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Libera Università di Bolzano

Didattica della matematica e delle scienze naturali 1 - Fondamenti

Semestre 2 · 12410 · Corso di laurea magistrale a ciclo unico in Scienze della Formazione primaria - sezione in lingua tedesca · 11CFU · DE


Knowledge
- the subject-specific and subject-didactic principles, in particular the subject-immanent structures and cross-age developmental lines that must be observed in order to be able to stimulate, accompany and promote children's learning processes in mathematics (in the content area of number/arithmetic) as well as chemistry and biology from kindergarten to the transition to secondary school as seamlessly as possible, both in a child-orientated and subject-specific manner and in accordance with the children's potential

Docenti: Camilla Wellstein, Michael Gaidoschik, Verena Stragenegg, Franziska Zemmer, Robert Philipp Wagensommer, Irene Köfele, Sonia Pichler, Vera Knapp

Ore didattica frontale: 70
Ore di laboratorio: 50
Obbligo di frequenza: In accordance with the regulation

Argomenti dell'insegnamento
See the individual course modules

Modalità di insegnamento
Lectures and laboratories (see detailed explanations for individual modules)

Obiettivi formativi
Skills - to recognise and use the potential of games and everyday situations in kindergarten for mathematical and scientific learning in the content areas addressed in the module - to observe, analyse, plan and design learning-promoting support for learning processes in kindergarten and school lessons in mathematics (content area number/arithmetic) as well as biology and chemistry (interdisciplinary also physics) based on the framework guidelines for kindergarten and primary school in South Tyrol, always with a view to the interdisciplinarity required in kindergarten and primary school - to promote general, process-related maths and science skills - for the qualitative, process-oriented assessment of competences/learning levels and for dealing with heterogeneity in a way that promotes learning in the content areas addressed in the module Expected learning outcomes and competences: Knowledge and understanding - Knowledge and understanding of the educational objectives of the framework guidelines for kindergarten and primary school related to the mathematical and scientific content areas covered, taking into account the general (process-related) mathematical and scientific competences throughout - Basic mathematical knowledge and fundamental insights into elementary mathematical structures and relationships in the content area "Number" (arithmetic); knowledge and understanding of current development models for the acquisition of arithmetic skills as well as current didactic concepts for promoting and further developing these skills - Knowledge and understanding of basic chemical-physical and biological concepts and their interdisciplinary connection; knowledge and understanding of basic relationships between animate and inanimate nature in the immediate living environment; knowledge and understanding of current concepts for the didactic implementation of the learning content addressed in the sense of moderate constructivism. Applying knowledge and understanding - Expertise in solving elementary mathematical tasks relevant to kindergarten and primary school in different ways and in justifying the mathematical correctness of such different solutions - Expertise in planning, implementing and evaluating qualitative, process-oriented learning assessments in the mathematical content areas covered - Expertise in identifying intuitive concepts and theories of children and pupils on scientific topics - Expertise in planning settings that promote learning in the mathematical and scientific content covered, taking into account heterogeneous learning requirements Judgement - Competence in the technically and didactically sound assessment of the potential of everyday and play situations for maths and science education in kindergarten as well as of tasks, exercise forms, learning environments, methods and didactic materials for the further development of maths and science skills in primary school in the content areas covered - Expertise in differentiated reflection on one's own and others' attitudes towards mathematics and science, their significance for learners, school and society, as well as attitudes towards learning mathematics and science Communication - Ability to present the content and contexts covered in a precise and target group-appropriate manner in both specialised and everyday language - Competence to present their own thought processes and solution strategies in an intersubjectively comprehensible way - Knowledge of the importance of language skills for learning arithmetic and science and of suitable forms of promoting these in kindergarten and primary school Learning strategies - (Further) development of cross-content and content-specific problem-solving strategies - (Further) development of the ability to independently learn and deepen subject-specific and didactic content

Modalità d'esame
Comprehensive final written examination (3 hours total working time) on the mathematical and scientific topics covered in the two lectures. The written examination consists of one part each on the mathematical and scientific topics.

Criteri di valutazione
For a positive completion of the course all four modules must be completed at least positively. If this condition is met, the overall assessment will take appropriate account of the work completed in the two laboratories or the two partial examinations of the written examination in accordance with the shares of these partial courses in the total number of credit points awarded for the whole course. The performance assessment of the written lecture examination is based on correctness of content and language, accuracy and clarity, in particular in the application of the content taught in the course when working on the examination tasks (transfer performance); correct use of technical language; reference to technical literature; depth and comprehensibility of the required reflection and argumentation. Performance assessment for the laboratory is based on work assignments, which must be completed outside of class by the specified deadlines, and on participation in laboratory sessions. In the event of a negative assessment of the course, any positively assessed partial examinations will be credited the next time you take the examination. Please note, however, that a negative assessment will also be counted in the number of examination attempts in this case. According to the examination regulations, three attempts without passing will result in a suspension for three examination dates.

Bibliografia obbligatoria

See the required reading listed for each module.



Bibliografia facoltativa

See the further reading listed for each module.




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Obiettivi di sviluppo sostenibile
Questa attività didattica contribuisce al raggiungimento dei seguenti Obiettivi di Sviluppo sostenibile.

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Modules

Semestre 2 · 12410A · Corso di laurea magistrale a ciclo unico in Scienze della Formazione primaria - sezione in lingua tedesca · 4CFU · DE

Module A — Elementi di base della matematica per la sua didattica

The aim of the lecture is to impart the basic subject-related and didactic knowledge necessary to stimulate and support learning processes in the content area of number (arithmetic) from kindergarten to the end of primary school, with an orientation towards both the child and the subject, and to be able to promote the individual potential of the children.

