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Didactics of Mathematics and Early Childhood Concept Development

Semester 2 · 400004 · 5 year master degree in Primary Education - German section · 12CP · DE


The course modules provide fundamental disciplinary, pedagogical, and developmental competencies for designing educational and learning processes in early childhood and primary education. The courses focus on fostering mathematical and scientific ways of thinking, as well as supporting the development of knowledge, concepts, and categories during early childhood. Students engage with theoretical foundations of learning and cognitive development while exploring how children can be guided in constructing mathematical and scientific understandings. Through the integration of theory and practice, participants examine, test, and reflect upon appropriate learning environments, materials, and didactic approaches, evaluating their educational effectiveness. Particular emphasis is placed on child-centered learning, the role of language in knowledge construction, and the balance between guided instruction and independent learning processes.

Lecturers: Christian Laner, Reinhard Tschiesner, Angelika Pahl, Vera Knapp, Robert Philipp Wagensommer, Irene Köfele, Sonia Pichler, Marion Zöggeler, Judith Kerschbaumer

Teaching Hours: 92
Lab Hours: 32
Mandatory Attendance: In accordance with the regulation

Course Topics
See the individual course modules.

Teaching format
See the individual course modules.

Educational objectives
1. Knowledge and understanding By the end of the course, students will be able to: - Demonstrate knowledge of key theories regarding cognitive and conceptual development in early childhood, with particular focus on Core Knowledge systems, executive functions, and Embodied Cognition. - Understand how young children build spontaneous explanations and construct physical and mathematical concepts through action, movement, gestures, and sensory experiences. - Master fundamental content within the "Numbers and Operations" conceptual domain (number systems, computation, early algebra, properties, and algorithms). 2. Applying knowledge and understanding By the end of the course, students will be able to: - Design learning units and educational activities for preschool and primary school, integrating mathematics, physics, science education, and developmental psychology. - Utilize physical artifacts, digital tools, and mediating instruments to foster exploration, modeling, and problem-solving in young learners. - Analyze and interpret educational situations and children's outputs (verbal, gestural, and graphical) related to mathematical and physical phenomena. - Implement laboratory-based teaching strategies and cooperative learning to promote hypothesis generation, reasoning, and active concept formation. - Comprehend theoretical and pedagogical frameworks in mathematics education (laboratory-based learning, Activity Theory, didactic transposition, didactic contract, semiotic registers of representation, and multimodality). 3. Making judgements By the end of the course, students will be able to: - Critically evaluate instructional materials, laboratory experiences, and pedagogical proposals concerning early childhood mathematics and science education. - Reflect critically on teaching practices, recognizing the teacher's role, the influence of the didactic contract, and the value of children's intuitive ideas. - Select and adapt mathematical and scientific tasks appropriately based on children's cognitive development levels and classroom needs. 4. Communication skills By the end of the course, students will be able to: - Use appropriate, precise disciplinary terminology across mathematics, science education, and developmental psychology. - Facilitate and orchestrate mathematical and scientific discussions in the classroom, encouraging peer reasoning, debate, and collaborative meaning-making. - Present, justify, and discuss instructional designs clearly with peers and instructors using digital tools and multimodal representations. 5. Learning skills By the end of the course, students will be able to: - Independently access and analyze research literature, bibliographic sources, and educational materials in early childhood mathematics and science education. - Cultivate a reflective attitude toward self-assessment and continuous professional development. - Apply acquired theoretical frameworks to analyze real educational settings and address future teaching challenges.

Assessment
Written exam

Evaluation criteria
Academic accuracy, depth of argumentation, use of appropriate academic language, knowledge of methodology, ability to reflect, formal correctness

Required readings

See the individual course modules.



Supplementary readings

See the individual course modules.




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Sustainable Development Goals
This teaching activity contributes to the achievement of the following Sustainable Development Goals.

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Modules

Semester 2 · 400004A · 5 year master degree in Primary Education - German section · 7CP · DE

Module A — Didactics of Mathematics for Early Childhood Education and Primary School 1: Numbers and Operations

The course covers the disciplinary and subject-specific pedagogical foundations that early childhood educators and primary school teachers must possess in order to initiate, support, and foster learning processes in the content domain of numbers and operations (arithmetic), from kindergarten through the end of primary education, in a manner that is both mathematically sound and responsive to the individual potential of each child.

