Teaching and Learning Arithmetic

- To know the curricular treatment of mathematics in Primary Education and its implications in teaching and learning it.
- To acquire a basic mathematical formation that trains students to conduct their teaching, with emphasis on the contents that reach the numbers and calculation.
- To understand the necessary elements to intervene in the teaching / learning of arithmetic: problems and mistakes, strategies, resources and didactic methods.
- To interlink the basics of mathematics with real-life situations, trying to encourage future primary teachers a positive idea about the teaching of mathematics and mathematics in general.

Topics to be developed:

1. Mathematics in Primary Education
- Specialty in mathematical knowledge
- Theories of Mathematics Education
- The mathematics curriculum in primary education

2. Natural numbers and number systems
- The concept of natural number
- Ways of representing numbers, number systems. Number Bases
- The Decimal System

3. Didactic treatment of arithmetic calculus
- The basic arithmetic operations
- Algorithms
- Mental calculation

4. Extending the Number System: Fractions and decimals. Integers.
- Different interpretations of the concept of fraction
- Equivalent fractions and operations with fractions
- Decimal expression of a fraction. Decimal numbers
- Errors and common obstacles related to the concept of decimal number
- Introduction to integers

5. School arithmetic problems. Strategies for treatment
Recurring Contents:
Problem solving
Materials and Resources
Math curriculum

Within the collection "MATHEMATICS: CULTURE AND LEARNING" of the Síntesis editorial, the books that deal with the contents of the program constitute a basic resource, these are:

- Castro, E., Rico, L., & Castro, E. (1987). Números y operaciones. Síntesis.
- Gómez Afonso, B. (1993). Numeración y Cálculo. Síntesis.
- Llinares, S., & Sánchez, M.V. (1988) Fracciones. Síntesis.
- Rico, L. y Flores, P. (Coords.) (2015). Enseñanza y aprendizaje de las matemáticas en Educación Primaria. Pirámide.

Other bibliographic material that guides the content:

- Alsina., A. (2004). Desarrollo de competencias matemáticas con recursos lúdico-manipulativos para niños y niñas de 6 a 12 años. Narcea.
- Canals, M. A. (2009). Fracciones. Los dossiers de María Antonia Canals, 102. Associació de Mestres Rosa Sensat.
- Castro, E. (Ed.) (2001). Didáctica de la matemática en la educación primaria. Síntesis.
- Centeno, J. (1988). Números decimales. ¿Por qué? ¿Para qué?. Síntesis.
- Chamorro, M. C. (2003). Didáctica de las matemáticas para primaria. Pearson.
- Godino, J. (2003). Sistemas numéricos y su didáctica para maestros. Proyecto Edumat-¬Maestros. Recuperado de http://www.ugr.es/local/jgodino/edumat-¬maestros/
- Goñi, J. M. (Coord.) (2000). El curriculum de Matemáticas en los inicios del siglo XXI, Biblioteca UNO. Graó.
- Hernán, F., & Carrillo, E. (1988). Recursos en el aula de matemáticas. Síntesis.
- Kamii, C. (1986). El Niño reinventa la aritmética: implicaciones de la teoría de Piaget. Visor
- MARTÍNEZ, J. (2000). Una nueva didáctica del cálculo para el siglo XXI. Cisspraxis.
- Maza, C. (1991a). Enseñanza de la suma y de la resta. Síntesis.
- Maza, C. (1991b). Enseñanza de la multiplicación y división. Síntesis.
- NCTM (2003). Principios y Estándares para la Educación Matemática. SAEM Thales.
- Polya, G. (1968). Let Us Teach Guessing. MAA Video.

Competences and learning outcomes that students should acquire:

General competences (G):
G1.To know the curriculum areas of primary education, the interdisciplinary relationship between them, the evaluation criteria and the body of didactic knowledge regarding the respective teaching and learning processes.
G2. To design, plan and evaluate teaching and learning, both individually and in collaboration with other teachers and staff of the centre.
G4. To design and regulate learning spaces in diverse contexts which attend to gender equality, to equity and to respect for human rights which satisfy the values of citizenship formation.
G11. To know and apply information and communication technologies in the classroom. Selectively distinguish audiovisual information that contributes to learning, civic formation and cultural richness.

Specific competences (E) of the subject:
E38. To acquire basic mathematical skills (numerical and calculus).
E39. To know the school mathematics curriculum.
E40. To analyze, reason and communicate mathematics proposals.
E41. To expose and resolve problems related to everyday life.
E42. To assess the relationship between mathematics and science as one of the pillars of scientific thought.
E43. To develop and evaluate curriculum contents with appropriate didactic resources and promote the relevant competences in students.

Transversal competences (T):
T3. Instrumental knowledge of information technologies and communication.

The weekly distribution of the classes will consist of one session of 1.5 hours in expository group and another of 1.5 hours in interactive group. Each student will also have 3 hours of scheduled tutoring, distributed along the course of the subject in two sessions of 1.5 hours each, properly arranged in the schedule.

