Universidad de Jaén

Chapter 1: Foundations of Mathematics Education.

Section 1.1. Mathematics Education for teachers.

Introduction to Mathematics Education. The mathematical activity in Early Childhood Education. Learning and Mathematics. The Theory of Didactic Situations in Mathematics. Didactic Engineering processes. Analysis and management of didactic variables. Mistakes and obstacles.

Chapter 2: Logical-mathematical activity in Early Childhood Education. Didactic analysis.

Section 2.1. Logical-mathematical activity in Early Childhood Education.

The naming of objects, collections and actions. The encoding and decoding processes. The logical processes of focusing and choosing. Discrimination, selection and classification activity. Equivalence and order relations. Design, construction and management of teaching and learning situations: didactic analysis. Analysis of mistakes and obstacles.

Chapter 3: Numbers, numbering, and numerical relations.

Section 3.1. Introduction to numbers and numbering.

Didactic considerations regarding numbers and numbering teaching and learning. The meaning of the numerical knowledge in Early Childhood Education. Teaching and learning situations: reference problems for the construction of teaching situations. Children's strategies to solve problems. The fundamental situation for the measurement of a collection. Design, construction and management of teaching and learning situations: didactic analysis. Analysis of mistakes and obstacles.

Section 3.2. Numbering systems.

Numeral systems. Foundations and principles of positional numeral systems. Spoken and written numbers. The decimal structure: its implication in the calculation algorithms and other mathematical notions. Materials and mathematical-didactic models that facilitate its understanding. Didactic engineering: design, construction and management of teaching and learning situations. Analysis of mistakes and obstacles.

Section 3.3: Elementary arithmetics. Arithmetic problems and algorithms.

Elementary arithmetic operations. The conceptual field of additive structures. The conceptual field of multiplicative structures. Structured materials for a meaningful learning of algorithms. Mental calculation techniques. Didactic Engineering design: construction and management of teaching-learning situations: didactic analysis. Analysis of mistakes and obstacles.

Chapter 4: Spatial and geometric relationships in Early Childhood Education. Didactic analysis.

Section 4.1. Spatial and geometric relationships in Early Childhood Education.
Construction and organization of space and geometric relationships. Difference between spatial and geometric knowledge. Different conceptual models depending on the size of space: microspace, mesospace, macrospace. Representation of spatial relationships. Topological, projective and metric transformations. Intuitive notion of rigid motions in the plane. Didactic Engineering design and construction of teaching and learning situations: didactic analysis. Analysis of mistakes and obstacles.

Theoretical activities

The development of the theoretical part of the subject will be based on lectures, documents and guidelines provided by the lecturer in the classroom, including the subject contents.

It is recommended to follow these steps in order to study the subject:

• Study of the contents of each chapter, extending the notes provided using the basic and recommended bibliography.
• Do the activities and tasks proposed in each chapter.
• Active participation during the lectures.

Practical activities

These lectures aim to promote cooperative group work. 

Throughout the course each student must:

• Participate in the preparation and writing of the work documents.
• Present the activities and tasks proposed before the corresponding deadlines.
• Other educational tasks on specific aspects of the Mathematics curriculum, properly justified, when required by the lecturer. 

The complementary bibliographic work is essential. In addition to the study of theoretical content, students must get involved seriously in studying documents and texts provided, as well as in doing the practical activities proposed to get to a mastery of the subject's contents. 

Other activities (subject to availability):

• Seminars with teachers.
• External experts' lectures
• Guided visits to schools.
• Reading of documents.
• Other.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

The evaluation of each student will be based on the following items:

• Level of understanding of mathematical and didactic knowledge of the topics covered in the course.
• Level, clarity and coherence of the arguments and reasoning expressed in the resolution of the different activities proposed.
• Level of development and consistency of the proposed activities and answers in the written tests, when they take place.
• Level and quality of participation in other scheduled academic activities (qualified expert lectures, seminars, readings, ...) when they take place.
• Absence of misspellings. In the written exam, 0.25 points are deducted for each misspelling.

Instruments and procedures:

• Control of the level of attendance in theoretical and practical classes by collecting signatures.
• Written exam with theoretical and theoretical-practical questions, in which the students have to use the theoretical knowledge in specific situations occurring in Early Childhood Education.

The theoretical part will allow lecturers to evaluate the degree of achievement of learning outcome R01.

The theoretical-practical part will allow lecturers to evaluate the degree of achievement of learning outcomes R02 and R03.

The written test will have a maximum value of 8 points (the remaining 2 points will correspond to attendance and participation). A minimum of 4 points in the written test is required to pass the course.