Research on teaching and learning quantum physics (QP) frequently explores students' conceptual difficulties to identify common patterns in their reasoning. The abstractness of QP is often found to be at the origin of students' conceptual difficulties. Due to this abstract nature students resort to common sense reasoning or classical thinking when they make meaning of QP phenomena. In this literature review, the 'abstractness' is closely investigated and nuanced to uncover what reasons for the abstractness students experience. Four reasons for students' conceptual difficulties can be categorised under the abstract nature of QP. These reasons are that students struggle a) to relate the mathematical formalism of QP to experiences in the physical world; b) to interpret counterintuitive QP phenomena and concepts; c) to transit from a deterministic to a probabilistic worldview; and d) to understand the limitations of language to express quantum phenomena, concepts, and objects. Combining these four reasons allows us to better understand the origin of conceptual difficulties in QP and why these difficulties persist over time. The implications of these findings for research and teaching practice are discussed.

The current trend in science curricula is to adopt a context-based pedagogical approach to teaching. New study materials for this innovation are often designed by teachers working with university experts. In this article, it is proposed that teachers need to acquire corresponding teaching competences to create a context-based learning environment. These competences comprise an adequate emphasis, context establishment, concept transfer, support of student active learning, (re-)design of context-based materials, and assistance in implementation of the innovation. The implementation of context-based education would benefit from an instrument that maps these competences. The construction and validation of such an instrument (mixed-methods approach) to measure the contextbased learning environment is described in this paper. The composite instrument was tested in a pilot study among 8 teachers and 162 students who use context-based materials in their classrooms. The instrument's reliability was established and correlating data sources in the composite instrument were identified. Various aspects of validity were addressed and found to be supported by the data obtained. As expected, the instrument revealed that context-based teaching competence is more prominently visible in teachers with experience in designing context-based materials, confirming the instrument's validity.

This study shows that using authentic contexts for learning differential equations in a differentiation-by-interest setting can enhance students' beliefs about the relevance of mathematics. The students in this study were studying advanced mathematics (wiskunde D) at upper secondary school in the Netherlands. These students are often not aware of the relevance of the mathematics they have to learn in school. More insights into the application of mathematics in other sciences can be beneficial for these students in terms of preparation for their future study and career. A course differentiating by student interest with new context-rich curriculum materials was developed in order to enhance students' beliefs about the relevance of mathematics. The intervention aimed at teaching differential equations through guided small-group tasks in scientific, medical or economical contexts. The results show that students' beliefs about the relevance of mathematics improved, and they appreciated experiencing how the mathematics was applied in real-life situations.

Background: Quantum physics has found its way into upper secondary school physics curricula worldwide. This trend coincides with increased attention for conceptual understanding in physics education in general and quantum physics education in particular. Students' conceptual difficulties of learning quantum physics are regularly reported. Little systematic attention has been paid to the opportunities and challenges teachers and students experience for teaching and learning quantum physics. Purpose: The opportunities and challenges secondary school teachers and their students experience were examined to gain insights into their perspectives teaching and learning quantum physics. These insights inform improvements in teaching and learning quantum physics at the secondary school level. Sample: Three teachers and five of each teacher's students participated in this study. Design & Methods: A context analysis was conducted to explore the experiences of the teachers and students. Teachers were individually interviewed; students were interviewed in a focus group session. The semi-structured interviews were analysed resulting in three case reports. These case reports were used to conduct a crosscase analysis to find common opportunities and challenges among teachers' and students' experiences. Results: Teachers and students felt that teachers had an important role in supporting students' understanding of quantum physics. Teachers were challenged to enthuse their students for quantum physics as they struggled to convey the relevance of the subject to their students. Freely available digital materials were considered as an opportunity to support students' conceptual understanding as they have the potential to engage students and benefit their conceptual development. Conclusion:Several implications are discussed to improve teaching and learning of quantum physics, such as opportunities for teacher professional development as well as ways to effectively use freely available digital materials.

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