This article presents a theoretical-didactic perspective on the formation and development of concepts concerning mathematical objects as a result of research on didactic difficulties in dealing with concepts in school. The theoretical foundation that supports the research is based on the contributions of the materialist approach to the theory of…

In this article, the author shares two investigations that relate the variables of height and volume using different contexts. Each of the investigations surfaced unfinished learning for students, regardless of their starting place, and facilitated growth in understanding of measurement and algebra. The Functions and Volume of Vases task…

Geometric concepts are fundamental to early geometry education, and developmentally appropriate practices are crucial for teaching them to young children. Robotic coding is an effective tool in many areas of early mathematics and has significant potential in teaching geometric concepts. This study aimed to test the impact of a research-based…

Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

This cross-sectional study investigated the conceptual understanding of linear relationships for 195 students enrolled in a single school in a large, urban district across five mathematics courses: Grade 7 Math (n = 24), Grade 8 Math (n = 52), Geometry (n = 43), Algebra 1 (n = 31), and Algebra 2 (n = 45). The following questions guided this study:…

Technology, in particular augmented reality (AR), has the potential to greatly enhance interactive learning environments for mathematics in both classrooms and other teaching environments. The purpose of the present study was to investigate existing literature on AR in mathematics education. We selected papers from 10 databases, Scopus, Web of…

This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry. The explorations flow from a simple change in sign: in the complex numbers a + bi, where…

In this article, we argue that folding back is successful when the learners engage in exploratory talk. To support our argument, we sourced data from a Grade 10 mathematics classroom of 54 learners who participated in a four-week teaching experiment conducted by the second author. We mainly focused on talks in two groups of learners to address the…

Special tasks for pre-service teachers (PSTs) in university mathematics courses ("interface tasks") are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and…

This study explored pre-service teachers' perceptions of a 3D printing integrated science, technology, engineering, and mathematics (STEM) module within a college-level mathematics content course. Data from surveys and reflections collected from nineteen participants were analyzed. Results indicated that the pre-service teachers perceived…

The concept of a mathematical definition causes severe difficulties among students during problem solving and proving activities. Students' difficulties with the use of mathematical definitions often arise from the fact that students are often given those definitions instead of constructing them. With the aim of developing an understanding of the…

In the world where we always meet geometric constructions, it is a necessity to make sense of the objects belonging to these constructions. In this respect, this study aimed to examine the teaching of volume with the blending of the realistic mathematics education (RME) and GeoGebra. The study group consisted of 12 students attending lessons…

In the 11th-grade Vietnamese Mathematics Curriculum, students learn about parallel relations between planes in space. This is cognitively challenging for many students. Studies have shown difficulties relating to limited spatial imagination and drawing representations. The teacher's approach also causes difficulties for some students; for example,…

This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

This survey paper presents recent relevant research in mathematics education produced in Spain, which allows the identification of different broad lines of research developed by Spanish groups of scholars. First, we present and describe studies whose research objectives are related to student learning of specific curricular contents and…