This study addresses high school students' conceptions of mathematical definitions of congruent and similar triangles. The findings indicate that many of the participants differentiated between definitions and theorems and did not always accept the congruent and similar triangles theorems as formal definitions of congruency and similarity. Based…

Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

This paper aims to clarify how the use of the GeoGebra dynamic geometry program helps students understand the relationships between different representations of a linear function and develop the ability to plot a linear function. The study was based on a quasi-experimental design. In control classes, the topic of functions was presented without…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

This study aims to establish a knowledge base on how to support students in learning. We develop an initial hypothetical learning trajectory by formulating learning activities and predicting the development of students' thinking and understanding. The methodological framework employed in this study is design research, which seeks to generate…

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

This work intends to disseminate a didactic experience in mathematics, in times of pandemic, in an emergency remote teaching situation, at the Portuguese School of Cape Verde, using the Desmos digital platform. The topic addressed was the study of the volume of geometric solids. The main objective was to contribute to the learning of mathematical…

Geometry is used in different ways in the teaching of linear algebra. In this paper, I offer a typology of these ways, which I call varieties, and address three central questions. The first question is, "What varieties of use of geometry in the teaching of linear algebra exist?" This question is addressed through an analysis of six…

This article presents activities focused on developing some essential Year 1-3 fraction understandings (i.e., joining/composing, decomposing/ partitioning) while aligning these activities to the Australian Curriculum content strands and content descriptions. Additionally, the authors describe the materials/resources needed, the key vocabulary…

The surface area of a sphere as a function of radius, "r," is a derivative of the volume of the sphere, and a few other families of solids with this property are known. Sometimes, the derivative relationship can be reached with a tricky choice of size parameter "r." This paper presents an activity for students that discovers…

Textbooks play an important part in teaching and learning mathematics. However, textbook research on spatial ability has so far received little attention. In this study, we investigated whether school mathematics textbooks provide enough opportunities for primary students to learn three-dimensional shapes and help them acquire spatial ability.…

This paper reports on a teaching experiment on mathematical modelling in an upper secondary school class that investigates how the constructs of "model eliciting" and "emergent modelling" may be brought together to inform teaching and learning. A prominent role is covered by the process of task design, seen as a complex process…

We present exploratory analyses of three cases in which groups of four (quartets) worked with video recordings of choreographed performances from the opening ceremony of the 2016 Rio Olympic Games. We asked quartets to view the recordings, explain what performers were doing by reenacting what they noticed in the video, and create their own…

In general, many people still view mathematics as a subject that is far from reality and culture in everyday life. Historically, in fact, mathematics is very close to daily life and was developed by humans in response to the surrounding phenomena. Indonesia has diverse cultures, including in Yogyakarta. This culture can be used to explore…