This study investigated the effectiveness of statistical adjustments applied to rater bias in many-facet Rasch analysis. Some changes were first made in the dataset that did not include "rater × examinee" bias to cause to have "rater × examinee" bias. Later, bias adjustment was applied to rater bias included in the data file,…

This rejoinder keeps the original focus on statistical computing pertaining to the correlation of student achievement between mathematics and science from the Trend in Mathematics and Science Study (TIMSS). Albeit the availability of student performance data in TIMSS and the emphasis of the inter-subject connection in the Next Generation Science…

Children who struggle in mathematics have a limited understanding of the foundational processes of mathematics. A lack of conceptual understanding causes students to fall behind as they progress through the core curriculum. Children at high risk for developing mathematics disabilities fail to gain numeracy knowledge. The purpose of this case study…

Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was…

The notation for vector analysis has a contentious nineteenth century history, with many different notations describing the same or similar concepts competing for use. While the twentieth century has seen a great deal of unification in vector analysis notation, variation still remains. In this paper, the two primary notations used for expressing…

Conditional independence (CI) between response time and response accuracy is a fundamental assumption of many joint models for time and accuracy used in educational measurement. In this study, posterior predictive checks (PPCs) are proposed for testing this assumption. These PPCs are based on three discrepancy measures reflecting different…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

The purpose of the current study was to examine dimensionality and concurrent validity evidence of the EARLI numeracy measures (DiPerna, Morgan, & Lei, 2007), which were developed to assess key skills such as number identification, counting, and basic arithmetic. Two methods (NOHARM with approximate chi-square test and DIMTEST with DETECT…

This study investigated developmental gender differences in mathematics achievement, using the child and adolescent portion (ages 6-19 years) of the Kaufman Test of Educational Achievement-Third Edition (KTEA-3). Participants were divided into two age categories: 6 to 11 and 12 to 19. Error categories within the Math Concepts & Applications…

An emerging literature demonstrates that relevance interventions, which ask students to produce written reflections on how what they are learning relates to their lives, improve student learning outcomes. As part of a randomized evaluation of a relevance intervention (N = 1,978 students from 82 ninth-grade classes), we used Complier Average Causal…

Studies comparing mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are hitherto scarce, inconclusive, and mainly focusing on elementary school children or adolescents. The present study wants to gain insight into the foundation of mathematics by looking at preschool performances. Five early…

The aim of this study are to examine the relationship between prospective classroom teachers' estimation skills based on calculation and their number sense and to investigate whether their number sense and estimation skills change according to their class level and gender. The participants of the study are 125 prospective classroom teachers…

A high comorbidity between reading and arithmetic disabilities has already been reported. The present study aims at identifying more precisely patterns of arithmetic performance in children with developmental dyslexia, defined with severe and specific criteria. By means of a standardized test of achievement in mathematics ("Calculation and…

This paper evaluates the influence of the classmates' age on individual academic achievement. The identification strategy explores a mechanism for the division of classes based on age homogeneity, with cutoff value determined by the Brazilian law of age at school entry. Fuzzy regression discontinuity estimates a local average treatment effect of…

School administrators across the nation are actively searching for solutions to increase student achievement due in part to the significant amount of knowledge that is lost annually each summer. Mathematical computation skills are especially at-risk. This quantitative research study was designed to investigate the impact of summer recess also…