TECH presenta esta titulación como una oportunidad para implementar a tus clases los conceptos más innovadores de la enseñanza de las Matemáticas a través de la resolución de problemas en el aula de infantil” 

Resolver problemas de Matemáticas es algo muy complicado para muchos niños, sobre todo para los más pequeños cuando se están iniciando en esta ciencia. Sin embargo, desarrollar su pensamiento lógico a través de esta práctica es fundamental ya que, tal y como han determinado muchísimos especialistas, el empleo de esta estrategia pedagógica es altamente beneficiosa para potenciar sus habilidades cognitivas. 

Por esa razón, cada vez son más los profesionales de la Educación que desean implementar a sus Currículums técnicas relacionadas con la Resolución de Problemas, para que los alumnos puedan comprender el sentido de cada una de las operaciones, establecer inferencias y relaciones causa-efecto.  

Y para que el egresado pueda conocer al detalle las mejores estrategias didácticas para ello, sobre todo aplicables a los primeros niveles de enseñanza (de 3 a 6 años), TECH presenta este completo Postgraduate diploma. Se trata de una experiencia académica multidisciplinar a través de la cual el docente podrá ahondar en la enseñanza de la Aritmética, el Álgebra, la Geometría y la medida, pero de manera dinámica e innovadora: a través del juego.  

Para ello contará con el mejor contenido teórico, práctico y adicional, el cual ha sido compactado en un cómodo y flexible formato 100% online. Así, el egresado podrá acceder al curso de este programa desde donde quiera y cuando quiera. Además, podrá descargar la totalidad del material para su consulta, incluso, cuando no disponga de cobertura o cuando haya culminado la experiencia académica. Así no tendrá que preocuparse por horarios ni clases presenciales, asistiendo a una titulación del máximo nivel que se adapta, no solo a sus necesidades, sino a las exigencias del sector educacional actual. 

El programa cuenta con la participación de un prestigioso Director Invitado Internacional. Este especialista, con una trayectoria investigadora sobresaliente, acompañará a los egresados en la exploración de las más recientes innovaciones en el ámbito de la Educación y la enseñanza Matemática, mediante exclusivas y detalladas Masterclasses. 

Potencia tu perfil académico con TECH y disfruta de un conjunto de Masterclasses exclusivas, dirigidas por un experto internacional de renombre en el área de la Enseñanza Matemática” 

Esta Postgraduate diploma en Problem Solving and Mental Arithmetic in the Early Childhood Classroom contiene el programa educativo más completo y actualizado del mercado. Sus características más destacadas son:

• El desarrollo de casos prácticos presentados por expertos en docencia de las Matemáticas
• Los contenidos gráficos, esquemáticos y eminentemente prácticos con los que está concebido recogen una información técnica y práctica sobre aquellas disciplinas indispensables para el ejercicio profesional
• Los ejercicios prácticos donde realizar el proceso de autoevaluación para mejorar el aprendizaje
• Su especial hincapié en metodologías innovadoras
• Las lecciones teóricas, preguntas al experto, foros de discusión de temas controvertidos y trabajos de reflexión individual
• La disponibilidad de acceso a los contenidos desde cualquier dispositivo fijo o portátil con conexión a internet

Una titulación que elevará tu talento docente al de Postgraduate diploma a través del conocimiento exhaustivo de las estrategias aritméticas, algebraicas, geométricas y de medida para Infantil”

El programa incluye, en su cuadro docente, a profesionales del sector que vierten en esta capacitación la experiencia de su trabajo, además de reconocidos especialistas de sociedades de referencia y universidades de prestigio.  

Su contenido multimedia, elaborado con la última tecnología educativa, permitirá al profesional un aprendizaje situado y contextual, es decir, un entorno simulado que proporcionará una capacitación inmersiva programada para entrenarse ante situaciones reales.  

El diseño de este programa se centra en el Aprendizaje Basado en Problemas, mediante el cual el profesional deberá tratar de resolver las distintas situaciones de práctica profesional que se le planteen a lo largo del curso académico. Para ello, contará con la ayuda de un novedoso sistema de vídeo interactivo realizado por reconocidos expertos.   

