Although algebra often functions as a gatekeeper to higher-level mathematics courses and higher education admissions, few quality measures exist for assessing conceptual understanding. This study explored the technical adequacy of three procedural and two conceptual algebra screening measures. We administered three rounds of assessments throughout…

In this study, the Mathematical Knowledge for Teaching-Elementary Patterns Functions and Algebra-Content Knowledge (MKT-PFA) test, originally developed in English as part of the "Learning Mathematics for Teaching Project" at Michigan University, was adapted into Turkish. The test comprises two equivalent forms, A and B, each translated…

This study was aimed to validate a digital tool for diagnosing mathematical proficiency in the Number and Algebra strand of 1,504 Thai seventh-grade students. Researchers employed a multidimensional approach, an extension of the Rasch model to measure its quality. A design-based research method was adopted to create the diagnostic tool which…

Within a multi-tier system of support (MTSS), results from universal screeners help teachers make instructional decisions early in the learning process to prevent and remediate skill gaps. Universal screeners help teachers determine students' need for and intensity of additional instructional support to reach their learning goals by efficiently…

Inquiry-oriented teaching is a specific form of active learning gaining popularity in teaching communities. The goal of inquiry-oriented classes is to help students in gaining a conceptual understanding of the material. My research focus is to gauge students' performance and conceptual understanding in inquiry-oriented linear algebra classes. This…

Elementary school students often exhibit a variety of conceptions associated with algebraic thinking that their teachers fail to recognize or understand. It is crucial that elementary school teachers possess knowledge of the variety of student conceptions and also have abilities to address varying states of conceptions. Otherwise, students who are…

This dissertation consisted of three different, but conceptually related manuscripts. The series of manuscripts examined psychosocial factors of learning including attitude towards mathematics, motivation to learn mathematics, and satisfaction from the mathematics instruction in both redesigned and traditionally- taught college algebra courses at…

This report provides a description of the development process, field testing, and psychometric properties of the fall 2015 grades 3-5 Elementary Mathematics Student Assessment (EMSA), a student mathematics test designed to be administered in a whole-group setting to students in grades 3, 4, and 5. The test was administered to 2,614 participating…

There has been increased attention to the development of assessment measures for evaluating mathematical skills in young children in order to inform instruction and intervention. However, existing tools have focused primarily on number sense with little attention to other areas of mathematical thinking such as geometry and algebra. The purpose of…

This study investigated longitudinal pathways leading from early spatial skills in first-grade girls to their fifth-grade analytical math reasoning abilities (N = 138). First-grade assessments included spatial skills, verbal skills, addition/subtraction skills, and frequency of choice of a decomposition or retrieval strategy on the…

This addendum to previously published results presents alternative analyses of data from large-scale effectiveness studies of Cognitive Tutor Algebra I in middle schools and high schools. These alternative analyses produce results that are substantively the same as previously reported. We find a significant positive effect of 0.21 standard…

Young children have an impressive amount of mathematics knowledge, but past psychological research has focused primarily on their number knowledge. Preschoolers also spontaneously engage in a form of early algebraic thinking-patterning. In the current study, we assessed 4-year-old children's knowledge of repeating patterns on two occasions…

In this article we discuss the findings of our research on students' understanding of vector concepts in problems without physical context. First, we develop a complete taxonomy of the most frequent errors made by university students when learning vector concepts. This study is based on the results of several test administrations of open-ended…

Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

The purpose of this study was to construct and evaluate an instrument for determining student preparedness in College Algebra. A 73-item instrument covering prerequisite arithmetic and high school Algebra knowledge for College Algebra was constructed. The instrument was pilot-tested on a freshman population of 595 students. Results of reliability…