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…

Linear algebra is gaining increased attention due to its applications in many modern high-tech industries, such as artificial intelligence, machine learning, and robotics. Coordinate systems underlie many concepts in linear algebra and promote students' spatial thinking of key concepts by imposing a visual aspect to courses that may otherwise be…

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…

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…

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla,…

Background and Context: Integrating computer science (CS) and math in classrooms is an increasingly recognized way for schools to address national CS mandates. There is a need to understand how professional development (PD) can support teachers to integrate. Objective: We examined math teachers' interest, and confidence, in math, CS, and student…

Spanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers' professional practice of designing tasks. According to this, our…

This article uses the concurrent mixed methods design to explore the errors made by 171 Grade Seven learners in algebraic problem-solving within the Assin Central Municipality in Ghana. The participants were categorized into low-achieving and high-achieving groups based on their performance in a pretest, to help provide a detailed examination of…

Conjectures are a key component of mathematical inquiry, a process in which the students raise conjectures, refute or dismiss some of them, and formulate additional ones. Taking a design-based research approach, we formulated a design principle for personal feedback in supporting the iterative process of conjecturing. We empirically explored the…