This study aims to describe the ability of students' mathematical connections in solving problems in the circle equation material through transposition studies. The method in this research is a descriptive qualitative approach, the techniques used in the study are tests, interviews, and documentation to explore data in research. Test and interview…

Geometry is one of the basic areas of school mathematics education, and it is important for elementary students. However, students with mathematics learning disabilities (MLD) struggle with geometry learning. Research has demonstrated that concrete-representational-abstract (CRA) teaching is an effective practice for students with learning…

This paper discusses an interesting, classic problem that provides a nice classroom investigation for dynamic geometry, and which can easily be explained (proved) with transformation geometry. The deductive explanation (proof) provides insight into why it is true, leading to an immediate generalization, thus illustrating the discovery function of…

Extreme Learning Machine (ELM) is a training algorithm for Single-Layer Feed-forward Neural Network (SLFN). The difference in theory of ELM from other training algorithms is in the existence of explicitly-given solution due to the immutability of initialed weights. In practice, ELMs achieve performance similar to that of other state-of-the-art…

This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students' competence in justifying an ellipse. We analyse the complex interactions between…

The solution of problems and the provision of proofs have always played a crucial part in mathematics. In fact, they are the heart and soul of this discipline. Moreover, the use of different techniques and methods of proof in the same mathematical field, or by combining fields, for the same specific problem, can show the interrelations between the…

One way to ease the solution of physics problems is to visualize the situation. However, by visualization we do not mean the pictorial representation of the problem. Instead, we mean a sketch for the solution of the problem. In this paper a new approach to solving physics problems, based on decomposing the problem into with and without gravity, is…

Gestures are associated with powerful forms of mathematical understanding. However, determining the causative role of gestures has been more elusive. In the present study, we inhibit students' gestures by restraining their hands, and examine how this impacts their problem-solving when presented with geometric conjectures to prove. We find no…

Visuospatial thinking is considered crucial for understanding of three-dimensional spatial concepts in STEM disciplines. Despite their importance, little is known about the underlying cognitive processing required to spatially reason and the varied strategies students may employ to solve visuospatial problems. This study seeks to identify and…

This paper concerns the design of a specific computer-based educational environment fostering students' shift from argumentation to proof in geometry. In particular, we focus on the language difficulties that such a shift might present and on the need for suitable interventions to overcome them. In this respect, we designed a specific device,…

There has been a large amount of research about the impact of dynamic geometry software (DGS) on the learning of mathematics mainly related to different representations of mathematical concepts and functional dependences. This paper goes beyond these investigations by suggesting meaningful connection and integration of DGS with physical resources…

We report the design of an analog technology, what we refer to as a SunRule, that uses sunlight to model multiplication. Physical models that explore multiplication are fixtures in elementary mathematics classrooms. Our interest in physical models of multiplication was driven by an overarching design problem: How could a physical tool realize a…

The instructional decisions made by classroom teachers impact the learning acquired by students. The Common Core Mathematics Standards and the history of mathematics education in the United States create a background for how geometry standards are taught in one Midwest middle school. A study of the pacing guides, lesson plans, and naturalistic…

This paper proposes an experimental path aimed at guiding upper secondary school students to overcome that discontinuity, often perceived by them, between learning geometry and learning algebra. This path contributes to making students aware of how the algebraic language, formalized in the most powerful form by Descartes, grafts itself onto the…

This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…