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Die besondere Situation der heterogenen Lehrer*innenschaft im Mathematikunterricht der Grundschule ruckt vor dem Hintergrund des aktuellen Lehrkraftemangels und dem damit forcierten Quereinstieg verstarkt in den Fokus. Bezuglich der Heterogenitat wird in der Regel zunachst formal in Lehrpersonen, die uber eine fachliche und fachdidaktische Qualifikation in Mathematik verfugen und Lehrpersonen, die Mathematik fachfremd unterrichten, unterschieden. Der zunehmende Bedarf an Lehrkraften fuhrt weiterhin dazu, dass die Lander Quereinsteiger*innen den Zugang in die Bildungseinrichtungen offnen. Das ist insbesondere mit speziellen zusatzlichen verpflichtenden Qualifizierung fur diesen Personenkreis verbunden. Die Personalsituation und das vorherrschende Klassenlehrer*innenprinzip haben an den Grundschulen zur Folge, dass auch Quereinsteiger*innen bereits Mathematik unterrichten und zur gleichen Zeit fachlich und fachdidaktisch in einem anderen Fach qualifiziert werden.

Jahnke, H. N., & Hefendehl-Hebeker, L. (Eds.). (2019). Traditions in German-speaking mathematics education reserach (ICME-13 Monographs). Cham: Spinger Open, , pp. 61-89., Considering mathematics education as a DESIGN SCIENCE has strong roots in Germany. E. Ch. Wittmann in particular contributed to the establishment of this approach. From a DESIGN SCIENCE perspective, substantial learning environments play a crucial role. They comprise mathematical tasks which are connected in an operative way, indicative of a specific epistemological structure. In such substantial learning environments, students are actively immersed in learning mathematics, and the learning environments allow for the pursuit of individual and differentiated learning processes. In this chapter, we first address the scope of Design Science and pay attention to characteristics of the learning environments and how teaching experiments can be conducted. We then focus on key ideas and their role as a design principle. In the next section, we provide a comprehensive example of designing a learning environment. Lastly, we shift our attention to the Design Research approach, which complements designing substantial learning environments by empirically studying the initiated learning processes to gain evidence for both theoretical considerations and design principles.

Guter Mathematikunterricht folgt den didaktischen Prinzipien der kognitiven Aktivierung, Differenzierung, Verstehensorientierung, Diagnosegeleitetheit und Sinnstiftung in allen Unterrichtsphasen. In dem Beitrag wird dargelegt, wie diese Prinzipien in prozessbezogener Perspektive in und fur Fortbildungen thematisiert werden konnen. Die Teilnehmenden der Qualifizierung fur Multiplikatorinnen und Multiplikatoren werden zum einen in ihrer Rolle als Lehrerin und Lehrer angesprochen, um gemeinsam zu erarbeiten, wie entsprechender Mathematikunterricht selbst gestaltet und durchgefuhrt werden kann. Zum anderen werden sie in ihrer Rolle als Multiplikatorin und Multiplikator adressiert und es wird thematisiert, wie die Prinzipien guten Unterrichts an Lehrerinnen und Lehrer vermittelt werden konnen. Beide Ebenen beziehen die Teilnehmenden als Expertinnen und Experten fur Unterricht und Fortbildung aktiv ein und bieten theoretische Rahmungen, um bisherige und wahrend der Fortbildung gemachte Erfahrungen einzuordnen und gemeinsam zu reflektieren.

This article reports about our efforts to determine engineering students' competence in mathematics. Our research is embedded in a larger project, KoM@ING–Modeling and developing competence: Integrated IRT based and qualitative studies with a focus on mathematics and its usage in engineering studies, within the program Modeling and Measuring Competencies in Higher Education (KoKoHS). KoKoHS provides the umbrella organization of several research projects addressing the modeling and measuring of competences at the college level. KoM@ING aims to model the role of engineering students' mathematical competences for their studies from both a quantitative and a qualitative perspective.Here, we report the development of a large-scale instrument assessing engineering freshmen's competence in mathematics by applying Rasch analysis to determine measures for item difficulties and student abilities. Several analyses were performed to provide insights into the measures' reliability and validity. In particular, to exami...

This paper describes and analyzes developments that have taken place in German mathematics education research during the last 40 years. Which developments and ideas were characteristic for the discussion and how was Germany influenced by and how did it interact with the international community? The themes range from subject matter didactics to large-scale studies.

The concept of teacher training has undergone a dramatic transformation in recent years and decades. Whereas teacher training was formerly applied to eliminate presumed shortcomings, it is now considered more and more as a needful process of continuous professional development (CPD). CPD as an obligatory standard of the teaching profession makes it necessary to develop training opportunities that convey innovative content in an appropriate manner. In this article we point out which guidelines CPD should suffice (section 2), give a brief overview of the conditions and requirements of successful innovations in the field of education (section 3), and discuss which strategies can be used in the implementation of innovations (section 4). Finally we present two examples of CPD aiming at spreading innovations (section 5).

Within the German-speaking tradition, considering “mathematics education as a design science” has primarily drawn on the work by Wittmann. The core of this approach has been designing and investigating learning environments that involve substantial mathematics. This ICME-13 Topical Survey summarises the state of the art by first exploring the roots and scope of design science. Second, two examples of current design science projects are presented that focus on substantial learning environments, including a student and a teacher perspective. Then, conceptualising empirical research within design science is elaborated on. Finally, developments of design science are examined from a national and international perspective and current trends of design research are also discussed.

The process of interpretation and assessment of students’ mathematical productions represents a crucial aspect of teachers’ practices. In such processes, teachers rely on the so-called interpretative knowledge, which includes particular aspects of their mathematical and pedagogical knowledge, their view of mathematics, and their values. In this paper, we analyze and discuss prospective primary teachers’ interpretative knowledge gained through their assessment of different subtraction algorithms.