In this exploratory study, we investigate undergraduate students' engagement with generative Artificial Intelligence (genAI) in proving mathematical statements. We selected six mathematical statements to conduct interviews with three students. We present the emergent framework, Students' Interactive Proving Experience with AI (SIPE-AI), which…

While there are many documented approaches to using technological tools to support collaboration in remote environments, studies related to proof-based courses are overwhelmingly situated in the context of geometry. This study uses instrumental genesis theory to study how students in an introduction to proofs course operationalize the…

This study explores the effects of a computer algebra system on students' mathematical thinking. Mathematical thinking is identified with mathematical thinking powers and structures. We define mathematical thinking as students' capacity to specialize and generalize their previous knowledge to solve new mathematical problems. The study was…

In this article, we provide an empirical example of how digital technology; in this case, GeoGebra may assist students in uncovering--or whiteboxing--the content of a mathematical proof, in this case that of Proposition 41 from Euclid's "Elements." In the discussion of the example, we look into the impact of GeoGebra's…

The aim of this study is to explore how structural and process aspects of secondary school students' mathematical reasoning support each other in a collaborative learning environment through the integration of "GeoGebra" software and the ACODESA method. The study involved four eighth-grade secondary school students, who participated in…

Traditional rote learning methods often fail to adequately develop reasoning skills in mathematics, particularly among pre-university students. This study addresses challenges in fostering mathematical reasoning abilities, as evidenced by declining TIMSS results and resistance to pedagogical innovations. My online teaching with GeoGebra (MyOT_G+)…

This paper presents research into closed orbits parallel to quadrilaterals inscribed in various geometric shapes that can be represented by mathematical functions: straight lines, circles, ellipses, parabolas, and hyperbolas. Mathematical proofs have been given for the existence of an infinite number of parallel orbits for each of these shapes.…

Algebra has long been a gatekeeper to more advanced mathematics and to tertiary education. International assessments, such as PISA, have also shown that this trend extends beyond borders, making the topic of when algebra should be learned quite political. Many reforms have been instituted since the early 1990s to infuse algebraic thinking into…

The purpose of this study was to compare two treatments, namely the use of hands-on activity media and computer-based media on the conceptual understanding of mathematics and the reasoning ability of junior high school students. In order to obtain complete information about the comparison of the two, researchers also use groups without learning…

Remote learning has reduced the mathematical performance of students. Mathematical reasoning is the critical skill that enables students to make use of all other mathematical skills. The aim of the present study was (1) to develop the mathematical reasoning skills of underachieving students and (2) to explore the application options, benefits and…

This study uses the 2011 Trends in International Mathematics and Science Study to investigate the relationships among students' and teachers' computer use, and eighth-grade students' mathematical reasoning in three high-achieving nations: Finland, Chinese Taipei, and Singapore. The study found a significant negative relationship in all three…

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance…

We present a geometrical investigation of the process of creating an infinite sequence of triangles inscribed in a circle, whose areas, perimeters and lengths of radii of the inscribed circles tend to a limit in a monotonous manner. First, using geometrical software, we investigate four theorems that represent interesting geometrical properties,…

This paper presents a small group computing environment in which four students each control a different point in a geometric space, such that as a group they collectively manipulate the vertices of a quadrilateral. Prior research has revealed that students have considerable difficulty in learning about the interrelationships among quadrilaterals…