Docenti: Michael Gaidoschik

Ore didattica frontale: 40
Ore di laboratorio: 0

Argomenti dell'insegnamento
- Mathematics as an activity of discovering, describing, creating and explaining patterns and structures - Development of maths-related interests, abilities and skills in early childhood - Concepts of early mathematical education in line with the framework guidelines for kindergarten in South Tyrol and current specialised didactics of mathematics - Subject-specific and subject-didactic basic knowledge for the learning-promoting treatment of the content area of number (arithmetic), upstream of classifying and sorting by characteristics and dealing with quantities, from kindergarten to the transition to secondary school (development of the concept of number; elements of number theory, number aspects; place value systems; addition, subtraction, multiplication, division), with continuous attention to the promotion of general, process-related mathematical skills (problem solving, communication, representation, argumentation and modelling) - The role of acting with material as well as of working with visualisations for the development of arithmetic operations and concepts - Substantive learning environments for the content that is covered in the lecture; natural differentiation to promote the learning of children of all levels of talent and inclination - Qualitative assessments and process-orientated learning progression on key content covered

Modalità di insegnamento
Lecture with media support, interspersed work phases (from individual work to small groups), repeated invitation to written interim reflections and differentiated feedback on the course

Bibliografia obbligatoria

Benz, Ch., Peter-Koop, A., & Grüßing, M. (2015). Frühe mathematische Bildung. Mathematiklernen der Drei- bis Achtjährigen. Springer.

Gaidoschik, M. (2025). Das dezimale Stellenwertsystem verstehen, verinnerlichen, flexibel anwenden: Ein Leitfaden für den Unterricht in der Grundschule. Klett-Kallmeyer.

Gaidoschik, M. (2022). Rechenschwäche verstehen – Kinder gezielt fördern. Ein Leitfaden für die Unterrichtspraxis (12. Auflage). Persen.

Gaidoschik, M. (2019). Einmaleins verstehen, vernetzen, merken. Strategien gegen Lernschwierigkeiten (5. Auflage). Kallmeyer.

Padberg, F. & Benz, Ch. (2020). Didaktik der Arithmetik. Springer.



Bibliografia facoltativa

Schipper, W., Dröge, A., & Ebeling, R. (2015-2018). Handbuch für den Mathematikunterricht, 1./2./3./4. Schuljahr. Bildungshaus Schulbuchverlage.

Wittmann, E.Ch. & Müller, G. (2017/2018). Handbuch produktiver Rechenübungen. Neufassung. Kallmeyer.



Semestre 2 · 12410B · Corso di laurea magistrale a ciclo unico in Scienze della Formazione primaria - sezione in lingua tedesca · 2CFU · DE

Module B — Elementi di base della matematica per la sua didattica con particolare attenzione alla fascia di età (0)-2-7 (lab.)

The aim of the laboratory is, on the one hand, to support students in acquiring the content of the lecture "Fundamentals of Mathematics and its Didactics" through practical exercises in small groups. On the other hand, it is about the practical testing of substantial tasks, materials, media... for early mathematical education, with a special focus on the age group (0-)2-7 (kindergarten and first/second grade). The essential content of arithmetic is continued until the end of primary school and, conversely, the content covered there is dealt with in the laboratory in the 4th year of study (focus on ages 5-12), starting from kindergarten. Reflecting on the experiences made in the exercises and relating them back to the theory covered in the lecture is essential for the laboratory.

Docenti: Irene Köfele, Sonia Pichler, Vera Knapp, Verena Stragenegg

Ore didattica frontale: 0
Ore di laboratorio: 30 Gruppe 1: Verena Stragenegg Gruppe 2: Dott. Mag. Irene Köfele Gruppe 3: Dott. Mag. Sonia Pichler Gruppe 4: Dott. Mag. Vera Knapp

Semestre 2 · 12410C · Corso di laurea magistrale a ciclo unico in Scienze della Formazione primaria - sezione in lingua tedesca · 3CFU · DE

Module C — Elementi di base della biologia e della chimica per la loro didattica

The aim of the lecture is to impart the basic subject-related and didactic knowledge required to stimulate and support learning processes in the field of science education, especially in the areas of biology and chemistry, from kindergarten to the end of primary school, orientated towards both the child and the subject, and to promote the individual potential of the children.

Docenti: Robert Philipp Wagensommer

Ore didattica frontale: 30
Ore di laboratorio: 0

Semestre 2 · 12410D · Corso di laurea magistrale a ciclo unico in Scienze della Formazione primaria - sezione in lingua tedesca · 2CFU · DE

Module D — Elementi di base della biologia e della chimica per la loro didattica con particolare attenzione alla fascia di età (0)-2-7 (lab.)

The aim of the laboratory is, on the one hand, to support students in acquiring the content of the lecture "Fundamentals of Biology and Chemistry and their Didactics" through practical exercises in small groups. On the other hand, it is about the practical testing of substantial tasks, materials, media... for early science education in the age group (0-)2-7 (focus) as well as for their continuation in primary school, as well as the reflection of the experiences made and their reference back to the theory dealt with in the lecture.

Docenti: Camilla Wellstein, Franziska Zemmer

Ore didattica frontale: 0
Ore di laboratorio: 20 Gruppe 1, 3 und 4: Dr. Franziska Zemmer Gruppe 2: Prof. Dr. Camilla Wellstein

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