A fully online program that offers you to delve into models and metamodels for the generation of strategies in Problem Solving”

The mastery of mathematics is key for human beings in their understanding and adaptation to current life and the environment that surrounds them. With the use of new technologies for teaching, management skills and numerical resources are of special interest, as new options have opened up in the labor market that support this.

The demand for professionals with extensive knowledge and proficiency in specific areas such as Problem Solving has increased exponentially. Therefore, in-depth management allows thousands of professionals to access newly created jobs. Technological advances are also reflected in the are also reflected in the classroom, so it is essential for teachers to keep abreast of the latest developments in their sector.   

In this way, and with the aim that professionals can be up to date on the keys to teaching Mental Calculus, TECH together with a team versed in this field have designed a program that gathers the most exhaustive information on the subject: the Postgraduate certificate in Mental Calculation and Problem Solving. Through this exclusive 6-week educational experience, the student will delve into the materials and games to work on mathematics and learn how to face obstacles in Problem Solving.  

All this through a 100% online program designed by experts in mathematics that includes, in addition to the most complete and up to date theoretical syllabus, hours of additional content presented in different audiovisual formats to motivate students in their learning. In addition, you will be able to access and download the material to consult it whenever you need it. Thanks to its totally online format, graduates will be able to choose their own study schedule and adapt it to their personal needs. 

Specialize in the study and scientific foundation of logical principles with this exclusive university qualification”

This Postgraduate certificate in Mental Calculation and Problem Solving contains the most complete and up-to-date educational program on the market. The most important features include: 

• The development of practical cases presented by experts in Arithmetic, Algebra, Geometry and Measurement
• The graphic, schematic, and practical contents with which they are created, provide practical information on the disciplines that are essential for professional practice 
• Practical exercises where the self-assessment process can be carried out to improve learning 
• Its special emphasis on innovative methodologies  
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments 
• Content that is accessible from any fixed or portable device with an Internet connection

You will be able to download all the content to any electronic device from the Virtual Campus and consult it whenever you need it”

The program’s teaching staff includes professionals from the industry who contribute their work experience , to this program, as well as renowned specialists from leading societies and prestigious universities.

The multimedia content, developed with the latest educational technology, will provide the professional with situated and contextual learning, i.e., a simulated environment that will provide immersive education programmed to learn in real situations.

This program is designed around Problem-Based Learning, whereby the professional must try to solve the different professional practice situations that arise during the academic year For this purpose, the students will be assisted by an innovative interactive video system created by renowned and experienced experts.

Upgrade your skills in teaching strategies for teaching mathematics and propel your career into a more ambitious professional future"

Enroll now and gain access to a multimedia library full of valuable content presented in a variety of different audiovisual formats"

The teaching team that TECH has selected for this program has worked intensively in the design of the 150 hours of theoretical, practical and additional content included in this Postgraduate certificate, thanks to which it has been possible to create a rigorous, complete and innovative syllabus. In this way, graduates will have access to a highly training program, which will allow them not only to improve their teaching competences, but also to implement in their pedagogical strategies the keys for the teaching of Mental Calculus.  

The most effective and dynamic educational program on the market is at your disposal thanks to this Postgraduate certificate”

Module 1. Mental Calculation and Problem Solving

1.1. Mental Calculation

1.1.1. What is Mental Calculation?

1.1.1.1. Definition
1.1.1.2. Mechanical or Stimulus-Response Calculation
1.1.1.3. Reflective or Thoughtful Calculation
1.1.1.4. Skills

1.1.2. Authors' Contribution

1.1.2.1. María Ortiz
1.1.2.2. Jiménez Ibáñez
1.1.2.3. Hope
1.1.2.4. Dickson
1.1.2.5. Carrol y Porter
1.1.2.6. Alistair McIntosh

1.1.3. Justification

1.1.3.1. MC Classroom Implementation
1.1.3.2. 6 Reasons why Mental Calculation is Important

1.1.4. Mental Calculation in the Basic Curriculum of Primary Education

1.1.4.1. Royal Decree 126/2014
1.1.4.2. Contents
1.1.4.3. Assessment Criteria
1.1.4.4. Assessable Learning Standards

1.1.5. Advantages of Mental Calculation

1.1.5.1. Bernardo Gómez
1.1.5.2. María Ortiz

1.1.6. Disadvantages of Mental Calculation

1.1.6.1. Definition
1.1.6.2. Four Areas of Difficulty
1.1.6.3. Causes

1.1.7. Approximate Calculation

1.1.7.1. Definition
1.1.7.2. Algorithmic Thinking
1.1.7.3. Onset

1.1.8. Mental Arithmetic

1.1.8.1. Definition
1.1.8.2. Elementary Forms
1.1.8.3. Levels of Use

1.1.9. Keys to Teaching Mental Calculation

1.1.9.1. Uses
1.1.9.2. Strategies
1.1.9.3. Practice
1.1.9.4. Decision
1.1.9.5. Mentality

1.2. Teaching Mental Calculation

1.2.1. Contents and Activities for the M.C

1.2.1.1. Basic Concepts of Number and Properties Related to Operations
1.2.1.2. The Tables
1.2.1.3. Strategies
1.2.1.4. Oral Problems
1.2.1.5. Games and Didactic Material

