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 connect the mathematical notions with real situations, trying to encourage the future Primary school teachers to think positively about teaching mathematics and this subject in general.

Themes 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 calculus

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

Basic bibliography

The chapters related with the program of the following references:
- ALBARRACÍN, L. et al. (2018). Aprender a enseñar matemáticas en la educación primaria. Madrid: Síntesis.
- CARRILLO, J. et al. (Eds.) (2016). Didáctica de las matemáticas para maestros de educación Primaria. Madrid: Paraninfo.
- FLORES, P., RICO, L. (Coords.) (2015). Enseñanza y aprendizaje de las matemáticas en Educación Primaria. Madrid: Pirámide.
- SEGOVIA, I., RICO, L. (Coords.) (2011). Matemáticas para maestros de Educación Primaria. Madrid: Pirámide.

Complementary bibliography

- ALSINA, Á. (2004). Desarrollo de competencias matemáticas con recursos lúdico-manipulativos para niños y niñas de 6 a 12 años. Madrid: Narcea.
- BINIÉS, P. (2008). Conversaciones matemáticas con Mª Antònia Canals o Cómo hacer de las matemáticas un aprendizaje apasionante. Barcelona: Graó.
- CASTRO, E. (Ed.) (2001). Didáctica de la matemática en la educación primaria. Madrid: Síntesis.
- CASTRO, E., RICO, L., CASTRO, E. (1995). Estructuras aritméticas elementales y su modelización. Bogotá: Grupo Editorial Iberoamérica.
- CHAMORRO, M. C. (Coord.)(2003). Didáctica de las matemáticas para primaria. Madrid: Pearson.
- CORBALÁN, F. (2007). Las matemáticas de la vida misma. Barcelona: Graó.
- ESTEPA, A. (2006). Reconstrucción de una organización matemática: Sistema de numeración posicional. Bases y relaciones entre ellas. En RUIZ-HIGUERAS, L., ESTEPA, A. E GARCÍA, J.A. (Eds.), Sociedad, escuela y matemáticas: aportaciones de la teoría antropológica de lo didáctico (pp. 339-358). Servicio de Publicaciones de la Universidad de Jaén.
- KAMII, C. (1986). El niño reinventa la aritmética: Implicaciones de la teoría de Piaget. Madrid: Visor.
- LUCEÑO, J. L. (1999). La resolución de problemas aritméticos en el aula. Archidona (Málaga): Aljibe.
- NCTM (2003). Principios y Estándares para la Educación Matemática. Sevilla: SAEM Thales.

Within the collection "MATHEMATICS: CULTURE AND LEARNING" published by Syntesis, the following books deal with the syllabus contents and constitute a good resource to study in depth:
- CASTRO, E. et al. (1987). Números y operaciones.
- CENTENO, J. (1988). Números decimales. ¿Por qué? ¿Para qué?
- GÓMEZ AFONSO, B. (1993). Numeración y Cálculo.
- LLINARES, S. Y SÁNCHEZ, M.V. (1988) Fracciones.
- MAZA, C. (1991a). Enseñanza de la suma y de la resta.
- MAZA, C. (1991b). Enseñanza de la multiplicación y división.
- PUIG, L. Y CERDÁ, F. (1988). Problemas aritméticos escolares.
- SEGOVIA, I. et al. (1989). Estimación en cálculo y medida


Spanish research journals and experience in mathematics education:
- "EPSILON", Sociedad Andaluza de Profesores de Matemáticas THALES.
- "GAMMA", Asociación Galega de Profesores de Educación Matemática.
- "NÚMEROS", Sociedad Canaria de P. de M. ISAAC NEWTON.
- "SUMA", Federación Española de Profesores de Matemáticas.
- "UNO", GRAÓ.

Competences and learning outcomes that students should acquire:

Basic competences (B):
B1. To understand the contents of an study area that comes from the basis os secondary school.
B2. To know how to apply their knowdledge to their job or vocation in a professional form and to own development, argumentation and problem solving competences.
B3. To own the capacity of collect and understand relevant data to give their opinion about relevant social, cientific and ethical themes.
B4. To communicate information, ideas, problems and solutions either to a specialized or not specialized audience.

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 math 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 or laboratory 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, G11; E38, E39, E40, E41, E42, 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 preferably in the framework of methods for solving mathematical and didactic problems, by using different resources and teaching materials, 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, G4, G11; E38, E39, E40, E41, E42, E43; 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 G1, G2, G11; E38, E39, E40; B1, B2, B3; T3.

Students will have also a virtual classroom to support the subject.

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:
A) PARTICIPATION IN THE CLASSROOM (G11, E38, E39, E40, E41, E42, E43, B1, B2, B3, T3): 10%

B) WRITTEN OR ORAL REPORTS AND OTHER PRODUCTIONS (G1, G2, G4, E38, E39, E40, E41, E43, B1, B2, B3, T3): 30%

C) ORAL PRESENTATIONS (G1, G2, G11, E38, E39, E40, E41, E43, B1, B2, B3, B4, T3): 10%

Part 2:
D) SPECIFIC TESTS (G1, E38, E39, E40, E41, B1, B2, B3): 50%

It will be necessary condition to pass the subject:
- Passing both parts, that is, obtaining at least 40% of the maximum mark possible at each one.
- The sum of the marks obtained in the two parts will have to be equal to or greater than 5.

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.

Points B and C correspond largely with the evaluation of a group work on manipulative materials for teaching arithmetic in Primary, to be presented at interactive group sessions (likely between mid-April and first week of May). Attendance to at least 50% of the sessions may be required to present the work.

The submitted works will must be original productions; a copied work will involve the suspense on the subject. For cases of fraudulent performance of exercises or tests, the provisions of the Regulations for evaluation of the academic performance of students and review of qualifications will apply.

Point D, part 2, will consist of one or more written test on knowledge of mathematics and its didactics that are reflected in the program.

July exams:
Being a continuous assessment, students attending the July exams would only make the specific test. The rest of marks obtained would remain.

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)
Discussion and reflection about the group work
Conversation about doubts or interesting subjects

AUTONOMOUS WORK HOURS: 99 hours
Reading documents
Study
Self-assessment activities
Doubts resolution
Written test preparation
Search for additional information
Work in small groups
Discussion and reflection in small groups
Preparation and practice of presentations
Projects discussion

TOTAL HOURS: 150

Attending and working at classes will favor the acquisition of the contents and the collection of information. Immersion in the recommended bibliography will help to advance and consolidate learning.

The students with some dificulty to ordinary follow the contents, should provide to the professor a note provided by the pertinet University service. A working plan will be agreed between the student and the professor.

- Students with exemption from attendance at 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. In any case, within 15 days of acceptance of the exemption, the teachers will determine with the student the assessment route to section A in his/her case.

- It is recommended to use inclusive language, both in everyday classroom work and in the academic works.

- It is recommended the use of the rai email account and the institutional technological tools: Virtual Campus, Microsoft Office 365, and other tools provided by the faculty and authorized as institutional tools by the university.

- The mobile phone may not be used, except when it is used as a resource in class following the instructions given by the teacher, and the students are responsible for the legal and academic consequences that may arise from inappropriate use.

- Mandatory compliance with data protection regulations
https://www.usc.gal/Is/politica-privacy-proteccion-data