In this paper, I propose an analysis of the structure of Clairaut's "Éléments de Géométrie" (1741), a book presenting geometrical knowledge organized around problems, with rich metadiscourse connecting problems and other elements of mathematical content. This analysis is inspired both by the "Series of problems at the crossroad of…

We characterize the thematic trends of the "Geometry and its Applications Meeting." This meeting is held periodically in Colombia, country in which our study was carried out. We used a taxonomy of key terms specific to mathematics education to code the proceedings of this meeting. The study variables are purpose, educational level,…

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 adopts a semiotic perspective on mathematical learning according to Peirce, in which the actions on material arrangements are considered the bases for diagrammatic work. The focus is on the learner's actions using digital and analogue material arrangements which are the starting point for the reconstruction of the learner's mathematical…

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…

However, geometry is the area with the most concrete possibility of mathematical topics which contains more abstract concepts, students experience difficulties while understanding. Therefore, the connection of issues with daily life to concrete the subjects and the ability of connecting geometric concepts with daily life of the teachers and…

The important role that geometry plays in the mathematics curriculum has been extensively documented. However, the reduction of geometry in school mathematics, and the focus on basic computation and procedures, raises the question of the competencies students acquire and the classroom atmosphere in geometry lessons. The goal of this multiple case…

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

To understand learners' appropriation of technological tools and geometrical understanding, we draw on the theory of instrumental genesis (Lonchamp, 2012; Rabardel & Beguin, 2005), which seeks to explain how learners accomplish tasks interacting with tools. To appropriate a tool, learners develop their own knowledge of how to use it, which…

The Common Core State Standards in Mathematics (CCSSM) represent a major attempt in a long line of attempts to reform the American Education system surrounding Mathematics. These standards aim to establish a nationwide set of curriculum, seeking to ensure equity for all students in the U.S.A. Some of the standards included are new to all teachers…

High school students (N=213) of various ability levels enrolled in first-year algebra classes were presented lessons concerning geometry concepts. The lessons were varied according to the degree of complexity of the examples that were presented. Students then were tested over their understanding of the concepts. The test questions ranged from…