The United States has relinquished its mathematical prowess enjoyed in the 20th century with trending declines in performance on international and national measures and must make a concerted effort to regain this standing in the 21st century. Success in mathematics education also is important for individual citizens because it gives them college…

The National Council of Teachers of Mathematics (NCTM) promotes creating resources that build procedural fluency from conceptual understanding through intentionally sequenced tasks that draw on students' prior knowledge and move from simple, concrete representations to more complex and abstract representations (Boston et al., 2017). Liljedahl…

The COVID-19 pandemic led to a global lockdown and compelled institutions to shift to emergency remote teaching. This transition and the lack of knowledge of using technology affected teaching practices, including assessment. Confronted with new contexts for assessment and threats to validity caused by ineffective proctoring, many instructors had…

Making sense of algebraic expressions in context is multifaceted and extends beyond representing real-world situations using algebra. As part of Project MathTalk, the authors created videos that feature a pair of Grade 9 algebra 1 students coming to understand algebraic expressions in context. The students found three aspects of making sense of…

This paper presents results of a study aimed at describing and discussing evidence/features of advanced algebraic thinking processes. To achieve these objectives, we analysed the written production of students enrolled in engineering courses working on mathematical modelling tasks related to differential equations. Our guiding question was as…

Here we investigate how college students may conceptualize symbolic algebraic properties. This work uses the theory of Grundvorstellungen (GVs) to analyze how learners' conceptions may or may not align with some desired goals of instruction. Through the analysis of interviews with students across a variety of courses, we describe several…

The ability to solve geometric construction problems is justly regarded as an essential component of mathematical culture. The dynamic, general nature of objects provided by dynamic geometry systems allows the development of intuitive methods for solving construction problems. The core mathematical concept underlying this approach is the loci…

This research examined the impact of the Cognitive-Communicative (C-C) model as a pedagogical strategy for teaching algebraic word problems (AWPs). The C-C model integrates structured dialogue, concept clarification, and systematic problem-solving steps to enhance students' comprehension and reasoning. Employing a mixed-methods framework, the…

The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

This article reports on an empirical study that investigates the way students' performance in solving arithmetical tasks may be related to their performance in solving algebraic tasks. The sample consisted of 203 Grade 6 students. The arithmetical tasks involved arithmetical expressions with known quantities, whereas the algebraic tasks involved…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

This study explores the effects of a computer algebra system on students' mathematical thinking. Mathematical thinking is identified with mathematical thinking powers and structures. We define mathematical thinking as students' capacity to specialize and generalize their previous knowledge to solve new mathematical problems. The study was…

When the challenges faced in the transition period from arithmetic to algebra are considered, it is important to research the differences between secondary school mathematics teachers from Generations X and Y, and their awareness levels. This study aims to compare the algebraic operation skills of mathematics teachers from Generations X and Y and…

This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence (AI) based educational platforms. The goal is to support the design of AI systems that can enhance learners' conceptual understanding of algebra by taking into account learners' current level of algebra comprehension. The dataset comprises…

This study accumulated empirical evidence pertaining to preservice teachers' (n = 62) reasoning processes while choreographing group formations with embedded algebra tasks. The activities were designed to facilitate examination of the potential pedagogical connections between choreographing formation and mathematics, with particular emphasis on…