Didacticum

Editorial

2022-09-15T13:20:52+02:00

Mathematics and German are two of the most elementary and important school subjects in Austria. Therefore, research on teaching and learning of these two subjects is a central task to which the academic disciplines of mathematics and German language education are dedicated. This issue aims to present articles taking up and analysing current research questions relevant to German language and mathematics education. Therefore, this issue is devided in two: the first part presents studies that focus on theories and models from neuro-, cognitive and developmental psychology relevant for mathematical education. The second part deals with current topics in German language education which are significant for everyday classroom teaching. They cover vocabulary acquisition, writing didactics and didactics of literature.

In this introduction we briefly present the two subject areas and the associated central questions related to this issue. Also, the articles included in this issue will be presented briefly here and finally, we will outline their relevance for mathematics and German language education.

Die neurokognitiven Korrelate numerischer und arithmetischer Fertigkeiten

2022-09-15T13:08:13+02:00

Rechenfertigkeiten sind ein wichtiger Grundstein moderner Gesellschaften. Laut
Schätzungen der OECD weisen jedoch rund 20 Prozent der Erwachsenen mangelhafte
Rechenfertigkeiten auf (OECD, 2016). Ein besseres Verständnis über Entwicklung und
optimale Förderung von Rechenfertigkeiten ist daher essenziell. Neurokognitive
Forschung konnte bisher zeigen, dass Rechenprozesse auf einem komplexen
Zusammenspiel von domänen-übergreifenden (z. B. Arbeitsgedächtnis,
Aufmerksamkeit) und domänen-spezifischen (z. B. mentale Repräsentation
numerischer Mengen) Fertigkeiten beruhen.
Der vorliegende Review-Artikel gibt einen Überblick über die aktuelle neurokognitive
Literatur domänen-spezifischer Prozesse, welche dem Erlernen von
Rechenfertigkeiten zugrunde liegen sowie deren Veränderung im Laufe der
Entwicklung. Dabei liegt der Fokus auf dem Aufbau basisnumerischer
Repräsentationen (semantisches Wissen über Ziffern und Zahlen) und arithmetischer
Lösungsstrategien (Faktenabruf und prozedurales Wissen). Abschließend wird ein
kritischer Blick darauf geworfen, inwieweit es atypische neurokognitive Ausprägungen
bei Dyskalkulie gibt und ob sich diese durch Interventionen verändern lassen.

Symbolic representation in mathematics: fMRI-based neuroeducation perspectives on the hypothesis that symbolism is a relief for our brain when thinking about fractions

2022-09-15T13:10:16+02:00

Eine symbolische Darstellung von Mathematik wird für das Lehren und Lernen häufig
als schwierig oder herausfordernd beschrieben. Aktuelle neurowissenschaftliche
Erkenntnisse legen jedoch nahe, dass diese für unser Gehirn besonders effizient zu
verarbeiten sind. So beschränkt sich die Anzahl aktivierter Hirnareale in symbolischen
Zusammenhängen auf eine relativ geringe Anzahl von Hirnarealen und erscheint
gleichzeitig als schneller verarbeitbar. In diesem Artikel befassen wir uns mit der
Forschungsfrage, inwieweit der Umgang mit symbolischen Darstellungen das Gehirn
entlasten kann. Wir gehen dieser Frage mit einem deskriptiven Ansatz und mit Hilfe
einer theoriebasierten Diskussion nach und nutzen dabei aktuelle fMRI-Studien, die
innovative Erkenntnisse für die Mathematik bereithalten.

Vital4Brain im Mathematikunterricht

2022-12-13T11:24:55+01:00

Over the past years, due to meaningful advances in brain research, a new understanding of learning has developed. Learning processes can now be explained neurobiologically. Due to imaging methods amongst others, it is possible to follow the structural changes in the brain during a learning process. Therefore, learning can be explained and understood in a new way: “Neurodidactics” (Friedrich, 2005, p. 240) combines didactics and neuroscience.

Learning is a complex process and it is closely related to the issues of attention and concentration. A certain attention span and level of concentration form the basis for successful learning. Nowadays there are many deficiencies in this regard among pupils, which can be explained by the way of life over the past decades and the changed living conditions (Heil, 2017, p. 4ff.).

Mathematics is known as a discipline in which a high degree of concentration is required. In order to counteract the deficiency in concentration and to support students in effective learning, the Vital4Brain exercise program was developed (Schwarz, 2012, p. 6). The program consists of coordinatively challenging exercises that can be used during the lessons to improve the ability to learn, think and concentrate. The effect of movement on cognitive abilities and learning has already been proven in numerous studies and is at least partially explained in neurodidactics (Walk, 2011).

Vital4Brain is designed for pupils of all Austrian school types and levels and can be implemented in the classroom in every lesson. The exercises can be instructed by the teachers, trained peer coaches or teacher coaches or they can be played back via beamer from the homepage www.simplystrong.at. All exercises can be practiced in everyday clothing.