Si lo que buscas es un programa que potencie tus habilidades para la práctica del pensamiento lógico matemático en Infantil, estás ante la oportunidad perfecta para ello”

Tendrás acceso a un Campus Virtual de última generación en el que encontrarás la totalidad del material desde el principio del curso y al cual podrás acceder desde cualquier dispositivo con conexión a internet”

For the design of the structure and, in general, the content of this program, TECH has taken into consideration the criteria of the teaching team, since, being developed by professionals in the field of Early Childhood Education, they know in detail the aspects that the graduate must master to improve their academic skills. Based on their research work, the 540 hours of theoretical, practical and additional material included in the Postgraduate diploma have been created, giving the student the opportunity to access it from any device with an Internet connection thanks to its convenient 100% online format.

Thanks to the dozens of hours of additional material that you will find in the Virtual Campus, you will be able to expand each section in a personalized way according to your interests and requirements”  

Module 1. Logical-Mathematical Thinking in Pre-School

1.1. Logical-Mathematical Thinking

1.1.1. What is Mathematical Logic?
1.1.2. How is Mathematical Knowledge Acquired?
1.1.3. The Formation of Logical-Mathematical Concepts at an Early Age
1.1.4. Mathematical Concepts
1.1.5. Characteristics of Logical-Mathematical Thinking

1.2. Training Skills Related to Logical-Mathematical Development

1.2.1. Cognitive Development (Piaget)
1.2.2. Evolutionary Stages
1.2.3. Division of Thought in Knowledge (Piaget)
1.2.4. Evolution of Logical-Mathematical Knowledge
1.2.5. Physical Knowledge vs. Logical-Mathematical Knowledge
1.2.6. Knowledge of Space and Time

1.3. Development of Logical-Mathematical Thinking

1.3.1. Introduction
1.3.2. Knowledge and Reality
1.3.3. Development of Mathematical Knowledge
1.3.4. Development of Logical Thinking by Age
1.3.5. Components of Logical Development
1.3.6. Mathematical Language
1.3.7. Logical-Mathematical Development and Core Curriculum

1.4. Psychopedagogical Foundations in the Construction of Mathematical Knowledge

1.4.1. Sensorimotor Intelligence
1.4.2. Formation of Objective Symbolic Thinking
1.4.3. Formation of Concrete-Logical Thinking
1.4.4. Reasoning and its Types
1.4.5. Bloom's Taxonomy in the Development of Logical-Mathematical Thinking

1.5. Logical-Mathematical Learning I

1.5.1. Introduction
1.5.2. Structuring of the Body Scheme

1.5.2.1. Body Concept
1.5.2.2. Body image
1.5.2.3. Postural Adjustment
1.5.2.4. Coordination

1.6. Notions of Order

1.6.1. Comparison
1.6.2. Correspondence
1.6.3. Quantifiers
1.6.4. Quantity Conservation
1.6.5. Sets or Groupings
1.6.6. Formation of Sets
1.6.7. Numerical Cardinality
1.6.8. The Number Concept
1.6.9. Comparison of Sets
1.6.10 Set Equivalence
1.6.11 Recognition of Natural Numbers
1.6.12 Ordinal Numbers
1.6.13 Mathematical Operations: Addition and Subtraction

1.7. Prenumerical Knowledge: Classification

1.7.1. What is Classification?
1.7.2. Processes
1.7.3. Types of Classification
1.7.4. Cross Classifications
1.7.5. Classification Games

1.8. Seriation Games

1.8.1. Importance of Making Series
1.8.2. Logical Operations in the Construction of Series
1.8.3. Types of Series
1.8.4. Seriation in Pre-school Education
1.8.5. Seriation Games

1.9. Prenumerical Knowledge: Enumeration

1.9.1. Conceptualization and Function of Enumeration
1.9.2. Logical Operations Involved in Enumeration
1.9.3. Enumeration in Pre-school Education Design of Activities
1.9.4. Design of Activities
1.9.5. Task-Based Achievements

1.10. Representation and Manipulative Mathematics

1.10.1. Development of Logical-Mathematical Thinking Through the Senses
1.10.2. Representation, Visualization and Reasoning
1.10.3. Design of Activities Supported by Representation
1.10.4. Manipulative Mathematics: Functions and Resources
1.10.5. Design of Activities that Rely on Manipulation

