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…

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original…

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…

This study investigated differences between students' multiplication fact automaticity scores and student competencies on five problems from Intermediate Algebra assessments with a sample of university students. The five types of problems were: (1) linear equations with fractions, (2) system of linear equations, (3) factor by grouping, (4)…

The purpose of the present research is defining the direction and level of the relationship between 8th grade students' translating among multiple representations skills and their algebraic reasoning and revealing the predictive power on algebraic reasoning. The research was conducted in accordance with relational survey model, which is a…

Background: One criterion of adaptive learning is appropriate generalization to new instances based on the original learning context and avoiding overgeneralization. Appropriate generalization requires understanding what features of a solution are applicable in a new context and whether the new context requires modifications or a new approach. In…

We describe 24 third (8-9 years old) and 24 fifth (10-11 years old) graders' generalization working with the same problem involving a function. Generalizing and representing functional relationships are considered key elements in a functional approach to early algebra. Focusing on functional relationships can provide insights into how students…