ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 102 Hours of tutorials: 6 Expository Class: 18 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Didactics
Areas: Didactics of Mathematics
Center Faculty of Education Sciences
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
OBJECTIVES (O):
O1) Study the main problems of teaching and learning mathematics at the levels of secondary education, related to arithmetic, alxebra and mathematical analysis.
O2) Knowing methodologies for teaching and learning mathematics at secondary education levels, related to Arithmetic, Alxebra and Mathematical Analysis.
O3) Use assessment instruments as part of the teaching and learning process of mathematics at the secondary levels. related to Arithmetic, Alxebra and Mathematical Analysis.
O4) Design learning situations, tasks and projects at the secondary education levels, related to Arithmetic, Alxebra and Mathematical Analysis.
CONTENTS (C)
C1) Difficulties, errors and obstacles in teaching - learning mathematics in secondary education: types of difficulties, errors and obstacles; diagnosis; prevention and remedial strategies (6 h).
C2) Didactic analysis of Arithmetic: curricular contents of the Arithmetic Block in secondary education; didactic guidelines; intervention proposals; available resources (12 h).
C3) Didactic analysis of Algebra: algebra as an instrument of mathematical modeling; curricular contents of the Algebra Block in secondary education; strategies and resources for learning algebraic language; intervention proposals (12 h).
C4) Didactic analysis of Mathematical Analysis: the functional relationship; curricular contents of the Function Block in secondary education; differential and integral calculus in high school; strategies and resources for teaching; intervention proposals (12 h).
BASIC BIBLIOGRAPHY :
BB1) Arce, M., Conejo, L. y Muñoz, J. M. (2019). Aprendizaje y enseñanza de las matemáticas. Síntesis.
BB2) Calvo, C., Deulofeu y J., Jareño, J. y Morera, L. (2016). Aprender a enseñar matemáticas en la educación secundaria obligatoria. Síntesis.
BB3) Saénz, C. y Lasa, A. (2018) Iniciación a la investigación y la innovación en educación matemática. Síntesis.
OTHER BIBLIOGRAPHY :
Books:
OB1) Azcárate, C., Casadevall, M., Casellas, E. y Bosch, D. (1996). Cálculo diferencial e integral. Síntesis.
OB2) Berenguer, L et al. (2001), Materiales para construir las matemáticas en la ESO. Guía didáctica. Proyecto Sur De Ediciones
OB3) Blanco, L. y Cárdenas, J. A. (2013). La Resolución de Problemas como contenido en el Currículo de Matemáticas de Primaria y Secundaria. Campo Abierto, 32(1), 137‑156.
OB4) Bozal, J. L. A. (1994). Taller de matemáticas. Narcea Ediciones, 17.
OB5) Corbalán, F. (1994). Juegos matemáticos para Secundaria y Bachillerato, Madrid, Síntesis.
OB6) Deulofeu, J y Azcárate C. (1998). Guías Praxis para el profesorado de ESO, matemáticas: contenidos, actividades y recursos. Wolters Kluwer Educación.
OB7) Dolores, C. (2004). Acerca del análisis de funciones a través de sus gráficas: concepciones alternativas de estudiantes de bachillerato. RELIME, 7(3), 195-218.
OB8) Edwards, B. S., Dubinsky, E. y Mc Donald, M. A. (2005). Advanced Mathematical Thinking. Mathematical Thinking and Learning, 7(1), 15‑25.
OB9) Font, V. (2011). Competencias profesionales en la formación inicial de profesores de matemáticas de secundaria. UNIÓN, 26, 9‑25.
OB10) Gairín, J. M. y Sancho, J. (2002). Números y algoritmos. Síntesis.
OB11) García, A. Martínez, A. y Miñano, R. (1995). Nuevas tecnologías y enseñanza de las Matemáticas. Síntesis.
OB12) Godino, J. D., Contreras, A. y Font, V. (2006). Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, 26(1), 39-88.
OB13) Ortiz, M. (2014), Cálculo Mental en el Aula en Educación Secundaria Obligatoria, Madrid, CCS.