Module 2. Arithmetic, Algebra, Geometry and Measurement Games with Numbers

2.1. Initiation to Number

2.1.1. Number Concept
2.1.2. Construction of the Number Structure
2.1.3. Numerical Development: Counting

2.1.3.1. Phases in Learning the Numerical Sequence

2.1.3.1.1. Rope or String Level
2.1.3.1.2. Unbreakable Chain Level
2.1.3.1.3. Breakable Chain Level
2.1.3.1.4. Numerable Chain Level
2.1.3.1.5. Bidirectional Chain Level

2.1.4. Counting Principles

2.1.4.1. One-to-one Correspondence Principle
2.1.4.2. Stable Order Principle
2.1.4.3. Cardinality Principle
2.1.4.4. Abstraction Principle
2.1.4.5. Irrelevance of Order Principle

2.1.5. Procedures used by the Child in Counting

2.1.5.1. Term to Term Correspondence
2.1.5.2. Subset to Subset Correspondence
2.1.5.3. Purely Visual Estimation
2.1.5.4. Subitization
2.1.5.5. Count the Elements of a Collection
2.1.5.6. Recount
2.1.5.7. Discount
2.1.5.8. Overcount
2.1.5.9. Calculation Procedures

2.1.6. Fundamental Cardinal and Ordinal Situations
2.1.7. The Importance of Zero
2.1.8. Strategies to Enhance the Concept and Use of Number

2.2. Number Acquisition Process

2.2.1. Introduction
2.2.2. Number Concept

2.2.2.1. Perception of General Quantities
2.2.2.2. Distinguishing and Comparing Quantities of Objects
2.2.2.3. Uniqueness Principle
2.2.2.4. Generalization
2.2.2.5. Summative Action
2.2.2.6. Capture of Named Quantities

2.2.2.6.1. Oral Numeric Series
2.2.2.6.2. Counting Objects
2.2.2.6.3. Cardinal Representation
2.2.2.6.4. Compare Magnitudes

2.2.2.7. Identification of the Name with its Representation
2.2.2.8. Invariance of Named Quantities

2.2.3. From Experimental Psychology

2.2.3.1. Distance Effect
2.2.3.2. Size Effect
2.2.3.3. Numerical Spatial Arrangement

2.2.4. From Developmental Psychology

2.2.4.1. Behavioral, Cognitive and Constructivist Theory

2.2.4.1.1. Exercise Law
2.2.4.1.2. Law of Effect

2.2.5. Theories on the Process of Number Acquisition
2.2.6. Piaget

2.2.6.1. Stages
2.2.6.2. Requirements for the Understanding of the Notion of Number

2.2.7. Dienes

2.2.7.1. Principles

2.2.7.1.1. Dynamic Principle
2.2.7.1.2. Constructive Principle
2.2.7.1.3. Economic Variability Principle
2.2.7.1.4. Constructive Variability Principle

2.2.7.2. Stages

2.2.7.2.1. Free Play
2.2.7.2.2. Game with Rules
2.2.7.2.3. Isomorphic Games
2.2.7.2.4. Representation
2.2.7.2.5. Description
2.2.7.2.6. Deduction

2.2.8. Mialaret

2.2.8.1. Stages

2.2.8.1.1. Action Itself
2.2.8.1.2. Action Accompanied by Language
2.2.8.1.3. Conduct of the Narrative
2.2.8.1.4. Application of the Story to Real Situations
2.2.8.1.5. Graphical Expression of the Actions already Reported and Represented
2.2.8.1.6. Symbolic Translation of the Studied Problem

2.2.9. Information Processing

2.2.9.1. Numerical Apprehension Model
2.2.9.2. Pre-Linguistic Numerical Skills

2.2.10 Counting Principles (Gelman and Gallistel)

2.2.10.1. Biunivocal Correspondence Principle
2.2.10.2. Stable Order Principle
2.2.10.3. Cardinality Principle
2.2.10.4. Abstraction Principle
2.2.10.5. Inconsequence of Order Principle

