The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

This study aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four…

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

Algebraic Thinking Skills (ATS) are one of the skills that students need to master in order to solve nonroutine problems. These skills are also necessary as a foundation for students preparing to enter university studies and fields of work that require logical and analytical thinking. However, Malaysian students' performance in solving algebraic…

"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…

In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and…