The research reported in this article sought to develop a taxonomy of grade 11 students' levels of understanding in algebraic problem-solving tasks. The student sample was from high schools in the province of Ontario in Canada. Problems from four areas in algebra namely, variables, expressions, equations and word problems were chosen to be…

An important topic of study in secondary mathematics is non-linear functions, including quadratic equations. In this study, findings from 25 Year 11 students indicated that difficulties with critical prerequisite concepts such as algebraic conventions impeded students' success in understanding and working with quadratics. Analysis of student…

In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…

The positive relationship between students' attitudes toward mathematics and mathematics achievement is well documented. Yet there is a worsening problem of low appeal of mathematics especially at the secondary level. Therefore, in this paper we focus on three high school students who report a strong dislike of mathematics. By analyzing student…

This paper reports changes in the extent to which a group of Year 11 students used a Computer Algebra System (CAS), pen-and-paper (P&P), or a combination of both, when solving routine problems across seven months in four different topics. Comparing the frequency of CAS use across topics shows students made greater use of CAS in the topics of…

School closures during the COVID-19 pandemic have resulted in substantial learning gaps in students' mathematical abilities. The problem was self-enrollment against teacher recommendation among Honors Algebra 2 students in 9th, 10th, and 11th grade students at a local high school. The purpose of the quantitative, quasi-experimental study was to…

Math consists of many components such as arithmetic, algebra, geometry, trigonometry, statistics, where each component holds its importance in the field of math. Students of Grades 11 and 12 are at an important stage in their career, where the attitude and performance in math determines their future choices. Therefore, the aim of this study was to…

Using the High School Longitudinal Study of 2009, we examine the association between taking Algebra I by the eighth grade and students' later achievements and advanced mathematics course-taking. To explore our research questions, we employ three distinct methods--regression analysis, fixed effects models, and propensity score matching. In all our…

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…

I explore students' discourses in small groups working on mathematical problems using GeoGebra, focusing on the Cartesian connection between algebra and geometry. Specifically, the interest lies in what is internally persuasive for students in upper-secondary school (11th grade) with histories of low attainment. Three problem-solving episodes are…

School algebra serves as the language of mathematics and a foundational subject for learning advanced mathematics courses. This makes developing learners' proficiency in algebra the most desirable instructional goal of school mathematics. Despite having such importance emphasis, however, studies indicate that the vast majority of learners are…

Critical thinking (CT) is a type of convergent thinking explored when students learn mathematics. This study aims to obtain a comprehensive representation of students' mathematical Critical Thinking (CT) abilities, based on the mathematical ability level. Data were obtained from 35 students using CT skills tests and semi-structured in-depth…

In this study, the authors examined a group of related literatures that used the same large-scale nationally representative dataset with algebra achievement as the outcome to explore why results from the same dataset may differ across studies. More specially, the authors synthesized the extant research literature that utilized data from the High…

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…

Backward transfer is when learning about a new topic influences an individual's prior ways of reasoning about a topic they previously learned about. This study looked at how quadratic functions instruction differentially influenced students' prior ways of reasoning about linear functions. Specifically, we compared students at three levels of…