1.2.2. General Didactic Guidelines

1.2.2.1. Strategies to be Proposed
1.2.2.2. Sequencing
1.2.2.3. Level of the Student Body
1.2.2.4. Playful Activity
1.2.2.5. Constancy
1.2.2.6. M.C Programming

1.2.3. Mental Calculation Strategies

1.2.3.1. Definition
1.2.3.2. Simpler Strategies

1.2.4. Strategies for Addition

1.2.4.1. Counting
1.2.4.2. Double
1.2.4.3. Commutative Property
1.2.4.4. Associative Property
1.2.4.5. Decomposition

1.2.5. Subtraction Strategies

1.2.5.1. Counting
1.2.5.2. Decomposition
1.2.5.3. Completing Numbers

1.2.6. Strategies for Multiplication

1.2.6.1. Sum Reduction
1.2.6.2. Distributive Property
1.2.6.3. Commutative Property
1.2.6.4. Factorization and Association
1.2.6.5. Basic Multiplications

1.2.7. Division Strategies

1.2.7.1. Division Test
1.2.7.2. Divide by 2 and 3
1.2.7.3. Basic Divisions

1.2.8. Approximation

1.2.8.1. Definition
1.2.8.2. María Ortiz
1.2.8.3. Utility and Advantages

1.2.9. Approximate Calculation Strategies

1.2.9.1. Reformulation
1.2.9.2. Translation Processes
1.2.9.3. Compensation Processes

1.3. Sequencing and Activities to Work on Mental Calculation

1.3.1. Manipulative Resources

1.3.1.1. What are they?

1.3.2. Design of Activities

1.3.2.1. Infant

1.3.3. Learning Calculation in Relation to Other Areas of Knowledge

1.3.3.1. Tongue

1.3.4. Number Tables

1.3.4.1. What are they?

1.3.5. Numerical Pyramids

1.3.5.1. What are they?

1.3.6. Numerical Triangles

1.3.6.1. What are they?

1.3.7. Magic Squares

1.3.7.1. What are they?

1.3.8. Mathematical Games

1.3.8.1. What are they?

1.3.9. Other Games

1.3.9.1. What are they?

1.4. Other Resources for the Development of Mental Calculation

1.4.1. Japanese Abacus
1.4.2. Flash Method
1.4.3. Smartick
1.4.4. Supertic
1.4.5. Geogrebra
1.4.6. Mothmatic
1.4.7. Arcademics
1.4.8. Kahn Academy
1.4.9. Gauss Project

1.5. Problem-Based Learning

1.5.1. General aspects of the PBL
1.5.2. Features of a PBL
1.5.3. Planning of a PBL
1.5.4. Role of the Teacher
1.5.5. Role of the Students
1.5.6. Design of the PBL
1.5.7. Implementation of the PBL
1.5.8. Evaluation of PBL
1.5.9. Benefits of PBL

1.6. Logic

1.6.1. Study and Scientific Basis of Logic Principles
1.6.2. Statements
1.6.3. Conditional Expressions
1.6.4. Explanation, Argumentation and Demonstration
1.6.5. Reasoning: Deduction, Induction and Abduction
1.6.6. Reduction to Absurdity
1.6.7. Logic for Learning, Logic for Teaching
1.6.8. Educational Intervention-Didactic Procedures
1.6.9. Resources for Mathematical Logic

1.7. Mathematical Problems

1.7.1. Concept of Problem
1.7.2. Didactic Methodology for Educational Intervention
1.7.3. Variables
1.7.4. Constants
1.7.5. Elaboration of Problems
1.7.6. Interpretation of Problems
1.7.7. Oral Problems
1.7.8. Practical Procedures to Avoid Difficulties and Blockages in Mathematical Problem Solving
1.7.9. Adaptation of the Statements

1.8. Metamodels and Models for the Generation of Problem-Solving Strategies

1.8.1. Introduction to Metamodels and Models
1.8.2. What are Metamodels for?
1.8.3. Generative Metamodels
1.8.4. Structuring Metamodels
1.8.5. Link Metamodels
1.8.6. Transformation Metamodels
1.8.7. Composition Metamodels
1.8.8. Interconnection Metamodels
1.8.9. ICT Metamodels

1.9. The Mathematical Task in Problem Solving

1.9.1. Mathematical Work
1.9.2. Factors Involved in Problem-Solving Learning
1.9.3. Problem Solving, the First Approach
1.9.4. Resolution Strategies
1.9.5. Problem Solving Phases
1.9.6. Problem Solving Guidelines
1.9.7. Obstacles and Problem-Solving Difficulties
1.9.8. Overcoming Obstacles
1.9.9. Resolution Check

1.10. Materials and Games to Work on the Problems

1.10.1. Manipulative Resources
1.10.2. Non-Manipulative Resources
1.10.3. Playful Resources
1.10.4. Design of Activities
1.10.5. Learning Problems in Relation to other Areas of Knowledge
1.10.6. Everyday Problems
1.10.7. Board Games to Work on Problems
1.10.8. Geoplane
1.10.9. Pentominoes

The most complete and up to date educational program in the market is within your reach in this first level Postgraduate certificate”