Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Researchers from multiple disciplines have found that fractions and algebra knowledge are linked. One major strand of research has identified children's "units coordination" structures as crucial for success with fractions and algebra via multiplicative reasoning, whereas a second strand of research points to "magnitude…

Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…

Background: Mastering fractions seems among the most critical mathematical skills for students to acquire in school as fraction understanding significantly predicts later mathematic achievements, but also broader academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

This study was performed to determine preservice elementary mathematics teachers' solution performance of systems of linear equations using geometric representation, algebraic representation and transition from geometric representation to the algebraic representation and the predictive role of preservice elementary mathematics teachers'…

Prior research showed a gender effect on spatial ability, math anxiety, and math achievement. Lacking, however, is a comprehensive study that tested the mediation effects of spatial ability and math anxiety between gender and math achievement in a sequential mediation model. To fill this gap, this pilot study tested two mediation relationships,…

This exploratory study examined whether instruction aligned with the Institute of Education Sciences recommendations (i.e., use of worked examples, representations, deep questions) predicts student learning of early algebra, particularly inverse relations, in elementary classrooms. Instructional quality was determined through an…

In this study we investigated the relationship between urban eighth grade students' Hands-On Exposure to Algebraic Thinking (HEAT) competition performance and their subsequent performance on standardized measures of mathematics achievement (ACT Composite Score, ACT Math Scores, and Louisiana Algebra End of Course Exams). It was found that the…

Recent research has boosted the inclusion of introductory group theory into secondary and undergraduate mathematics education due to manifold potentials, e.g., with regards to the promotion of students' abstract thinking. However, in addition to research on cognitive processes, learners' affective characteristics have largely remained unexplored…

Algebraic competence is a major determinant of college access and career prospects, and equal sign knowledge is taken to be foundational to algebra knowledge. However, few studies have documented a causal effect of early equal sign knowledge on later algebra skill. This study assessed whether second-grade students' equal sign knowledge…

Recent methods have sought to improve precision in randomized controlled trials (RCTs) by utilizing data from large observational datasets for covariate adjustment. For example, consider an RCT aimed at evaluating a new algebra curriculum, in which a few dozen schools are randomly assigned to treatment (new curriculum) or control (standard…

Does the timing of children's formal understanding of mathematical equivalence matter for algebra readiness? A change-resistance account (McNeil & Alibali, 2005) predicts that it is beneficial for children to construct a formal understanding of mathematical equivalence in the early grades before overly narrow operational patterns become…

With close to a million Texas students attending rural schools, research on what influences student achievement is needed to guide policy, practice, and further research. Building on research relating student demographic variables and per student spending in rural schools to student achievement, through this dissertation research I used…