement and Math Difficulties in Elementary School Children

Conservation Abilities, Visuospatial Skills, and Numerosity Processing Speed: Association With Math Achievement and Math Difficulties in Elementary School Children

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

The Association of Strategy Use and Concrete-Operational Thinking in Primary School

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