2.2.11 Comparison of Counting Principles between Piaget's, Gelman's and Gallistel's Theory

2.3.  Informal Arithmetic I

2.3.1. Introduction
2.3.2. Towards an Informal and Intuitive Arithmetic in Pre-School Education

2.3.2.1. Recognize Quantities
2.3.2.2. Relate Quantities
2.3.2.3. Operate Quantities

2.3.3. Objectives
2.3.4. Early Arithmetic Skills

2.3.4.1. Preservation of Inequality

2.3.5. Arithmetic Skills and Chants

2.3.5.1. Preliminary Considerations

2.3.5.1.1. Socio-Cognitive Conflict
2.3.5.1.2. Role of the Language
2.3.5.1.3. Creation of Contexts

2.3.5.2. Procedures and Mastery of the Chants

2.4. Informal Arithmetic II

2.4.1. Memorization of Numerical Facts

2.4.1.1. Activities to Work on Memorization
2.4.1.2. Domino
2.4.1.3. Hopscotch

2.4.2. Didactic Situations for the Introduction of Addition

2.4.2.1. Dialed Number Game
2.4.2.2. Race to 10
2.4.2.3. Christmas Greeting

2.5. Basic Arithmetic Operations

2.5.1. Introduction
2.5.2. Additive Structure

2.5.2.1. Phases of Mialaret

2.5.2.1.1. Approach Through Manipulation
2.5.2.1.2. Action Accompanied by Language
2.5.2.1.3. Mental Work Supported by Verbalization
2.5.2.1.4. Purely Mental Work

2.5.2.2. Strategies to Add
2.5.2.3. Initiation to Subtraction
2.5.2.4. Addition and Subtraction

2.5.2.4.1. Direct and Object Modeling
2.5.2.4.2. Counting Sequences
2.5.2.4.3. Recalled Numeric Data
2.5.2.4.4. Strategies to Add
2.5.2.4.5. Subtraction Strategies

2.5.3. Multiplication and Division
2.5.4. Arithmetic Problem Solving

2.5.4.1. Addition and Subtraction
2.5.4.2. Multiplications and Divisions

2.6. Space and Geometry in Pre-school Education

2.6.1. Introduction
2.6.2. Objectives Proposed by the NCTM
2.6.3. Psychopedagogical Considerations
2.6.4. Recommendations for Teaching Geometry
2.6.5. Piaget and his Contribution to Geometry
2.6.6. Van Hiele Model

2.6.6.1. Levels

2.6.6.1.1. Visualization or Recognition
2.6.6.1.2. Analysis
2.6.6.1.3. Sorting and Classification
2.6.6.1.4. Rigor

2.6.6.2. Learning Phases

2.6.6.2.1. Phase 1: Consultancy
2.6.6.2.2. Phase 2: Directed Guidance
2.6.6.2.3. Phase 3: Explication
2.6.6.2.4. Phase 4: Guidance
2.6.6.2.5. Phase 5: Integration

2.6.7. Geometry Types

2.6.7.1. Topological
2.6.7.2. Projective
2.6.7.3. Metrics

2.6.8. Visualization and Reasoning

2.6.8.1. Spatial Orientation
2.6.8.2. Spatial Structuring
2.6.8.3. Gálvez y Brousseau

2.6.8.3.1. Microspace
2.6.8.3.2. Mesospace
2.6.8.3.3. Macrospace

2.7. Magnitudes and their Measurement

2.7.1. Introduction
2.7.2. Construction of the Notion of Magnitude in the Child

2.7.2.1. Piagetian Phases in the Construction of Magnitudes

2.7.2.1.1. Consideration and Perception of a Magnitude
2.7.2.1.2. Conservation of Magnitude
2.7.2.1.3. Ordering with Respect to Magnitude
2.7.2.1.4. Correspondence of Numbers to Quantities of Magnitude

2.7.2.2. Stages in the Construction of the Measure

2.7.2.2.1. Direct Perceptual Comparison
2.7.2.2.2. Displacement of Objects
2.7.2.2.3. Operability of the Transitive Property

