The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…

This study investigated the scalability of a cognitive multiple-choice test through the Mokken package in the R programming language for statistical computing. A 2019 mathematics West African Examinations Council (WAEC) instrument was used to gather data from randomly drawn K-12 participants (N = 2866; Male = 1232; Female = 1634; Mean age = 16.5…

This dissertation is guided by my driving research question: what works for whom in education and why? I examine issues of instruction, assessment, and research approaches that begin to answer this question. Study 1 examines a classroom intervention's child x instruction interactions. Study 2 examines underlying cognitive factors, including…

Research on number sense presents contradictory arguments and results regarding the effects of context-based tasks and activities on students' number sense. The aim of this study was to examine fourth-grade elementary school students' number sense as they solve context-based (CB) and non-context-based (NCB) items. A survey design was employed and…

Math courses graded on homework, tests, and a final examination can result in students putting together enough partial credit to pass the class without gaining a reasonable mastery of the course content. Mastery-based testing can help to address this by allowing the instructor to align course grades with mastery of the learning objectives for the…

We focus on teachers' ways of leading whole class discussions (WCDs) in mathematics, with the goal of uncovering their traces (if any) in their students' responses (a) while participating in the WCDs and (b) in the written responses in a final test. For this purpose, two 8th-grade probability classes learning a 10-lesson unit with different…

Drawing from the developmental and cognitive mathematics literature, the purpose of this study was to investigate the reliability, validity, and diagnostic utility of a widely-researched number line task in kindergarten. Specifically, the Number Line Assessment 0-100 (NLA 0-100) as compared to an established kindergarten screening measure was…

School leadership ranks as an essential factor for successful schools. The purpose of this study is therefore to investigate the effects of two central leadership practices -- "setting directions" and "managing instructional processes" -- on both instructional quality (mediator) and student achievement (target) in Austrian…

This study investigates the relationship among working memory (WM), mathematics, and language, with the aim of understanding: (1) whether the functions and capacities of WM components can predict achievement in language and mathematics; and (2) whether competence in the first language (L1) and achievement in mathematics can predict success in…

The research is clear: Math achievement drives success in academics and life. Yet, even as students' math outcomes stagnate--or decline--most states haven't adopted bold, comprehensive strategies to turn the tide. When states prioritize policies that support teacher effectiveness, they build the foundation for lasting gains in student math…

Extended testing time is a common accommodation given to students with disabilities. However, little is known about whether students who are eligible for the accommodation actually use it, and with what effect. The present study used process data available from the digitally delivered 2017 National Assessment of Educational Progress (NAEP)…

When cognitive and educational tests are administered under time limits, tests may become speeded and this may affect the reliability and validity of the resulting test scores. Prior research has shown that time limits may create or enlarge gender gaps in cognitive and academic testing. On average, women complete fewer items than men when a test…

Mathematics reading and spatial ability are important learning components in mathematics education. However, in traditional instruction, it is difficult to develop learners' mathematics reading and spatial abilities. Therefore, many students struggle to understand real-world problems and lack the spatial ability to form internal imagery. To cope…

In this paper, we assess the pedagogical approaches we employ in our US-based undergraduate mathematics courses during the COVID-19 pandemic. Our goal is to share anecdotal evidence on the use of math journals, oral exams, and learning portfolios in the synchronous online mathematics classroom. We reflect on our experience using artifacts of…

The National Council of Teachers of Mathematics (NCTM), has made an effort to increase the use of technology and the use of calculators into the classroom and curriculum. As a result, many studies and articles have been written on the subject of calculator use in the classroom. A review of over 600 studies revealed that it is not curricula that…