Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when describing real fields such as magnetic and electric fields, as the vector arrows can overlap. The present study…

In this work, a bibliometric analysis of the investigations of the last 54 years focused on the teaching of topology and its applications in the learning of other areas of knowledge was carried out. The articles that appear in the SCOPUS database were taken into account under the search criteria of the words topology and teaching, connected with…

Learning Analytics is concerned with the use of data collected in educational settings to support learning processes. We take a Learning Analytics approach to study the use of immediate feedback in digital classification tasks in mathematics. Feedback serves as an opportunity for learning, however its mere existence does not guarantee its use and…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

We investigated how students' strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of geometry. We conducted a pre-posttest experimental study with 473 students in grade 9. Students were randomly assigned to one of three treatment…

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from…

In a Swedish second semester course on Euclidean and non-Euclidean geometry in mathematics education at Karlstad University, a bridging teaching strategy comprising elements from Mathematics, Didactics, History, Literature, and Technology was applied by using the concept of Narrative Didactics and Digital Interactive Mathematical Maps developed by…

Learning content in mathematics, such as vector geometry, is still predominantly taught in an abstract manner, as the visualization and interaction of three-dimensional problems are limited with classical forms of teaching such as blackboard lessons or exercise sheets. This research article proposes the use of augmented reality (AR) in mathematics…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

Most people would agree that helping students learn new information is important; however, there are numerous methods for achieving this goal, and not all of them have been proven to be effective. One method with intuitive appeal and some empirical backing is prompting students to self-explain. A self-explanation can be defined as generating…

It is easy to fall into the trap of thinking that teaching mathematics should greatly differ from teaching language arts. Classroom teachers at Munich International School in Starnberg, Bavaria, Germany, did not pay much attention to what language means to learning and teaching mathematics--until their geometry students offered language surprises…

Modern geometry teaching in schools in Japan was modeled on the pedagogies of western countries. However, the core ideas of these pedagogies were often radically changed in the process of adaptation, resulting in teaching differing fundamentally from the original models. This paper discusses the radical changes the pedagogy of a German mathematics…

These proceedings contain the papers of the International Conference e-Learning 2014, which was organised by the International Association for Development of the Information Society and is part of the Multi Conference on Computer Science and Information Systems (Lisbon, Portugal July 15-19, 2014). The e-Learning 2014 conference aims to address the…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…