2.7.2.3. Stages in the Teaching-Learning of Magnitudes

2.7.2.3.1. Sensory Stimulation
2.7.2.3.2. Direct Comparison
2.7.2.3.3. Indirect Comparison
2.7.2.3.4. Choice of Unit
2.7.2.3.5. Irregular Measurement System
2.7.2.3.6. Regular Measurement System

2.7.3. Measuring Magnitudes
2.7.4. Length Measurement
2.7.5. Length Measurement
2.7.6. Measurement of Capacity and Volume
2.7.7. Measurement of Time
2.7.8. Phases of the Different Magnitudes

2.7.8.1. Preparation Phase
2.7.8.2. Measurement Practice Phase
2.7.8.3. Consolidation Phase of Techniques and Concepts

2.8. Play in Pre-school Education

2.8.1. Introduction
2.8.2. Objectives
2.8.3. Playing Features
2.8.4. Evolution of the Game

2.8.4.1. Types of Games

2.8.4.1.1. Functional Game
2.8.4.1.2. Imitation or Symbolic Play
2.8.4.1.3. Game with Rules
2.8.4.1.4. Construction Game

2.8.5. Chance and Strategy
2.8.6. Competition in the Games
2.8.7. Didactic Considerations on the Game

2.9. Didactic Resources of the Game

2.9.1. Games and Logical Thinking

2.9.1.1. Three in a Row
2.9.1.2. Quarto
2.9.1.3. Portrait Games

2.9.2. Quantitative Games

2.9.2.1. Number to Compare

2.9.2.1.1. Home!

2.9.2.2. Number to Calculate

2.9.2.2.1. Couples
2.9.2.2.2. No more!
2.9.2.2.3. Cat and Mouse

2.9.3. Games and the Structure of Space

2.9.3.1. Puzzles

2.9.3.1.1. Two-Color Paintings
2.9.3.1.2. The Hex

2.10. Games in Different Spaces

2.10.1. Introduction
2.10.2. Games in the Classroom

2.10.2.1. The Butterfly Game
2.10.2.2. The Partitioning Game
2.10.2.3. Image Trains
2.10.2.4. The Newspaper
2.10.2.5. Flat Figures
2.10.2.6. The Containers

2.10.3. Games in Psychomotor Skills

2.10.3.1. Working with Sizes
2.10.3.2. Classify
2.10.3.3. We Play with the Hoops

2.10.4. Outdoor Games
2.10.5. Mathematical Games with ICT

2.10.5.1. Playing with the Turtle's Mind
2.10.5.2. Geometric Figures
2.10.5.3. For 3-Year-Old Students
2.10.5.4. Variety of Activities
2.10.5.5. Didactic Unit

Module 3. Problem Solving and Mental Arithmetic

3.1. Problem in Pre-School Education

3.1.1. Methodological Considerations
3.1.2. Psychopedagogical Considerations of the Initiation of Problem Idea Representation
3.1.3. What is a Problem?
3.1.4. How to Pose Problems in Pre-School?

3.2. Idea of a Problem to be Introduced in Pre-School Education

3.2.1.  Why do We Solve Problems?
3.2.2. Perspectives for the Inclusion of Comprehension and Problem Solving in Pre-school Education
3.2.3. Specific Didactic Contract for Problem Solving in Pre-School Education
3.2.4. Most Appropriate Models for Introducing the idea of Problem in Pre-School Education
3.2.5. Reading and Understanding Statements

3.2.5.1. Factors of Understanding Statements

3.2.6. Didactic Variables of the Statements

3.3. Towards a Didactic Approach to the Introduction to the idea of Problem in Pre-School Education

3.3.1. Factors to be Taken into Consideration in the Approach and Resolution of Problems in Pre-School
3.3.2. Learning Logical-Mathematical Concepts Through Problem Solving

3.3.2.1. Heuristic Strategies
3.3.2.2. Technique Most Commonly Used at These Ages for Problem Solving
3.3.2.3. Numerical Strategies

3.3.3. Various Situations for the Teaching of Proposition and Problem Solving
3.3.4. Problem Solving Constituent Elements of a Problem

3.3.4.1. Problems that Serve as Exercises to Practice the Problem Idea

3.3.5. Main Recommendations for Approaching the Problem Idea in Pre-school Education

3.4. Mathematical Value of Stories

3.4.1. Pre-school Learning and Mathematics
3.4.2. Stories and Mathematics
3.4.3. Examples of Stories and Mathematical Learning

