The implementation of large-scale intervention and development projects is often problematic, and the impacts of such projects usually fall somewhat short of what was expected. Additionally, the rationalities of intervention projects are not carried over into classroom teaching as directly as expected. This problem is generally known, but…

This article reports on the design and implementation of a didactic sequence in the frame of a design-based research study. The research aim is to test the hypothesis that affordances of dynamic geometry may support students' awareness of logical relationships between geometrical properties of constructed figures. We elaborate on the task design…

When students engage with a digital tool to tackle a mathematical task, the interplay between their digital competencies and mathematical abilities gives rise to what is termed mathematical digital competency (MDC). Recognising the significance of MDC as an integral component for contemporary students, the relevance of cultivating mathematical…

Running two separate two-stage randomized trials, we implement and test three variants of a small group instruction intervention aimed at improving mathematics competencies for the 20% lowest achievers in mathematics in grades 2 and 8 in Danish public schools. We calculate immediate impacts on math competencies as well as impacts in the medium…

The aim of this longitudinal study was to examine the differences between high- and low-performing students' development of fraction proficiency over a school year and to investigate how those differences were related to instruction in fractions versus instruction in other mathematics topics. The data for this study were drawn from a group of (n =…

Transfer functions are convenient representations to analyse cause-and-effect relationships of linear time-invariant dynamic systems. Traditionally, transfer functions are introduced using the Laplace transform. In this paper, we argue that the Laplace transform method is not a necessary prerequisite to understanding the topic 'transfer…

This paper presents empirical findings from a qualitative study on Minecraft as a mathematical tool and learning environment. Even though Minecraft has been used for several years in classrooms around the world, there is a lack of detailed empirical studies of how students learn subject-related content by working with the game. This study is based…

For the past decade, philosophers of mathematical practice have examined the nature and function of proofs in mathematical practice, most often in mathematical research practice. More recently they have examined how mathematicians assess and get to know a proof not just by reading it, but through active engagement with the proof. For example,…

The article is based on reforms in the Danish educational system, encouraging a new focus on learning goals. The use of learning goals is investigated with a teacher in one mathematics class. Inspired by categories from goal theory, different types of students are described regarding their understanding of the usefulness of visible learning goals…

In our investigation of university students' knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was…

The growing use of technology for mathematics in higher education opens new pedagogical and technological challenges for teachers. The objective of this study was to analyze the teaching approaches and technology-related pedagogical competencies of 29 mathematics teachers (15 females and 14 males) from nine European countries. After conducting…

We investigate the challenges students face in the transition from calculus courses, focusing on methods related to the analysis of real valued functions given in closed form, to more advanced courses on analysis where focus is on theoretical structure, including proof. We do so based on task design aiming for a number of generic potentials for…

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

This study draws on the concept of cultural capital to determine whether the cultural capital of students is related to their perceptions of classroom interactions, specifically teacher--student feedback practices. The analysis of new data in 'Feedback and Cultural Capital,' a Danish survey of feedback practices among 14-year-old and 15-year-old…

This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis…