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…

We examine what kind of concept definitions of area a group of Finnish primary and lower secondary student teachers (N = 82) use, and how the quality of the definitions is associated with the participants' success in seven exercises involving area. We are especially interested in how the understanding of the two-dimensionality of area appears in…

The paper presents the results of a case study examining students' difficulties in the learning of integral calculus. It sought to address the misconceptions and errors that were encountered in the students' work solution. In quantitative study, the marks obtained by 147 students of Diploma in Computer Science in advanced calculus examinations…

This correlational, explanatory study utilized multiple linear and hierarchical regression to examine the predictive power of socioeconomic, parental and district factors on the total percentage of students who scored Proficient or Advanced Proficient on the 2013 MCAS Grade 4 language arts and mathematics test. The population for this study…

Improving mathematical student performance in K-12 education has been a focus in the U.S. Students in the U.S. score lower on standardized math assessments than students in other countries. Preparing students for a successful future in a global society requires schools to integrate effective digital technologies in math classroom curricula.…

There is a consequential amount of research in regards to coteaching and student achievement in students with disabilities. Although there is a substantial body of research, there is still uncertainty whether achievement in mathematics differs between students with and without disabilities in cotaught and non-cotaught classrooms. Therefore, the…

This is a quantitative study examining whether STAR Math, a student monitoring system, can improve PSSA Math scores. The experimental school used STAR Math during the 2015-2016 school year in grouping students for remediation and intervention. The control school used traditional curriculum measures to group students for remediation and…

In this study, we investigated students' thinking about the use of letters in algebra. Responses from over 1,400 Australian secondary school students to a set of three algebra items were analysed to determine the prevalence of the "letter as object" misconception. We estimate that 50% to 80% of Year 7 students bring this misconception to…

In this study, we examined students' mathematical understanding and retention in a problem-based learning (PBL) classroom. The participants were 48 Grade 10 students, and the data were collected in December of 2016. After the end of the PBL lessons, the Mathematical Understanding of Function Test (MUFT) and the Retention Test (RT) were…

In this paper, we report on developments in the Mastery Learning (ML) curriculum and assessment model that has been successfully implemented in a metropolitan university for teaching first-year mathematics. Initial responses to ML were positive; however, we ask whether the nature of the ML tests encourages a focus on shallow learning of…

This study provides the results of a latent class analysis (LCA) using data from the Trends in International Mathematics and Science Study -- 2011 (TIMSS-2011) with a focus on the 8th grade mathematics section. The study presents the analysis of item data with Mplus 7.31 to determine if results obtained yielded distinct latent subgroups. The data…

A growing literature has demonstrated that early math skills are associated with later outcomes for children. This research has generated interest in improving children's early math competencies as a pathway to improved outcomes for children in elementary school. The Making Pre-K Count study was designed to test the effects of an early math…

There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

This study compares two methods of defining groups for the detection of differential item functioning (DIF): (a) pairwise comparisons and (b) composite group comparisons. We aim to emphasize and empirically support the notion that the choice of pairwise versus composite group definitions in DIF is a reflection of how one defines fairness in DIF…

The alignment of test items to content standards is critical to the validity of decisions made from standards-based tests. Generally, alignment is determined based on judgments made by a panel of content experts with either ratings averaged or via a consensus reached through discussion. When the pool of items to be reviewed is large, or the…