Training activities in expository group are designed to develop, clarify and discuss the contents that offer greater difficulty in understanding, focusing on the basic and most important aspects, while early learning problems that students may come across, are resolved. The teachers will use the exposition, and students will resolve certain practical cases in accordance with the contents addressed. These activities may allow to develop the following basic competences: G1, G8, G11, E38, E40, E41, E43, B1, B4, T3. They will also enable the students to make their oral presentations to their peers, and group discussion in the class.

Interactive group activities will be developed in the framework of methods for solving mathematical and didactic problems, preferably involving an important autonomous individual and group work. This will facilitate the development of competences more related to critical thinking, to the use of information and communication technologies and in general to most of the competences mentioned (G1, G2, G11, E38, E40, E42, B2, T3). The debate, reading and document commentary and the presentation of works will involve a high percentage of autonomous work by students, in order to promote autonomous and cooperative learning and to develop the ability to present in public the results of the work performed.

In the scheduled tutorial sessions students will be addressed in very small groups and they will be guided at their work and learning, in order to develop the competences mentioned.

The students will have also a virtual classroom, through which official communications will be made and every effort will be made to provide all the material necessary to carry out the proposed activities.

Other planned activities:
According to situation, Field Practices and complementary lectures will be considered to complete learning.

The evaluation will be carried out according to the following planning:

Part 1: 50%
A) PARTICIPATION IN THE CLASSROOM (G8, G11, E38, E40, E41, E42, E43, B1, B2, B3, T3).

B) WRITTEN OR ORAL REPORTS AND OTHER PRODUCTIONS (G1, G2, G4, G8, E38, E40, E41, E43, B1, B2, B3, T3).

C) ORAL PRESENTATIONS (G1, G2, G8, G11, E38, E40, E41, E43, B1, B2, B3, B4, T3).

Part 2: 50%
D) SPECIFIC TESTS (G1, G8, E38, E40, E41, B1, B2, B3).

- Passing both parts, 1 and 2, will be necessary condition to pass the subject.

- Likewise, positive grade in (A) requires participation in at least 80% of the sessions. The teachers of the subject will inform the students with exemption from attendance at lectures of the alternative assessment that corresponds to (A).

- The SPECIFIC TEST, part 2, will consist of one or more written test on knowledge of mathematics and its didactics that are reflected in the program.
- According to teachers, students who fail the subject may retain some of the grades for the July exams or the next academic year.

For cases of fraudulent exercises or examination, the provisions of the Regulations for the evaluation of students' academic performance and the review of grades will be applied.

ATTENDANCE HOURS: 51 hours depending on
- EXPOSITORY GROUP ACTIVITIES (24 hours)
Expository activity
Class group practice
Presentation of a work plan
Written tests
- INTERACTIVE GROUP ACTIVITIES (24 hours)
Problem resolution
Case Study
Debates
Projects and works
- ACTIVITIES IN SMALL GROUP OR INDIVIDUAL (3 hours)
Reflection group work
Project discussion
AUTONOMOUS WORK HOURS: 99 hours depending on
- EXPOSITORY GROUP ACTIVITIES (35 hours)
Reading documents
Study
Written Test Prep
- INTERACTIVE GROUP ACTIVITIES (45 hours)
Reading documents
Preparing presentations
Search for additional information
Reflection in small groups
- ACTIVITIES IN SMALL GROUP OR INDIVIDUAL (19 hours)
Doubt resolution
Project and work discussion in small group work
Self-assessment activities
TOTAL HOURS: 150

We recommend the immersion in the recommended bibliography, in order to raise doubts and questions in the sessions. The active nature of the methodology requires the main role of students in their own learning.

USC is an attendance-modality university; therefore the attendance to a minimum of 80% of the class sessions is compulsory. Students with exemption from attendance at theoretical classes must respect due dates to hand in the assignments and all the established requirements and it will be advisable and necessary to keep in touch with the subject teachers through the tutorials and the virtual platform in order to ensure the excellent development of the subject as well as passing it.

For cases of fraudulent exercises or examination, the provisions of the Regulations for the evaluation of students' academic performance and the review of grades will be applied.

The works carried out by the students must be delivered, preferably, through the virtual classroom.

Environmental responsibility:

o Avoid plastic lids or other unnecessary external wrapping.
o Whenever possible, use staples instead of binding.
o Print on both sides in “ink saving” quality.
o Do not use blank pages as chapter or part separators.
o Avoid annexes that do not have direct reference to the topics developed.

Gender perspective:
It is recommended to use non-sexist language, both in daily classroom work and in entrusted academic assignments.

Mandatory use of the rai email account.

Mandatory use of institutional technological tools: Virtual Campus, Microsoft Office 365, and other tools provided by the faculty and authorized as institutional tools by the university (Lifesize, etc.).

The mobile phone may not be used, except when it is used as a work tool according to the indications given by the teacher, the students being held responsible for the legal and academic consequences that may arise from improper use of it.

Bear in mind that teaching-learning (classes / tutorials) is a private process, understood as private as a process of communication and exchange between the teacher and the students enrolled in the subject.

Mandatory compliance with data protection regulations https://www.usc.gal/es/politica-privacidad-proteccion-datos