In 2020, Germany and Spain experienced lockdowns of their school systems. This resulted in a new challenge for learners and teachers: lessons moved from the classroom to the children’s homes. Therefore, teachers had to set rules, implement procedures and make didactical–methodical decisions regarding how to handle this new situation. In this paper, we focus on the roles of mathematics teachers in Germany and Spain. The article first describes how mathematics lessons were conducted using distance learning. Second, problems encountered throughout this process were examined. Third, teachers drew conclusions from their mathematics teaching experiences during distance learning. To address these research interests, a questionnaire was answered by N = 248 teachers (N1 = 171 German teachers; N2 = 77 Spanish teachers). Resulting from a mixed methods approach, differences between the countries can be observed, e.g., German teachers conducted more lessons asynchronously. In contrast, Spanish teachers used synchronous teaching more frequently, but still regard the lack of personal contact as a main challenge. Finally, for both countries, the digitization of mathematics lessons seems to have been normalized by the pandemic.
The COVID-19-induced distance education was perceived as highly challenging by teachers and students. A cross-national comparison of five European countries identified several challenges occurred during the distance learning period. On this basis, the article aims to develop a theoretical framework and design requirements for distance and online learning tools. As one example for online learning in mathematics education, the ASYMPTOTE system is introduced. It will be freely available by May 2022. ASYMPTOTE is aimed at the adaptive and synchronous delivery of online education by taking a mobile learning approach. Its core is the so-called digital classroom, which not only allows students to interact with each other or with the teacher but also enables teachers to monitor their students’ work progress in real time. With respect to the theoretical framework, this article analyses to what extent the ASYMPTOTE system meets the requirements of online learning. Overall, the digital classroom can be seen as a promising tool for teachers to carry out appropriate formative assessment and—partly—to maintain personal and content-related interaction at a distance. Moreover, we highlight the availability of this tool. Due to its mobile learning approach, almost all students will be able to participate in lessons conducted with ASYMPTOTE.
Discovering mathematics in one's own environment inspires students. Numerous everyday objects offer potentials for posing interesting and motivating measuring tasks. To organize the mathematics lesson outdoors, teachers can create so-called math trails in their environment using the MathCityMap system: a web portal and a smartphone app are available to prepare and conduct a math trail. Equipped with the app and measuring tools, the students work in small groups on the object side. Hereby, the MathCityMap app supports the independent and collaborative learning of students offering hints and direct answer validation. In the following paper, the components of MathCityMap are presented.
Within the ASYMPTOTE project, a system of the same name has been developed to prepare, conduct, and evaluate mathematics lessons online. It consists of three components, namely a web portal, a mobile app, and the Digital Classroom feature. In the web portal, teachers can select available or create own learning contents. These learning contents can be downloaded by the students to their smartphones by entering a related code in the app. Within the Digital Classroom feature, synchronous mathematics lessons can be carried out – it offers a monitoring tool allowing teacher to retrace students’ working processes. In addition, a chat function is integrated for a direct teacher-student interaction. In the workshop, the participants get to know the ASYMPTOTE system and explore it from the student’s and teacher’s side. In the following, the ASYMPTOTE web portal and app are briefly introduced. In addition, the Erasmus+ project’s outputs are presented.
Mathematical modelling addresses numerous demands of modern mathematics education: The learning of mathematics is directly linked to reality and hence to real objects. At the same time, these tasks are very challenging for students, especially when their own solution process needs to be validated and refined. Studies even show that some students do not validate their results at all. Recent research has shown that digital tools can enhance the support of modelling activities in different ways. In this paper, we take the modelling step of validation into a deeper account and explore the potential of MathCityMap, a digital tool for outdoor mathematics education. Hereby, its automatic solution validation by means of a predefined interval and assessment of the result’s quality are taken into consideration. The modelling activities of secondary school students are compared on a quantitative and qualitative level – half of the students working with the MathCityMap app and half of them solving the tasks without any digital support. Based on the quantitative results, we can see that the app functionalities for elaborative feedback are used to varying degrees: While student groups frequently access the hints, the sample solution is hardly accessed. Moreover, our analysis can show the value of corrective app feedback. Student groups that used the app solved a comparable number of problems, but failed significantly less often than student groups that worked on math trails without the app. The qualitative results show that in particular the solution validation forces the students to proceed with a second run in the modelling cycle if a result is valued as wrong in the app. In addition, it helps the students to assess their own result in terms of its correctness. Based on the combined results, we draw conclusions about the app usage in mathematical modelling tasks.
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