The nonlinear relations of the approximate number system and mathematical language to early mathematics development.

Purpura, David J.; Logan, Jessica

doi:10.1037/dev0000055

Cited by 93 publications

(132 citation statements)

References 33 publications

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“…A growing body of evidence has indicated that mathematical language is malleable (Hassinger-Das et al, 2015;Hojnoski et al, 2014;Jennings et al, 1992;Powell & Driver, 2014) and is a strong predictor of mathematical knowledge (Purpura & Logan, 2015;Toll & Van Luit, 2014a, 2014b, and that exposure to mathematical language is highly predictive of mathematical knowledge growth across the early years (Boonen et al, 2011;Gunderson & Levine, 2011;Klibanoff et al, 2006;Levine et al, 2010). However, there is limited evidence supporting the causal connection between mathematical language and mathematical knowledge.…”

Section: Current Studymentioning

confidence: 96%

“…Children were awarded one 12 point for each correct response. In prior work (Purpura & Logan, 2015), these items were selected from a larger battery (i.e., broader range) of items using an item response theory framework. The selected items had a range of difficulty parameters and strong discrimination parameters.…”

Section: Mathematical Languagementioning

confidence: 99%

“…Assessments of mathematical language that broadly include quantitative and spatial language are some of the strongest predictors of the acquisition of early mathematical knowledge (Purpura & Logan, 2015;Toll & Van Luit, 2014a), and mathematical language mediates the relations between general language and early mathematics skills (Toll & Van Luit, 2014b).…”

mentioning

confidence: 99%

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Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

Purpura

Napoli

Wehrspann

et al. 2016

Journal of Research on Educational Effectiveness

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138

123

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The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of children's mathematics skills, but there is limited causal evidence supporting this link. To address this research gap, 47 Head Start children were randomly assigned to a mathematical language intervention group or a business-as-usual group. Over the course of eight weeks, interventionists implemented a dialogic reading intervention focused on quantitative and spatial mathematical language. At posttest, students in the intervention group significantly outperformed the students in the comparison group not only on a mathematical language assessment, but on a mathematical knowledge assessment as well. These findings indicate that increasing children's exposure to mathematical language can positively affect their general mathematics skills. This study is an important first step in providing causal evidence of the importance of early mathematical language for children's general mathematical knowledge and the potential for mathematical language interventions to increase children's overall mathematics abilities.

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Section: Current Studymentioning

confidence: 96%

Section: Mathematical Languagementioning

confidence: 99%

See 1 more Smart Citation

Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

Purpura

Napoli

Wehrspann

et al. 2016

Journal of Research on Educational Effectiveness

Self Cite

138

123

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“…The ANS is thought to be the foundation on which math ability builds (Verguts & Fias, 2004), although some work has found no significant relation between the ANS and future math performance (e.g., de Smedt, Noël, Gilmore, & Ansari, 2013). A meta-analysis has found that there does appear to be a small but stable relation between the ANS and math performance (Chen & Li, 2014) but this relation appears to be non-linear (Bonny & Lourenco, 2013;Purpura & Logan, 2015) with the ANS more related to earlier skills than with later skills (Chu, vanMarle, & Geary, 2015;Libertus, Feigenson, & Halberda, 2013). Given this mixed literature on the role of the ANS in complex math performance, we found it surprising that the ANS was one of the most important predictors of performance in Calculus II.…”

mentioning

confidence: 99%

Individual Differences Related to College Students’ Course Performance in Calculus II

