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 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…

Creative thinking transforms existing information, either from long-term memory or external sources, into new representations and innovative ideas. Creative thinking is an activity that processes received information to produce new representations and innovative ideas. Developing this skill is essential for students; however, recent research has…

The basic notions of combinatorics, including systematic listing and permutations, are important topics of mathematics that are recommended to be learned eventually from elementary schools. However, there is little research in mathematics education regarding elementary students' combinatorial strategies. The purpose of this research is to…

Students are required to have the ability to implement mathematics in solving everyday life problems. A good solving process will produce an excellent solving ability. The existing problem-solving stages cannot be used in solving problems with the Higher Order Thinking Skills (HOTS) category. The aims of this research are 1) to know students'…

The reasons for teaching programming in school are indeed manifold. Programming can for example be utilized as a vehicle for understanding and learning particular mathematical subject matter, or as a tool for solving mathematical problems. In this paper, however, we propose to utilize programming as a vehicle for developing mathematical…

This investigation explored the role of artificial intelligence (AI)-powered gamification on mathematics cognition through a mixed-methods design, blending an intervention with a gamified learning application (app) and a survey to evaluate student engagement and performance. The study explores the nexus of gamification, AI, and mathematics…

With the aim of engaging more students in meaningful thinking in mathematics, a cohort of Year 7 students were introduced to a 'Building Thinking Classrooms' framework for learning in mathematics. In this paper, the authors outline the key features of the implemented framework and share reflections on challenges and benefits.

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…

This paper aims at using a Use-Modify-Create approach to explore students' mathematical problem solving by means of computational thinking (CT) and programming activities. The data collection method is participant observation, in which the researcher also has the role as teacher, guiding the group activities. In our study, two groups of students…

Critical thinking is a fundamental competence in 21st-century education, particularly in mathematics, where students frequently encounter contradictory information that requires logical reasoning and reflective judgment. This study explores the stages of critical thinking among junior high school students when solving contradictory mathematical…

This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

This study introduces a framework for analyzing opportunities for mathematical reasoning (MR) in school mathematics, using MR-relevant claims and their derivation as the unit of analysis. We contend that this approach can effectively capture a broad range of opportunities for MR across various teaching situations. The framework, rooted in…

Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

The aim of this study is to show how the GeoGebra software-supported collaborative learning environment contributes to a group of students using multiple representations and reaching generalisations while solving problems collectively. Blending individual and collaborative learning activities were carried out with a learning method called ACODESA…