"Representational transformation diagrams" are used to compare and contrast standard textbook presentations of vector line integrals in undergraduate courses in both mathematics and physics. These presentations are taken as the lower anchor in a learning trajectory. Two principal approaches in the lower division are identified, roughly…

This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The…

Although there is high enrollment in online college courses, there are concerns about student engagement (Martin & Bolliger, 2018; Dumford & Miller, 2018). Gamification has been shown to have the potential to improve student engagement. The purpose of the study was to describe how academic student engagement is impacted by Nicholson's…

With the sudden onset of the pandemic, little was known about the implications of transitioning college mathematics classes to online environments. In light of many students' difficulties in passing remedial and first-year mathematics courses in both synchronous and asynchronous classrooms, gaining an understanding of the impact of this transition…

Higher levels of student achievement are required to meet the needs of a changing workforce. The effect increases in education spending have on student learning gains among algebra students in Florida was unknown. Most research on per-pupil funding and student achievement is qualitative and measures opinions on the long-term effects of increased…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

Background: In fourth grade, students must solve single- and multi-step word problems during classroom instruction and on standardized tests. The majority of mathematics items on high-stakes assessments are word problems; thus, word-problem proficiency is necessary to demonstrate successful mathematics performance. However, many students are…

This study describes students' learning obstacles in solving early algebra problems requiring functional thinking ability. To reach this aim, qualitative research was conducted in this study. Participants of this study were 39 ninth graders and a mathematics teacher at one of the lower secondary schools in Bandung, Indonesia. The data were…

This study investigated the relationship between reading skills and math achievement among high school students in the Central Delta Areas of Mississippi. The data sources included Reading skills measured by English II Criterion Reference Test (CRT) scores and Algebra I CRT scores from the Mississippi Academic Assessment Program (MAAP) for the…

Although existing research suggests that students benefit on a range of outcomes when they enroll in early algebra classes, policy efforts that accelerate algebra enrollment for large numbers of students often have negative effects. Explanations for this apparent contradiction often emphasize the potential role of teacher and peer effects, which…

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 purpose of this article was to evaluate the quality of research studies and the evidence base for algebra instruction for secondary students with learning disabilities (LD) from 2000 to 2020. We evaluated the quality of methodological rigor of a total of eight single subject and three group design research studies using the 2014 Council for…

Algebra is a gatekeeper. For the 6% of students with dyscalculia (i.e., mathematical learning disabilities), an inability to pass algebra may significantly limit academic and career opportunities. Unfortunately, prior research on dyscalculia has focused almost exclusively on elementary-aged students' deficits in speed and accuracy in arithmetic…

At a research university near the east coast, a college algebra class has been restructured into two large lectures a week, an active recitation size laboratory once a week, and an extra day devoted to active group work called Supplemental Practice (SP). SP was added as an extra day of class where the SP leader has students work in groups on a…

This research focuses on ways in which balance scales mediate students' relational understandings of the equal sign. Participants included 21 Kindergarten-Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students…