Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means…

The teacher's use of representations is a crucial aspect of instructional quality in mathematics education, given their pivotal role in facilitating mathematics learning. However, in our international research community, perspectives on what constitutes high-quality use of representations may vary. This cross-cultural study aims to explore whether…

Introduction: Across the world, mathematical expressions are represented very differently in braille. The aim of this study was (1) to gain an overall insight in mathematical braille notations and (2) to investigate how mathematical braille notations support braille readers in reading and comprehending mathematical expressions. Method: Twenty…

In tertiary mathematics courses, students often have difficulties acquiring an understanding of the mathematical concepts covered. One approach to address this problem is to implement so-called Concept-Tests. These are multiple-choice questions whose distractors represent common problems and misconceptions related to the concepts. While there…

This paper presents a modified approach to subject-matter didactics, in which the focus is not on the content itself, but on the students' view of the content. The introduction deals with an overview of subject-matter didactics and the notion of beliefs used in this paper. The main portion of the paper deals with presenting the concepts of a book…

The integration of dynamic visualisations, feedback formats and digital tools is characteristic of state-of-the-art digital mathematics textbooks. Although there already is evidence that students can benefit from these technology-based features in their learning, the direct comparison between the use of a comparable digital and printed resource…

When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

This article reports on the understanding of the function concept by pre-service mathematics teachers from two countries (Germany and Croatia). We focused on investigating students' concept definition and concept image of the function in relation to their curriculum experiences. Data were collected using a questionnaire in the form of open-ended…

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…

Although it is widely known that reading plays a significant role in mathematics performance, it remains unclear how specific reading component skills and item characteristics are associated with adults' mathematics performance. The aim of this study was to investigate reading component skills (printed vocabulary, sentence processing, passage…

Previous research on the role of prior skills like proportional reasoning skills for the development of mathematical concepts offers conclusions such as "more (prior skills) is better (for later learning)." Insights, which prior skill "level" goes along with which "level" of learning outcomes, may advance the…

This paper presents a replication study investigating the effectiveness of a strategy to assist students with learning difficulties in adding fractions. Drawing on the research conducted by Grünke et al. (2023), this single-case analysis extends the application of the "Look, Ask, Pick" (LAP) mnemonic technique initially introduced by…

Fractions are an integral part of the mathematics curriculum. Most students acquire proficiency with these concepts during the course of their elementary education and are usually able to perform basic fractions operations when reaching middle-school age. However, a considerable number of students require extra help to not fall further and further…

"The limits of my language are the limits of my mind. All I know is what I have words for" (Wittgenstein). When learning something completely new, we connect the unknown term to an already existing part of our knowledge. We can only build new ideas and insights upon an existing conceptual foundation. In the field of statistics, we…

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…