Hart¹,

Daucourt²,

Ganley³

2017

Learning Analytics

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ABSTRACT. In this study, we explore student achievement in a semester-long flipped Calculus II course, combining various predictor measures related to student attitudes (math anxiety, math confidence, math interest, math importance) and cognitive skills (spatial skills, approximate number system), as well as student engagement with the online system (discussion forum interaction, time to submission of workshop assignments, quiz attempts), in predicting final grades. Data from 85 students enrolled in a flipped Calculus II course was used in dominance analysis to determine which predictors emerged as the most important for predicting final grades. Results indicated that feelings of math importance, approximate number system (ANS) ability, total amount of discussion forum posting, and time grading peer workshop submissions was the best combination of predictors of final grade, accounting for 17% of variance in a student's final grade. The point of this work was to determine which predictors are the most important in predicting student grade, with the end goal of building a recommendation system that could be implemented to help students in this traditionally difficult class. The methods used here could be used for any class.Keywords: Math performance, calculus, flipped classroom, math attitudes, cognitive performance, student engagement INTRODUCTIONOver the past few years, the attrition of STEM-focused undergraduates in the United States has become a critical national concern, with "a substantial number of undergraduate students initially enrolled in STEM degree programs [dropping] out in the first two years" (PCAST, 2012). In order to maintain highquality instructional practices in the face of STEM undergraduate attrition, growing demand for large (2017 130 numbers of graduates, and diminishing financial and human resources, many colleges and universities are turning to technologically aided teaching practices. This technological shift aims to integrate the traditional classroom environment with online course resources to enhance, replace, and supplement face-to-face instruction to reach more students in a cost-effective way (Garrison & Kanuka, 2004).To accommodate this shift toward technologically aided teaching methods, schools have implemented campus-wide Learning Management Systems (LMS), such as Moodle and Blackboard. These web-based management systems provide data related to the "user," with every action of the student tracked and recorded online. The underlying advantage of these LMS data is that they unobtrusively record individual student activity and interaction with course materials in real-time, providing a lens into traditionally unobservable learning-related behaviours and silently tracking individual students' learning progression (Macfadyen & Dawson, 2010; Gašević, Dawson, & Siemens, 2015). In traditional college courses, many performance measures, for example midterm or final exams (Lee, Speglia, Ha, Finch, & Nehm, 2015;Macfadyen & Dawson, 2010), are taken too late in the semester to identify st...

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“…Some studies (Mazzocco, Feigenson, & Halberda, 2011a; Piazza et al, 2010) have reported poorer ANS acuity in children with MLD, but other studies have not (Iuculano, Tang, Hall, & Butterworth, 2008; Rousselle & Noel, 2007). In preschool children, ANS acuity at the beginning of prekindergarten was found to be predictive of math achievement at the end of the prekindergarten year, but only for children in the lowest quantile of the mathematics performance continuum (Purpura & Logan, 2015). In a micro-analytic approach to studying these relations, Bugden and Ansari (2015) found that children with MLD did not differ from typically developing peers on items in which number and area are correlated (i.e., where 10 dots take up more area than 5 dots), but did differ on items in which number and area are uncorrelated (i.e., where 10 dots take up the same area as 5 dots).…”

Section: Early Numeracy Skills and Their Relation To Mathematical Achmentioning

confidence: 99%

Early numeracy skills in preschool-aged children: a review of neurocognitive findings and implications for assessment and intervention

Raghubar

Barnes

2016

The Clinical Neuropsychologist

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Objectives: The goals are to 1) provide a review of the typical and atypical development of early numeracy; 2) present what is known about the neurocognitive underpinnings of early numeracy; and 3) discuss the implications for early assessment and intervention. Method: Studies on the development of typical and atypical early numeracy are reviewed with a particular focus on longitudinal findings including those from our work on spina bifida myelomeningocele. Implications of this research for assessment are presented. The paper ends with a discussion of early math interventions. Results: Learning to count, identify numbers, and compare and manipulate quantities are key early numeracy skills. These are powerful predictors of school-age mathematical learning and performance. General neurocognitive abilities such as working memory and language, are also important for the development of early numeracy. It is recommended that early assessment for risk of mathematical learning difficulties include tests of both early number knowledge and key neurocognitive abilities. Math-specific interventions are most effective for improving early numeracy. There is currently little evidence that training of general cognitive functions transfers to mathematical learning. Conclusion: Understanding the development of early numeracy skills and their neurocognitive predictors offer important insights into early assessment and intervention for children at risk for or with mathematical learning difficulties.

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The nonlinear relations of the approximate number system and mathematical language to early mathematics development.

Cited by 93 publications

References 33 publications

Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

Individual Differences Related to College Students’ Course Performance in Calculus II

Early numeracy skills in preschool-aged children: a review of neurocognitive findings and implications for assessment and intervention

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