Across multiple age groups and academic disciplines, research has shown that incorporating multimodal signs into instruction can enhance student learning. For instance, gesture might be synchronized with speech or written signs. The present study reports on the semiotic resources used by a teacher-researcher to support kindergarten students'…

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…

There is mixed evidence as to whether concrete manipulatives (e.g., toy animals) are better than abstract manipulatives (e.g., counters) for teaching mathematical concepts to children. Concreteness is defined as the amount of extraneous information a manipulative provides, and in this study we aimed to unpick which dimensions of concreteness…

This article presents and analyses a didactic proposal based on manipulative material (Knobless Cylinders) used in a Montessori classroom of 3-6-year-old pre-schoolers. Choosing this material is justified in relation to the competencies/strategies/skills used during the development of mathematical patterning. Numerous studies emphasise the…

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…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

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…

This article addresses the nature of student-generated representations that support students' early algebraic reasoning in the realm of generalized arithmetic. We analyzed representations created by students for the following qualities: representations that distinguish the behavior of one operation from another, that support an explanation of a…

In addressing the challenge of fostering functional thinking (FT) in secondary school students, our research centered on the question of how an embodied design can enhance FT's different aspects, including input-output, covariation, and correspondence views. Drawing from embodied cognition theory and focusing on an action- and perception-based…

In this note we describe the mathematics that emerges from the construction of an origami box. We first construct a simple origami box from two rectangular sheets and then discuss some of the mathematical questions that arise in the context of algebra, geometry and calculus.

LEGO® stop-motion animations were developed to engage first-year university students in the topics of matrices, vectors, linear geometry and linear transformations. LEGO® provided a versatile medium through which a wide range of concrete and abstract concepts could be physically demonstrated in both two and three dimensions. It was also familiar…

The aim of the research was to examine and evaluate how preservice mathematics teachers' use of manipulatives to teach mathematics. In the current research, one of the qualitative research methods, case study was used. The research was conducted with 21 preservice mathematics teachers. Ten instructional sessions with manipulatives were carried out…

Providing all students with equitable treatment and access has been a cornerstone of mathematics education reform (Association of Mathematics Teacher Educators, 2015; National Council of Teachers of Mathematics, 2014). Studies in mathematics classrooms show that using hands-on and interactive materials (i.e., "manipulatives") support…

This paper addresses the ways that real objects are important for conceptual development and understanding of pi. While using real objects in teaching and learning pi with nine university pre-service teachers (PSTs) of Mathematics, the teaching and learning processes were framed under the lens of social constructivist perspective (Vygotsky, 1978).…