Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling competencies. The study described in this paper was a systematic literature review of the literature on modelling competencies published over the past two decades. Based on a full-text analysis of 75 peer-reviewed studies indexed in renowned databases and published in English, the study revealed the dominance of an analytical, bottom-up approach for conceptualizing modelling competencies and distinguishing a variety of sub-competencies. Furthermore, the analysis showed the great richness of methods for measuring modelling competencies, although a focus on (non-standardized) tests prevailed. Concerning design and offering for fostering modelling competencies, the majority of the papers reported training strategies for modelling courses. Overall, the current literature review pointed out the necessity for further theoretical work on conceptualizing mathematical modelling competencies while highlighting the richness of developed empirical approaches and their implementation at various educational levels.

Innovative methods can change the paradigm of teaching mathematics and inspire teachers to espouse new ideas and gain new experiences. The flipped classroom (FC) is currently an innovative pedagogical approach that has high potential to transform the teaching of mathematics. In the case study described in this paper, we investigated one mathematics teacher’s transformation of teaching in two mathematics classrooms through implementing interventions based on FC methods; furthermore, we identified several key points of FC design as well as challenges and opportunities afforded by teaching mathematics in FCs. The results of the study showed that the tasks posed by the teacher, the implemented discourse, teacher feedback and scaffolding, and the teaching–learning environment were changed in FCs, although the approaches used by the teacher to analyze the tasks and students’ learning were similar to those used in non-FCs, which points out the strengths of traditional teaching approaches. The study indicates that although teaching mathematics in FCs created some difficulties for teaching, well-designed FCs offered a great opportunity to promote students’ mathematical thinking and understanding. Overall, the results highlight that through FC, teachers can develop students’ mathematical potential with FCs.

Many students are becoming increasingly disengaged in school, particularly in mathematics. This is an important problem as lack of engagement may threaten students’ achievement and performance in mathematics. A flipped learning pedagogy, which encourages students to take an active role in learning mathematics, has become a widely researched topic in recent years. However, few empirical studies to date have focused on the influence of flipped learning on student engagement in secondary mathematics classrooms. This qualitatively oriented study aimed to extend existing research on the role of flipped learning in behavioral, cognitive, and emotional engagement by adopting a social constructivist perspective to examine a secondary mathematics classroom. The participants were 33 high school students and their mathematics teacher, from whom data were gathered using multiple empirical methods. The results indicate that a flipped learning pedagogy has the potential to play a positive role in behavioral, cognitive, and emotional engagement as it provides learners with many possibilities for the learning of mathematics. However, to successfully flip learning, it is important to have a well-developed interactive design and to encourage social interaction in mathematics teaching and learning. Engagement was found to be negatively affected when the students had a negative perception of flipped learning and failed to complete the pre-class tasks. Overall, our results indicate that mathematics education can benefit from a flipped learning pedagogy as it has the potential to strengthen students’ engagement and mathematics learning in a social environment.

Lesson planning is of central importance to the teaching of all subjects in school. However, despite its high relevance, there is still a substantial need for a comprehensive review of factors affecting lesson planning. Empirical evidence on how teachers’ competence in lesson planning can be developed, what challenges may be encountered during the lesson planning process, and successful lesson planning designs and practices should come to light on. To close this gap the current paper presents the results of a systematic review of 20 empirical research studies on teacher competence in mathematics lesson planning. For detailed insight into the most recent contributions of the reviewed studies on mathematics lesson planning, we analyzed studies conducted during the past decade, adapting the “process model of lesson planning” and the model of “competence as continuum” as a heuristic for approaching lesson planning. We present key results of the studies related to four major themes: (1) dispositions and their influence on developing and implementing lesson plans, (2) quality aspects of lesson plans and the development of lesson planning skills, (3) difficulties in lesson planning, and (4) the relationship between lesson planning skills and performance in implementation of lesson plans. The results of our literature review reveal that teachers (especially novice teachers) face difficulties in lesson planning and their overall competence (and knowledge) are not at an expert level. However, as the results of the examined studies pointed out, teachers can acquire such competence and knowledge through training within initial teacher education and professional development. Overall, teachers need support in planning mathematics lessons by delineating their lesson plan to improve their awareness of students’ thinking, possible learning trajectories, effective usage of the curriculum and teaching resources, and the potential of innovative pedagogies that incorporate new technology.

Despite the growing interest in the field, the overall impact of augmented reality (AR) and virtual reality (VR) on mathematics learning remains unclear, with previous studies reporting mixed results. Moreover, to date, no systematic review has evaluated the potential of AR/VR in mathematics education, including its benefits and drawbacks for learners. To address this gap, the present systematic literature review aims to identify research trends, determine characteristics and methodologies, and explore the potential benefits and drawbacks of AR/VR technologies in mathematics learning based on existing empirical studies. In accordance with the PRISMA guidelines, we analyzed 59 peer-reviewed journal articles published in English that focused on AR/VR implementation in mathematics education. The review determined that geometry was the most widely studied topic of mathematics, with several studies focusing on the use of AR/VR to assist students with learning disabilities. The present review offers evidence for the potential of AR/VR potential in consolidating learners’ socio-emotional, cognitive/meta-cognitive, and pedagogical development in mathematics learning. Nevertheless, a few issues, including technological glitches, cost, start-up effort, health issues, and unfamiliarity with AR/VR, pose challenges to the successful application of AR/VR in the classroom. This systematic review contributes to the existing body of knowledge in the field and recommends avenues for future research.

Educators sometimes effect changes in education through the implementation of new ideas, and sometimes extraordinary circumstances force them to change their educational approaches, as during the COVID-19 crisis. Although we live in a digital age, the limited use of technology in education, particularly prior to the COVID-19 pandemic, and teachers’ insufficient experience with online or hybrid learning and teaching approaches resulted in several countries being unprepared for education during the pandemic. The flipped classroom (FC) is an innovative pedagogy with the potential to engage students in mathematics education using hybrid education combined with online and face-to-face learning, which is especially important during a pandemic. However, despite the high expectations surrounding this innovative approach, to date, no systematic literature review has discussed the opportunities and pitfalls of FCs in mathematics education regarding pandemic-related issues. In the present systematic review, we aim to bridge this gap and highlight the importance of flipping mathematics instruction during the pandemic and beyond. The results, which are based on textual analysis of 97 eligible articles, demonstrate that FC is a promising pedagogy that has numerous benefits for mathematics teaching and learning, although it is not a panacea for pandemic-related issues, as it also has several significant pitfalls. Overall, if the mechanism of mathematics education is to be crisis-ready, we should learn from experiences during the pandemic. In this regard, the current review contributes to research in mathematics education with the aim of gaining insight into successful implementations of FC pedagogy, not only during the pandemic but also beyond the crisis era of a pandemic.