Combining new educational approaches and educational technologies can make mathematics education more adaptable to pupils’ needs in the 21st century. Our explorative educational study aimed to identify how learning settings and learning environments should be designed to facilitate synthesising flipped approaches to education and using GeoGebra. To discover how to combine flipped approaches and GeoGebra in mathematics education, we conducted a nine-month educational study at a Viennese secondary school. In our study, we focused on pupils’ needs, as pupils are key to combining successfully new educational approaches and using technologies. Analysing our qualitative research data following design-based and grounded theory approaches indicates that the categories (a) clear task definition and task design, (b) feedback, (c) context and benefits, and (d) single-source learning environments are important for pupils when utilising GeoGebra for enhancing flipped education.

Most often, flipped classroom approaches in science and mathematics classrooms follow a traditional approach to teaching, where students receive direct instruction as homework and have to apply and deepen their knowledge in a follow-up lesson. Little is known about the arrangements of in-class and out-of-class phases fostering learning through inquiry in flipped classroom scenarios. To support teachers’ lesson planning practices, we developed a design heuristic for flipped classroom scenarios based on the 5E inquiry model. We implemented this design heuristic in an online professional development course for secondary mathematics teachers and collected 18 lesson plans. To explore how participating teachers adopted the design heuristic in their lesson plans, we conducted a document analysis on our data. We identified the following three major categories: (a) pre out-of-class phases to engage students, (b) in-class phases for student-centred learning activities and (c) post out-of-class phases for consolidation. Furthermore, we analysed lesson plans with the 5E model scoring instrument. Findings indicate that teachers’ lesson plans were mainly in line with the 5E model, but most participants struggled with selecting appropriate assessment techniques. Based on the analysis, this paper discusses revision decisions regarding the proposed design heuristic.

The effectiveness of flipped classroom approaches can be improved by combining it with other pedagogical models such as inquiry-based learning. Implementing inquiry-based learning in flipped classroom scenarios requires teachers to plan arrangements for in- and out-of-class activities carefully. In this study, a design heuristic based on the 5E inquiry model was developed to support teachers’ practice of planning inquiry-based flipped classroom lessons. Following a design-based research approach, the design heuristic progressed through two cycles within 2 years. The design heuristic was implemented in both cycles in an online professional development course for secondary mathematics teachers. In the first cycle, 18 lesson plans were collected and analysed using the 5E lesson plan scoring instrument. Results showed that the design heuristic helped teachers to set up lesson plans for flipped classroom scenarios which were mostly in line with the 5E model. However, the evaluation phase was insufficiently addressed. Revision decisions were made at the end of the first cycle, and the design heuristic was revised and re-implemented in a second cycle. Results of the second cycle showed another 19 participating teachers who also struggled in choosing appropriate assessment techniques, an issue which could not be resolved with the proposed design heuristic. This paper describes the development of the design heuristic as well as relevant design principles for inquiry-based flipped classroom scenarios. The proposed design heuristic is not domain specific. Hence, further research could examine its use in other subjects or interdisciplinary as inquiry-based flipped classroom approaches are one of the emerging pedagogies.

Towards Flipped Learning in Upper Secondary Mathematics Education

In parallel with the rapid digitalization of society in the 21st century, GeoGebra evolved in the last 20 years from an interactive geometry software to a comprehensive software package for learning mathematics. This chapter presents how teaching and learning scenarios based on GeoGebra tools or resources could be designed to meet the needs and desires of both teachers and students. First, we introduce new GeoGebra tools such as GeoGebra Notes and GeoGebra Classroom and illustrate how digital learning environments could be developed with them. Based on qualitative empirical results, in the next section we describe the potential and problems of digital resources addressing functional relationships and suggest an approach to integrate such resources in a formative assessment tool such as GeoGebra Classroom. In a final section, we link modern digital tools such as GeoGebra to flipped learning approaches, as a contemporary way of teaching and learning mathematics. <!----> <!----> <!----> <!---->

As AI becomes integral to students’ learning, educators must adapt to this AI-driven landscape. However, there is a notable gap in research focusing on fostering AI literacy among higher education lecturers. This paper presents a design-based research project aimed at developing a professional development curriculum for educators at the tertiary level through iterative cycles. In the first cycle, a voluntary internal professional development course was offered as a blended learning scenario. Evaluation involved a validated AI literacy performance test and AI readiness scale items. The results of the first cycle are going to be presented and discussed. Based on these findings, modifications to the course are outlined.