Similarity is a crucial concept introduced in the 8th grade, and it is further developed and reinforced through associations during high school. This research aims to investigate how 8th grade students construct the concept of similarity using concrete manipulative support within the framework of APOS theory. The research was conducted as a…

Integer arithmetic is difficult for students worldwide. Although students' integer thinking has frequently been studied, little is known about typical instructional practice for this difficult topic. Thus, to investigate what resources teachers use, we surveyed U.S. middle-grade teachers who teach negative numbers. About half the teachers said…

This article investigates the incorporation of loose parts as a means to enhance student creativity within educational environments. Loose parts refer to flexible, movable objects that can be manipulated, combined, and repurposed in various ways. The study delves into the theoretical underpinnings that support the connection between loose parts…

This study investigated the effect of a paper folding activity prepared to develop the sixth-grade students' concept definitions and images of parallelism and perpendicularity concepts. The study also examined how the concept definition and images changed after the paper folding activity. A combination of quantitative and qualitative methods was…

In this study, a paper folding activity task, which involved reaching the Pythagorean Theorem with a series of steps was designed. The aim of the task is to reach the Pythagorean Theorem with folding activities by deductive reasoning and logical inference. The study aimed to examine the effectiveness of the task and to share the patty paper…

Physical manipulatives enhanced knowledge acquisition by engaging learners in hands-on experiences that supported spatial reasoning. These tools allowed learners to see, touch, and manipulate objects, improving their ability to mentally rotate and visualize structures. This study challenged the assumption that most learners are purely visual by…

Learning Transformation Geometry (TG) needs a more informal approach to concern situational problems. This study aims to develop actionable knowledge of TG in the form of design related to context and yet general enough to use digital manipulative activities in new situations. We propose such knowledge in the form of conjectured Local…

Mathematical inquiry involving hands-on activities has received increasing attention in mathematics education. Besides various customized physical teaching aids, subject-specific information technology, such as Dynamic Geometry System (DGS), finds extensive use in mathematical inquiry activities. However, effects of DGS and physical manipulatives…

An alternating treatments design was used to analyze the effects of concrete and virtual manipulatives on the duration and number of correctly solved linear equations by three middle school students with cognitive disabilities. Participants physically manipulated algebra tiles to solve an equation during the concrete manipulative condition. During…

South African learners' performance in mathematics, both locally and internationally, has raised significant concerns, particularly in the realm of algebra. To address this issue, a mixed-methods study was conducted to explore the effectiveness of using algebra tiles to teach algebraic expressions. The study aimed to investigate algebraic…

This paper aims to present ways in which origami can be used in the mathematics classroom. Origami provides powerful tools for examining mathematical concepts. The authors explain how origami can be used in senior high school and tertiary levels to explore a Platonic octahedron by focusing on connections between mathematical topics. The folding…

The teaching of first-degree equations is a key point in secondary school curricula and requires the careful planning and selection of appropriate teaching materials. On the other hand, dyslexia, a specific learning disability, is increasingly common in the classroom. Thus, in the context of inclusion, the teaching methodology used by the…

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students' geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the…

How do people use objects and gestures to shape scientific argumentation? This paper engages the concept of "entanglement" as a heuristic for considering the potentials and constraints that gestures and materials create for interactants. Drawing on video recorded data from an academic-year-long linguistic ethnography of a high school…

Finding teaching methods that foster students' development of geometric thinking and visualization skills is still a current challenge. This study analyses the effects of the combined use of paper folding and dynamic geometry on high school students' geometric thinking and visualization skills. A quasi-experimental study pretest/post-test design…