This contribution focuses on reasoning about quadrilaterals provided by lower secondary school students when working with pre-prepared dynamic constructions. On this topic, we present an exploratory empirical qualitative study carried out within a GeoGebra Classroom environment, and our diagnostic instrument consists of a set of dynamic…

This qualitative case study, grounded within the interpretive paradigm, analyzed the errors and misconceptions made by 11th-grade learners when tackling the tangent-chord theorem task in Euclidean geometry. Studying Euclidean geometry helps learners develop critical thinking skills, such as constructing arguments and applying logical reasoning.…

The problem in this study is to evaluate the improvement of students' geometry skills using the GeoGebra application by focusing on two key indicators: logical thinking and drawing skills. This study employs both quantitative and qualitative methods. In the first stage, quantitative data were collected through pretests and posttests to measure…

This study focuses on the design and the implementation of a digital environment aimed at fostering strategic planning competence in problem-solving through individualization features: the Individualized Planned Strategy Environment (IPSE). Within IPSE, students are engaged in a sequence of oriented activities, guiding them in constructing and…

This study investigates the associations of spontaneous "dynamic gesture" and "transformational speech" with the production of "deductive proofs" in participants' reasoning about geometric conjectures (N=77). Although statistical analysis showed no significant association, the result suggests that purposefully…

In a dynamic geometry environment (DGE) conjectures can be generated by manipulating figures with different dragging strategies. One strategy (maintaining dragging) that has been the focus of various studies, consists of inducing a specific geometric property and trying to maintain it. In this paper I focus on abduction and evidence within such…

Robust understanding of geometry is important for students' future studies in mathematical sciences, many careers, and for understanding the world around them. Therefore, the aim of this study was to understand the geometric thinking levels of 9th graders in Ghana before they enter the Senior High School. This study used the van Hiele theory (Van…

In this article, the authors describe their experiences with planning, implementing, and revising a lesson for which the goal is for students to consider the mathematical and pragmatic issues that are related to a task of maximizing the area for a fixed perimeter. The authors also wanted students to engage in the Standards for Mathematical…

Many students share a certain amount of discomfort when encountering proofs in geometry class for the first time. The logic and reasoning process behind proof writing, however, is a vital foundation for mathematical understanding that should not be overlooked. A clearly developed argument helps students organize their thoughts and make…

In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…

In this design experiment study, we investigated the problem: What conditions might foster students' discernment of a critical aspect--variation in unidirectional change (e.g., discerning a "decreasing" increase)? At a public middle school in a large US city, we led a sequence of three days of whole class lessons, followed by task-based,…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

In this study, it was aimed to examine the relation between seventh-grade students' quadrilaterals achievement levels and Van Hiele geometric thinking levels. Survey method was used. The sample of the study was 160 students from the three different districts of Kayseri, as Melikgazi, Incesu, and Tomarza. Van Hiele geometric thinking test and…

The geometry in flipbook multimedia can improve the necessary skills of the 6th graders, so that they achieve the highest level of geometric thinking that is informal deductive. The flipbook which uses technology with flipping experience, animation, video, and music is different than the ordinary printed book. Also, it looks more exciting and…

In this report, we discuss the findings from 2 pilot studies investigating the effects of interventions designed to provide students in Grades 3-5 with opportunities to work with dynamic and static models of angles in a dynamic geometry environment. We discuss the effects of the interventions on the children's development of quantitative reasoning…