3.4.3.1. Logical Development
3.4.3.2. Numerical Development
3.4.3.3. Development of Magnitudes and their Measurement
3.4.3.4. Development of Geometric Thinking
3.4.3.5. Problem Solving

3.5. Logical Basis of Mental Arithmetic in Pre-school Education

3.5.1. Logical Operations

3.5.1.1. Classifications
3.5.1.2. Relationships of Order

3.5.2. Mental Arithmetic, Written Arithmetic and Estimated Arithmetic
3.5.3. Counting Process
3.5.4.  Phases for Learning the Counting Activity

3.6. Informal Arithmetic

3.6.1. Arithmetic Strategy
3.6.2. Comparison and Equivalence
3.6.3. Composition and Decomposition
3.6.4. Initiation to Operational Activity: Adding, Subtracting, Folding and Distributing

3.7. Mental Arithmetic in Pre-school Education

3.7.1. Calculation Examples for Pre-school Education
3.7.2. Perform Calculation by Manipulating Material
3.7.3. Calculation Without Material Handling
3.7.4. Proposal for Mental Arithmetic in Pre-School Education

3.7.4.1. Guessing Game
3.7.4.2. It Is Learned by Heart

3.7.5. Mechanics Acquired at the End of Pre-School Education
3.7.6. Resources to Achieve Apprenticeships
3.7.7. Practical Issues

3.8. Resource Bank for Calculation in Pre-School Education

3.8.1.  Abacus

3.8.1.1. Description
3.8.1.2. Possibilities for Didactic Use
3.8.1.3. Classroom Didactic Situations

3.8.2. Multibase Blocks

3.8.2.1. Description
3.8.2.2. Possibilities for Didactic Use
3.8.2.3. Classroom Didactic Situations

3.8.3. Cuisenaire Strips

3.8.3.1. Description
3.8.3.2. Possibilities for Didactic Use
3.8.3.3. Classroom Didactic Situations

3.8.4. Domino

3.8.4.1. Description
3.8.4.2. Possibilities for Didactic Use
3.8.4.3. Classroom Didactic Situations

3.8.5. Battle Game

3.8.5.1. Description
3.8.5.2. Possibilities for Didactic Use
3.8.5.3. Classroom Didactic Situations

3.9. Open Calculation Method based on ABN Numbers

3.9.1. What is the ABN Algorithm Method?

3.9.1.1. Quantity and Cardinality of Sets
3.9.1.2. Number Structure and Set Comparison

3.9.1.2.1. Figurative Representation
3.9.1.2.2. Symbolic Representation
3.9.1.2.3. Symbol-Sign Representation
3.9.1.2.4. Representation by Signs

3.9.1.3. Counting Well Over Ten
3.9.1.4. Number Transformations First Operations

3.9.2. Background of the ABN Method
3.9.3. Intuitive Approach vs. Traditional Approach

3.10. ABN Method Activities Proposal

3.10.1. Block 1: Numerical and Cardinal

3.10.1.1. Search for Equivalent Sets
3.10.1.2. Establishment of a Physical Pattern
3.10.1.3. Pattern Sorting
3.10.1.4. Numeric String Start of Counting
3.10.1.5. Subitization
3.10.1.6. Estimate

3.10.2. Block 2: Number Structure and Comparison

3.10.2.1. Introduction to the Ten
3.10.2.2. Ordering, but not Counting
3.10.2.3. Arrangement of Disordered Sets
3.10.2.4. Interaction of Missing Elements
3.10.2.5. Arrangement with Non-Manipulable Material
3.10.2.6. Comparison of Real Objects
3.10.2.7. Comparison of Figurative Elements

3.10.3. Block 3: Number Transformations

3.10.3.1. Number Transformations
3.10.3.2. Addition with the Number Line
3.10.3.3. Subtraction with Toothpicks
3.10.3.4. Finding the Double with Grid
3.10.3.5. Finding Half with the Number Line

3.10.4. Assessment

The teaching materials of this program, elaborated by these specialists, have contents that are completely applicable to your professional experiences"