Initial algebra is a critical stage in the teaching of algebra and occurs when students are transitioning from arithmetic to algebra. Irish mathematics education at post-primary level has undergone a period of major reform beginning in 2010, which encompassed a radical change in the methods for teaching algebra. Despite this reform evidence…

Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

This study analyzes the mathematical knowledge to teach early algebra exhibited by pre-service early childhood education teachers, from the perspective of the Mathematical Knowledge for Teaching (MKT) model. The research adopts a mixed exploratory-descriptive methodological approach, based on the application of the MKT-early algebra questionnaire…

Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…

This study used the Motivated Strategies for Learning Questionnaire (MSLQ) to assess the motivation and learning strategies of students in a self-paced developmental mathematics class. A total of 194 undergraduate students participated in this study. Descriptive statistics, correlation coefficients, and regression analysis were conducted to assess…

Background: Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice. Objectives: However, a wide…

This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…

Large language models (LLMs) have significantly advanced smart education in the artificial general intelligence era. A promising application lies in the automatic generalization of instructional design for curriculum and learning activities, focusing on two key aspects: 1) customized generation: generating niche-targeted teaching content based on…

Meaningful collaborative interactions in asynchronous online mathematics teacher professional development (PD) may provide teachers with valuable opportunities to learn. We studied collaborative interactions in online teacher PD activities that involved embedded videos, prompts, discussions, and multiple online tools. Analysis of teacher responses…

This paper describes the design, implementation, and results of a training action with prospective primary education teachers, focusing on the creation of problems involving proportional and algebraic reasoning. Prospective teachers must solve a proportionality problem using both arithmetic and algebraic procedures, and then vary it to motivate…

In this study, we focus on a specific visual representation that is used across several mathematics and science content areas: the 'partitioned square' (PS). Previous research has examined PSs in single content areas in isolation, such as for mathematics polynomials or biology random mating, where the PS was generally in the service of other…

Students' success in physics problem-solving extends beyond conceptual knowledge of physics, relying significantly on their mathematics skills. Understanding the specific contributions of different mathematics skills to physics problem-solving can offer valuable insights for enhancing physics education. Yet such studies are rare, particularly at…

The most common challenges students face in solving first-order ordinary differential equations (ODEs) can be overcome by identifying the types of errors, understanding the factors that cause difficulties, and finding appropriate solutions. Therefore, this research aimed to adopt a descriptive qualitative approach, including nine sixth-semester…

Research literature about visually impaired students' approach to mathematics is still very scarce, especially in the case of algebra, even though mathematical content is becoming increasingly accessible thanks to assistive technologies. This paper presents a case study aimed at describing a blind subject's process of algebraic symbol manipulation…

This article examines the integration of financial numeracy in secondary mathematics textbooks. It addresses the gap in literature on how financial concepts are portrayed in textbooks, contributing to the establishment of financial numeracy as a field of research and practice. The study analyzed financial numeracy tasks in three published textbook…