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Didactics of Mathematics and Early Childhood Concept Development

Semester 2 · 500004 · 5 year master degree in Primary Education - Italian section · 12CP · IT


This course provides foundational theoretical knowledge and pedagogical skills essential for early childhood and primary education, linking children's cognitive and conceptual development with the teaching of mathematics and physics. On one side (Seminar), the course delves into how categories and scientific/mathematical concepts are structured in early childhood, analyzing Core Knowledge systems, executive functions, embodied cognition, and children's spontaneous generation of scientific explanations anchored in sensory and bodily experiences. On the other side (Lectures and Workshop), the course focuses on the core mathematical domain of "Numbers and Operations" (natural, integer, and rational numbers, mental calculation, early algebra, problem-solving, and mathematical reasoning), combining theoretical frameworks from mathematics education research with the design and critical analysis of laboratory practices using physical and digital artifacts.

Lecturers: Federico Corni, Antonella Brighi, Sara Bagossi, George Richard Paul Santi

Teaching Hours: 92
Lab Hours: 32
Mandatory Attendance: According to the Academic Regulations

Course Topics
- Cognitive and Conceptual Development in Early Childhood: Core Knowledge systems (number, space, objects, causality); conceptual development; Embodied Cognition, gesture, movement, and image schemas in constructing physical and mathematical concepts; phases of understanding; executive functions and self-regulation in inquiry-based science learning; the child as a theory-builder and intuitive explanations of physical/mathematical phenomena. - Numbers and Operations in Mathematics Education: Number sense, counting, enumeration, and calculation processes; natural numbers (operations, properties, number line, multiples/divisors); integers, rational numbers (fractions, decimals, percentages), and introduction to real numbers; mental calculation and standard algorithms; early algebra, pattern recognition, and generalization; exploring, conjecturing, and arguing in numerical contexts. - Theoretical and Pedagogical Frameworks in Mathematics Didactics: Laboratory-based teaching and Activity Theory; mathematical modeling and problem-solving; semiotic registers of representation, multimodality, and mediating tools; didactic transposition, didactic contract, mathematical discussion, and assessment; historical/cultural perspectives on numbers (positional systems, ancient cultures, symbol acquisition).

Teaching format
The course employs a diverse and highly interactive pedagogical approach, combining lectures (face-to-face and synchronous online) with hands-on workshop sessions. Teaching methods include interactive and expository lectures, laboratory work, micro-teaching design, cooperative learning activities (in small groups and breakout rooms), and plenary mathematical discussions. The methodology also features collaborative analysis of learning scenarios (using video observations of children during play/exploration), direct simulations, embodied activities, the hands-on use of physical artifacts and digital collaborative tools, and the application of Activity Theory principles.

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
- Content knowledge from an interdisciplinary perspective - Translating theoretical knowledge into learning activities, also with cultural artefacts, consistent with the Learning Unit's objective??? - Language proficiency and clarity of presentation

Required readings

See the bibliography for each module




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

4 7 11 13 14 15

Modules

Semester 2 · 500004A · 5 year master degree in Primary Education - Italian section · 7CP · IT

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

The course aims to provide students with a solid background in mathematics and mathematics education, which is essential for teaching in kindergarten and primary schools. The course aims to provide students with the tools to: consolidate and acquire mathematical knowledge and skills relating in particular to the ‘Numbers’ core concept of the National Guidelines, with a focus on problem-solving and problem-formulation processes, exploration, hypothesis formulation, and argumentation; acquire teaching knowledge and skills related to the topics covered; carry out practical activities and engage in critical pedagogical reflection on the topics covered.

Lecturers: George Richard Paul Santi

Teaching Hours: 56
Lab Hours: 0

Course Topics
Numbers and their meanings; processes of enumeration, counting, and calculation. Natural numbers: operations, meanings, and properties; the number line; the meaning of multiples, divisors, and prime numbers. Integers. Rational numbers: definition, properties, and various forms of representation (decimals, fractions, percentages); an introduction to irrational and real numbers. Mental arithmetcalculationorithwritten ms for the four operations. Early algebra and processes of generalisation. Identifying and describing patterns. Exploring, conjecturing, and reasoning in a numerical context. Theoretical elements from research in mathematics education: laboratory methodology and problem-solving; mathematical modelling; registers of representation and multimodality; didactic transposition, didactic contract, mathematical discussion. Examples of teaching activities related to the topics covered. Assessment in mathematics.

Teaching format
Laboratory activities and cooperative learning. Class discussions to introduce activities and consolidate learning. Lesson planning

Required readings

D'Amore, B., & Sbaragli, S. (2011). Principi di base di didattica della matematica. Pitagora.

Sabena, C, Ferri, F, Martignone, F., & Robotti E. (2019). Insegnare e apprendere matematica nella scuola dell'infanzia e primaria. Mondadori



Supplementary readings

Baccaglini-Frank, A., Di Martino, P., Natalini, R., Rolini, G. (2017). Didattica della matematica. Mondadori



Semester 2 · 500004B · 5 year master degree in Primary Education - Italian section · 2CP · IT

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

The laboratory aims to provide students with practical experience of mathematics laboratories. The sessions will not only offer ideas and teaching materials, but will also encourage students to reflect on teaching practices, the use of tools, the importance of visual representations, and the role of the teacher.

Lecturers: George Richard Paul Santi

Teaching Hours: 0
Lab Hours: 32 Gruppi 1,2,3+4: Prof. George Richard Paul Santi

Semester 2 · 500004C · 5 year master degree in Primary Education - Italian section · 1CP · IT

Module C — Development of Scientific 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: Antonella Brighi

Teaching Hours: 12 Gruppo 1+2: Prof. Antonella Brighi
Lab Hours: 0

Semester 2 · 500004D · 5 year master degree in Primary Education - Italian section · 1CP · IT

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

The seminar aims to provide future kindergarten teachers with an opportunity to link the theoretical knowledge acquired in the "Developmental and Educational Psychology" course with the observation and practical understanding of how pre-school children think and reason about their experiences with physical phenomena and mathematical concepts. Building on basic knowledge of cognitive development processes in early childhood, the course will explore the ways in which children construct spontaneous explanations of the world around them. Through examples, discussion of educational situations, and analysis of teaching activities, children’s intuitive ideas will be explored. Particular attention will be paid to the ways in which children formulate hypotheses through experimentation and action, use language and expressive gestures to explain what they observe and feel, and progressively construct representations of phenomena, always deeply rooted in bodily and sensory experience.

Lecturers: George Richard Paul Santi, Sara Bagossi

Teaching Hours: 12 Gruppo 1: Dr. Sara Bagossi 12 Gruppo 2: Prof. George Richard Paul Santi
Lab Hours: 0

Semester 2 · 500004E · 5 year master degree in Primary Education - Italian section · 1CP · IT

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

The seminar aims to provide future kindergarten teachers with an opportunity to link the theoretical knowledge acquired in the "Developmental and Educational Psychology" course with the observation and practical understanding of how pre-school children think and reason about their experiences with physical phenomena and mathematical concepts. Building on basic knowledge of cognitive development processes in early childhood, the course will explore the ways in which children construct spontaneous explanations of the world around them. Through examples, discussion of educational situations, and analysis of teaching activities, children’s intuitive ideas will be explored. Particular attention will be paid to the ways in which children formulate hypotheses through experimentation and action, use language and expressive gestures to explain what they observe and feel, and progressively construct representations of phenomena, always deeply rooted in bodily and sensory experience.

Lecturers: Federico Corni

Teaching Hours: 12 Gruppo 1+2: Prof. Federico Corni
Lab Hours: 0

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