The purpose of this study was to investigate what common errors and misconceptions about fractions exist among Saudi Arabian college students. Moreover, the study aimed at investigating the possible explanations for the existence of such misconceptions among students. A researcher developed mathematical test aimed at identifying common errors…

Many studies have claimed that traditional testing actually promotes students' use of superficial approaches to learning. When preparing to take tests, students typically memorize and cram rather than understanding the material and gaining new perspectives. This article describes how the author recast traditional tests by having students take a…

In this article, we discuss the potential of a critical approach to standardized tests and their results. In particular, we explore and discuss this potential not only for the assessment of students' mathematical competence, but also for teachers' professional development. We identify and describe two kinds of potential: the Informational…

This study investigated cognitive patterns of strengths and weaknesses (PSW) and their relationship to patterns of math errors on the Kaufman Test of Educational Achievement (KTEA-3). Participants, ages 5 to 18, were selected from the KTEA-3 standardization sample if they met one of two PSW profiles: high crystallized ability (Gc) paired with low…

This study is focused on the structure of equivalence problem to probe the evolution from operational to relational view of students' understanding of the equals sign. We propose a modified construct map which incorporates the intermediate levels in such a transition which were previously ignored. Our findings suggest that the structure of number…

Before an assessment is used to make decisions, the validity of the intended interpretation must be evaluated. The purpose of this paper is to describe how the argument-based approach and an interpretation/use argument (IUA) (Kane, 2013) were used to validate the interpretations made from the new Early Grade Mathematics Assessment (EGMA)…

Gifted students have potential to improve countries and this potential can be revealed and developed in schools where they spend most of their times with other regular students. However, these classrooms have some limitations for them; hence, they need some differentiated activities. Usage of dynamic geometry in mathematics lessons could be an…

A persistent problem in education is underrepresentation of certain cultural and linguistic groups such as American Indian, African American, and Hispanic, in special programs for exceptionally talented students, especially in science, technology, engineering, and mathematics (STEM). An assessment with demonstrated reliability and validity as an…

In this study, we analyzed the imprecise (i.e., less mathematically precise) responses that 148 third- to fifth-grade Chinese students made on selected-response problems that were part of a spontaneous mathematical focusing task, the Quantitative Relations Test for Chinese Children (QRTC[superscript 2]). The purpose for this analysis was to…

In recent ACT mode comparability studies, students testing on laptop or desktop computers earned slightly higher scores on average than students who tested on paper, especially on the ACT® reading and English tests (Li et al., 2017). Equating procedures adjust for such "mode effects" to make ACT scores comparable regardless of testing…

Children start preschool with large individual differences in their early numerical abilities. Little is known about the importance of heterogeneous patterns that exist within these individual differences. A person-centered analytic approach might be helpful to unravel these patterns and the cognitive and environmental factors that are associated…

We examined semiotic exchangeability in pop-up glossary translations and illustrations used as supports for second language learners (SLLs) in computer-administered mathematics tests. In a sample of 516 mathematics items, Grades 3-8 and 11, from a large-scale assessment program in the US, test developers identified terms that could be translated…

The purpose of this study was to assess the effectiveness of explicit instruction, compared to constructivist instruction, in teaching subtraction in schools with a high concentration of students from a disadvantaged social background: eighty-seven second graders (mean age in months = 90.95, SD = 5.30). Two groups received explicit versus…

Many studies have found a strong relationship between the mathematics students study in school and their performance on an academic or school mathematics assessment but not on an assessment of mathematics literacy (ML). With many countries, like the USA, placing emphasis on finishing secondary education being mathematically literate and prepared…

Community college administrators face a dilemma in the implementation of placement policies regarding college algebra students. Extensive literature devoted to this subject has been generated in the last 100 years without consensus. Furthermore, faculty opinions of the current placement policies contribute to the presence of a discrepancy in the…