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…

Learners' choices as to whether and how to use visual representations during learning are an important yet understudied aspect of self-regulated learning. To gain insight, we developed a "choice-based" intelligent tutor in which students can choose whether and when to use diagrams to aid their problem solving in algebra. In an…

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…

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…

Eighth-grade students who are placed into Algebra 1 but fail end-of-course exams may experience lowered grade point averages (GPAs) and loss of motivation for math or avoid taking advanced mathematics courses in high school. Middle-achieving students present challenges in terms of mathematics placement. Self-efficacy theory and locus of control…

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…

This latent class analysis study used a bias-adjusted three-step approach to empirically identify mutually exclusive clusters of teacher professional qualifications based on commonly studied indicators of teacher quality. We then examined the relationship between cluster membership and the mathematics gains of adolescents at risk for mathematics…

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…

Prior research in mathematical assessments has indicated varying results of predictive variables and further research has been recommended to support students, parents, teachers, and school administration. The purpose of this research was to determine how well a student's performance on a mathematics domain at the state level may be predicted…

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…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

Students in any grade level vary widely in their mathematics achievement, with the typical classroom including four to seven grade levels of mathematics proficiency. Due to this large range of mathematics learning needs, some schools offer certain courses in earlier grades than is typical. In this study, we analyzed multiple, large, national…

We know from previous survey research that teachers who hold high expectations for all of their students significantly increase the odds that those young people will go on to complete high school and college. One indicator of teachers' expectations is their approach to grading--specifically, whether they subject students to more or less rigorous…