This convergent parallel mixed-methods study examines the relationship between high school mathematics teachers' research-based instructional practices and students' learning outcomes in Algebra 1 classrooms at a high school in a central region of a Southern U.S. State. The research addresses improving mathematics proficiency in the United States,…

Worked examples are effective learning tools for algebraic equation solving. However, they are typically presented in a static concise format, which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e.,…

The problem addressed in this study was that teachers underestimate the benefits of technology usage in grade nine Algebra mathematics classrooms. The purpose of this quantitative quasi-experimental study was to examine how the use of a supplemental digital mathematics tool affected achievement scores among grade nine Algebra mathematics students…

Faded worked examples have been used to promote problem solving performance, such as mathematics performance in many laboratory studies and short-term classroom studies. However, few studies have examined the ways educators may use fading in their own classroom on more accessible platforms that do not require programming experience. Further, few…

We examined the influences of pre-solving pause time, algebraic knowledge, mathematics self-efficacy, and mathematics anxiety on middle-schoolers' strategy efficiency in an algebra learning game. We measured strategy efficiency using (a) the number of steps taken to complete a problem; (b) the proportion of problems completed on the initial…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination…

A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

Powell, Berry, et al. (in press) conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a…

This project is aimed at generating new knowledge and improving our understanding of how Modified for Language Support-Worked Example Pairs (MLS-WEPs) contribute to effective mathematics learning and teaching in an ESOL (English to Speakers of Other Languages) context. The current study investigated a novel instructional approach to help English…

Student insight into algebraic formulas, including the ability to identify the structure of a formula and its components and to reason with and about formulas, is an issue in mathematics education. In this study, we investigated how 16- and 17-year-old pre-university students' insight into algebraic formulas can be promoted through graphing…

Tutorials in introductory physics (TIP) are a well known resource for use in third level insititutions for developing students' understanding of physics concepts. However, this resource is only sparingly used at second level. This study presents an adaptation of the approach taken in TIP to enhance the understanding of vector addition of a group…

Understanding equivalence is fundamental to STEM disciplines, yet misunderstandings and misconceptions inhibit students from fully appreciating or leveraging the concept. Using the game-based algebraic notation system, From Here to There! (FH2T), students explore ideas of equivalence by dynamically transforming expressions or equations among…

The literature shows that the integration of technological tools, like "GeoGebra," has the potential to improve the teaching and learning of mathematics. The aim of this study was to see whether "GeoGebra" could be used to address identified, systematic misconceptions that National Certificate Vocational (NCV) students hold…

An impediment to conducting high-quality quantitative research studies in education is the paucity of valid measures of learning gains. Studies often seek to investigate students' deep, conceptual understanding yet many measures assess only surface, procedural understanding. One reason is that the development of validated measures of conceptual…

Psychologists and mathematics educators have long viewed flexibility as critical to students' mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified…