Shafer-Fink type inequalities for the elliptic function sn(u|k)

Mercer, A. McD.

doi:10.7153/jmi-02-33

Cited by 5 publications

(2 citation statements)

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“…Previous research syntheses of the mathematics literature identified effective instructional elements that are beneficial to the learning needs of all students, including low–achieving students, those with learning disabilities, and students with emotional or behavioral disorders (Baker, Gersten, & Lee, 2002; Kroesbergen & Van Luit, 2003; Kunsch, Jitendra, & Sood, 2007; Swanson & Sasche–Lee, 2000; Templeton, Neel, & Blood, 2008). Much of this earlier work examined instruction or intervention across several mathematic content areas including basic skills (Baker et al, 2002; Kroesbergen & Van Luit, 2003; Kunsch et al, 2007; Swanson & Sasche–Lee, 2000) and isolated the impact of direct instruction (Baker et al, 2002; Kroesbergen & Van Luit, 2003; Swanson & Sasche–Lee, 2000), strategy instruction (Kroesbergen & Van Luit, 2003; Swanson & Sasche–Lee, 2000; Templeton et al, 2008), and peer–mediated (Kroesbergen & Van Luit, 2003; Kunsch et al, 2007; Templeton et al, 2008) treatment types. Direct and strategy instruction or a combination of the two were found to be highly effective across studies for ameliorating mathematics difficulties and peer–mediated instruction produced moderate effects (Kunsch et al, 2007).…”

Section: Research Designsmentioning

confidence: 99%

“…Much of this earlier work examined instruction or intervention across several mathematic content areas including basic skills (Baker et al, 2002; Kroesbergen & Van Luit, 2003; Kunsch et al, 2007; Swanson & Sasche–Lee, 2000) and isolated the impact of direct instruction (Baker et al, 2002; Kroesbergen & Van Luit, 2003; Swanson & Sasche–Lee, 2000), strategy instruction (Kroesbergen & Van Luit, 2003; Swanson & Sasche–Lee, 2000; Templeton et al, 2008), and peer–mediated (Kroesbergen & Van Luit, 2003; Kunsch et al, 2007; Templeton et al, 2008) treatment types. Direct and strategy instruction or a combination of the two were found to be highly effective across studies for ameliorating mathematics difficulties and peer–mediated instruction produced moderate effects (Kunsch et al, 2007). Only three of these research syntheses included single–case design studies (Kroesbergen & Van Luit, 2003; Swanson & Sachse–Lee, 2000; Templeton et al, 2008).…”

Section: Research Designsmentioning

confidence: 99%

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Meta–Analysis of Mathematic Basic–Fact Fluency Interventions: A Component Analysis

Codding

Burns

Lukito

2011

Learning Disabilities Research & Practice

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Mathematics fluency is a critical component of mathematics learning yet few attempts have been made to synthesize this research base. Seventeen single-case design studies with 55 participants were reviewed using meta-analytic procedures. A component analysis of practice elements was conducted and treatment intensity and feasibility were examined. Findings suggest that drill and practice with modeling produced the largest effect sizes. Treatments with more than 3 components yielded higher effect sizes than those with fewer than 3, and a combination of treatment agents lead to better outcomes than a single agent. Other findings pertaining to prebaseline assessment, treatment time, experimental design employed, and treatment setting are also discussed. About the AuthorsRobin S. Codding, PhD is currently an associate professor of school psychology at the University of Massachusetts, Boston. Her research interests include data-based decision-making, academic assessment and interventions, and treatment integrity.Gracia Lukito earned her EdS in school psychology at the University of Massachusetts-Boston and is currently employed as a school psychologist in the Quincy Public School District. Her research interests include data-based decision making and interventions.Matthew K. Burns, PhD is a professor of educational psychology and coordinator of the school psychology program at the University of Minnesota. He has published over 100 articles and book chapters on topics including response to intervention, assessing the instructional level, academic interventions, and facilitating problem-solving teams.

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Section: Research Designsmentioning

confidence: 99%

Section: Research Designsmentioning

confidence: 99%

Meta–Analysis of Mathematic Basic–Fact Fluency Interventions: A Component Analysis

Codding

Burns

Lukito

2011

Learning Disabilities Research & Practice

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Shafer–Fink type inequalities for arc lemniscate functions

Wei

Wang

2020

RACSAM

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In this paper, we investigate the monotonicity and inequalities for some functions involving the arc lemniscate and the hyperbolic arc lemniscate functions. In particular, sharp Shafer-Fink type inequalities for the arc lemniscate and the hyperbolic arc lemniscate functions are proved.Keywords. arc lemniscate functions, hyperbolic arc lemniscate functions, lemniscate functions, hyperbolic lemniscate functions, Shafer-Fink type inequalities Mathematics Subject Classification (2010). 26D07, 33E05

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The inverse hyperbolic tangent function and Jacobian sine function

Wang

2017

Journal of Mathematical Analysis and Applications

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Shafer-Fink type inequalities for the elliptic function sn(u|k)

Abstract: Abstract. The inequalities of Shafer and Fink, namely,are generalized to similar inequalities for the elliptic function sn(u|k) .

Cited by 5 publications

References 4 publications

Meta–Analysis of Mathematic Basic–Fact Fluency Interventions: A Component Analysis

Meta–Analysis of Mathematic Basic–Fact Fluency Interventions: A Component Analysis

Shafer–Fink type inequalities for arc lemniscate functions

The inverse hyperbolic tangent function and Jacobian sine function

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