In an empirical survey of a total of 176 pupils in the 5^th, 7^th and 11^th grade of a grammar school (high school), the research question was investigated whether their ability to concentrate can be trained with the Vital4Brain exercise program and thereby improve their mathematical and cognitive performance. The Vital4Brain interventions that took place three times per week during a six-week intervention phase show (significant) increases in performance both in geometric tasks in the plane and for spatial imagination and in math-specific speed work. For this purpose, pre- and post-tests were carried out on intervention and control groups (Voit, 2020).

Multimodales Lernen mit didaktischen Arbeitsmitteln im mathematischen Erstunterricht: Eine qualitative Analyse

2022-09-15T13:15:54+02:00

This paper presents embodied cognition approaches as a theoretical explanatory
approach to learning with manipulatives. Nine different types of manipulatives are
introduced, compared, and analysed. The analysis mainly focuses on the possibilities
offered by the manipulatives regarding non-counting enumeration and non-counting
quantity display. With the help of a theoretically based coding guide, the manipulatives
were coded and compared. The results show that different manipulatives have
strengths and weaknesses in building a cardinal number concept and part-whole
knowledge. Fingers and “Rechenschieber”-like manipulatives seemed to have
advantages over other manipulatives in terms of handling, whereas coloured rods
appeared to have greatest weaknesses regarding the selected criteria.

Forschen, planen, bauen, begreifen

2022-09-15T13:14:57+02:00

This article examines whether learning workshop work at the primary level can
contribute to the promotion of motivation and interest in the subject of mathematics.
Learning workshop work is defined for the primary level and aligned with mathematics
didactics. Based on subject didactic concepts as well as theories of interest
development and the promotion of motivation, the article presents a practical example
of learning workshop work in a third grade mathematics classroom. The article
describes learning workshop work on the topic of calculating circumferences and
reflects on it with regard to the development of interest and the promotion of
motivation. Finally, the conclusions on the learning workshop work in the subject
mathematics in the primary level are presented.

Besondere Anforderungen von Unterrichtsmaterial für Mathematiklernende mit Deutsch als Zweitsprache

2022-09-15T13:05:42+02:00

Although there is a profound body of published research on the situation of students
who learn mathematics in a different language than their first language, there is no
synthesis of these insights with a focus on the creation of appropriate learning
materials for the respective learners. This article first discusses the state of the art of
the international and of the Germanophone research field, thereby discussing the
issues of language policy, student achievement, and cultural and linguistic differences.
On this basis, the article later features seven principles for teaching successfully with
respective students, and derives guiding questions for the analysis and development
of suitable learning materials

„Kenn’ ich nicht ...“ – strukturierter und evidenzbasierter Wortschatzaufbau im Klassensetting

2022-09-15T13:11:39+02:00

The aim of the following article is to present possibilities of observing and documenting vocabulary development based on the knowledge of developmental steps, dimensions and influencing factors in vocabulary acquisition. In doing so, classroom-based language level observations and more specific procedures can be used separately or in combination. The main points, the focus of observation, and the advantages and disadvantages of individual procedures are summarized in the following article in the first section.

The second section is devoted to the essential elements of didactics in the area of lexis and semantics. From various evaluated remedial concepts and teaching principles elements for vocabulary work in inclusive classroom settings are derived. Regardless of the underlying cause of the vocabulary level (German as a second language, need for language support in the case of an existing language development disorder, educational remoteness of the parents’ home, cognitive impairment), possibilities for immanent support are presented and general principles of qualitative and quantitative vocabulary development are shown to ensure the transfer of theoretical concepts into daily practice.

In this individual support process, digital formats can be used in a supportive manner. These are shown for specific areas of vocabulary development and described by way of example. Finally, essential media-didactic, linguistic and developmental- psychological aspects for the evaluation and integration of tools for vocabulary expansion and differentiation are found.

Schreibprozessbegleitung in der Unterrichtspraxis

2022-09-15T13:12:32+02:00

The acquisition of writing competence can be described as a task of schools, since this key qualification is acquired almost exclusively there. Writing research offers starting points for a successful teaching of writing competence. The design of writing lessons, especially with focus to support of writing process, is the topic of this paper. A current, competence-oriented didactics of writing focuses not only on the text product but also on the writing process and supports learners on their way to become competent writers.

Kafka in intermedialer Verflechtung – Die Verwandlung im Original und als Graphic Novel als Gegenstand literaturwissenschaftlicher und rezeptionsästhetischer Überlegungen

2022-09-15T13:13:34+02:00

Movies based on literature have a fixed place in German classrooms. Adaptations in the form of comics and Graphic Novels still fight for this kind of appreciation. This might be due to its reputation as a trivial form of literature or to the fact that few teachers feel like they lack knowledge when it comes to read, analyze and interpret these mediums.

In order to understand why adaptions in these forms earn the same attention as other intermedial translations, I conducted a qualitative empirical study with students of Higher Classes. In this research pupils were asked to perform a think-aloud while reading either a part of Kafka’s Die Verwandlung (“metamorphosis”) or the similar part of Corbeyran’s and Horne’s adaption Die Verwandlung von Franz Kafka. The aim is to understand similarities and differences between Kafka’s narrative and its comic- adaption on various levels. It is of no interest, what the better approach in classes might be, but to gain more insight in what is happening, when pupils read.