Teaching Hours: 56
Lab Hours: 0

Course Topics
Mathematics as an activity of discovering, describing, constructing, and justifying patterns and structures; the development of mathematics-related interests, abilities, and skills in early childhood; concepts of early mathematics education in alignment with the curricular guidelines for kindergarten in South Tyrol and with current research in mathematics education; disciplinary and subject-specific pedagogical foundational knowledge for the learning-supportive treatment of the content domain of number (arithmetic), preceded by classifying and sorting according to attributes and engaging with sets, from kindergarten through the transition to lower secondary education (development of the concept of number; elements of number theory; foundations of fractions and rational numbers in decimal representation; place-value systems; laws of arithmetic; methods and strategies for the four basic operations), with continuous attention to the overarching mathematical competencies of problem solving, communication, representation, reasoning, and modelling/mathematisation.

Teaching format
Lecture supported by multimedia presentations, interspersed with individual and small-group activities, complemented by regular opportunities for (also written) reflection and for providing detailed feedback on the course.

Required readings

Benz, Ch., Peter-Koop, A., & Grüßing, M. (2015). Frühe mathematische Bildung. Mathematiklernen der Drei- bis Achtjährigen. Springer Spektrum. - Daraus: Kapitel 1, 2 und 4

Gaidoschik, M. (2025). Lernschwierigkeiten in Mathematik. Warum wir nicht von Rechenschwäche und Dyskalkulie sprechen und was wir ab dem Kindergarten tun sollten. Persen.

Padberg, F. & Benz, Ch. (2021). Didaktik der Arithmetik (4. Auflage). Spektrum.



Supplementary readings

Benz, Ch., Maier, A., Reuter, F., Sprenger, P., Zöllner, J. (2024). Mathematik entdecken in Kita und Grundschule. Spiel- und Lernsituationen aus der Mach-mit-Werkstatt MiniMa. Klett-Kallmeyer.

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

Gaidoschik, M. (2026). Einmaleins verstehen, vernetzen, merken. Strategien gegen Lernschwierigkeiten (7. Auflage). Kallmeyer-Klett.



Semester 2 · 400004B · 5 year master degree in Primary Education - German section · 2CP · DE

Module B — Didactics of Mathematics for Early Childhood Education and Primary School 1: Numbers and Operations (lab.)

The laboratory serves, on the one hand, to support students in acquiring the content of the lecture “Didactics of Mathematics for Kindergarten and Primary School 1: Numbers and Operations” through practical exercises in small groups. On the other hand, it provides opportunities for the practical exploration and testing of substantial tasks, materials, and media for early mathematics education. A central element of the laboratory is the critical reflection on the experiences gained in these exercises and their systematic connection to the theoretical frameworks addressed in the lecture.

Lecturers: Christian Laner, Vera Knapp, Irene Köfele, Marion Zöggeler, Judith Kerschbaumer

Teaching Hours: 0
Lab Hours: 32 Gruppe 1: Dr. Marion Zöggeler Gruppe 2: Mag. Christian Laner Gruppe 3: Dott. Mag. Vera Knapp Gruppe 4: Dott. Mag. Irene Köfele Gruppe 5: Dott. Mag. Judith Kerschbaumer

Semester 2 · 400004C · 5 year master degree in Primary Education - German section · 1CP · DE

Module C — Development of Categories and Concepts in Early Childhood (sem.)

This seminar focuses on the structuring of knowledge in early childhood. Central to this are the terms category and concept. The course explores how categories and concepts change throughout the process of cognitive development.

Lecturers: Reinhard Tschiesner

Teaching Hours: 12 Gruppe 1 und 2: Prof. Dr. Reinhard Tschiesner
Lab Hours: 0

Semester 2 · 400004D · 5 year master degree in Primary Education - German section · 1CP · DE

Module D — Development of Categories and Concepts in Early Childhood (sem.)

Complementing and extending the lecture “Didactics of Mathematics for Kindergarten and Primary School 1: Numbers and Operations,” the seminar elaborates the subject-specific pedagogical perspective on early mathematics education, both theoretically and, in particular, with regard to its practical and pedagogical implications. It addresses a dual orientation toward the child and the discipline, the continuous effort to balance instruction and construction, the significance of language for learning mathematics, and the possibilities as well as the limitations of the three principal organizational forms of early mathematics education: everyday situations, play, and structured learning activities.

Lecturers: Sonia Pichler

Teaching Hours: 12 Gruppe 1 und 2: Dott. Mag. Sonia Pichler
Lab Hours: 0

Semester 2 · 400004E · 5 year master degree in Primary Education - German section · 1CP · DE

Module E — Development of Categories and Concepts in Early Childhood (sem.)

The seminar illustrates how children develop intuitive conceptions of the physical world in early childhood. Based on this insights, the course examines how the development of physical concepts and the categorization of phenomena can be specifically fostered through suitable learning environments and didactic stimuli.

Lecturers: Angelika Pahl

Teaching Hours: 12 Gruppe 1 und 2: Prof. Dr. Angelika Pahl
Lab Hours: 0

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