OB14) Shell Centre (1990). El lenguaje de funciones y gráficas. Ministerio de Educación y Ciencia. Centro de Publicaciones. Servicio Editorial Universidad del País Vasco, Bilbao.
OB15) Stein, M. K . y Smith, M. (2018), Five practices for orchestrating productive mathematics discussions. Reston, NCTM.
Spanish magazines of investigation and experiences in mathematical education:
1) "EPSILON", Sociedad Andaluza de Profesores de Matemáticas THALES.
2) "GAMMA", Asociación Galega de Profesores de Educación Matemática.
3) "NÚMEROS", Sociedad Canaria de P. de M. ISAAC NEWTON.
4) "SUMA", Federación de profesores de Matemáticas. Análisis didáctico. Recursos en el Aula de Matemáticas.
5) "UNO", Barcelona. Graó. Análisis didáctico. Formación de Profesores.
IMPORTANT NOTE:
- THE NECESSARY RESOURCES FOR STUDENT LEARNING WILL BE PROVIDED IN DIGITAL FORMAT THROUGH THE VIRTUAL CLASSROOM.
A) COMPETENCES OF THE DEGREE:
General (G):
G1. Know the curricular contents of the subjects related to the corresponding teaching specialization.
G2. Know the body of didactic knowledge around the respective teaching and learning processes.
G3. Plan, develop and evaluate the teaching and learning process, promoting educational processes that facilitate the acquisition of the competences of the respective teachings, taking into account the level and previous training of the students, as well as their orientation, both individually and in collaboration with other teachers and professionals at the center.
B) OTHER SPECIFIC COMPETENCES:
OSC1. Create learning situations based on the mathematics curriculum, in which the students are the protagonists through a technological, cooperative and interdisciplinary didactic methodology, based on problems, that attends to the diversity of the students, that stimulates them and motivates them, promoting autonomous learning, developing their logical-mathematical thinking skills and solving learning problems in the area of mathematics.
OSC2. Use assessment strategies integrated into the teaching-learning process in such a way that they guide the students, stimulate them and reinforce their learning.
TEACHING METHODOLOGY:
- Regarding the timing, the weekly distribution of the classes will consist of 3 hours in an exhibition group and 3 hours in an interactive group. Each student will also have 3 hours of scheduled tutorials, distributed throughout the course of the subject in two sessions of 1.5 hours duly fixed in the schedule.
EXHIBITION SESSIONS:
- The training activities in an exhibition group are designed to develop, clarify and comment on the contents related to the curriculum, with learning difficulties, with methodologies, with resources, with evaluation, with projects, ...
- The exhibitions will be brief, giving way to the realization of a group work of tasks and projects related to the exhibition (two individual and optional challenges and four collective and mandatory tasks: curriculum, skills, rubrics and portfolio), so that students are the protagonists of their learning through presentations, exhibitions and debates that promote the enrichment of the group and reflection on the content addressed.
- They allow the development of the following skills: G1, G2, OSC1, OSC2
INTERACTIVE SESSIONS:
- Interactive group activities will be developed based on collaboration on platforms in the development of tasks such as:
- The resolution of challenges (two individual and optional challenges).
- The design of teaching-learning situations (six tasks of a collective and compulsory nature: problem-based learning, cooperative learning, gamification in classrooms, flipped classroom, evaluation, didactic units), through the search for complementary information and reflection in small group. Related to:
- The planning of tasks, teaching units and projects.
- Elaboration of learning through problems.
- Creation of gamified proposals.
- Production of inverted classes.
- This will involve an important autonomous group and individual work that will require a high number of hours in order to promote autonomous and cooperative learning that promotes the ability to publicly expose the results of the work carried out.
- The competences that will be developed will be the following: G3, OSC1, OSC2
Likewise, students will be able to attend the tutoring sessions, both those scheduled in the subject schedule and the common sessions set by the teacher in their schedule, to be attended individually or in very small groups trying to guide their work and direct their learning, in order to develop skills: G1, G2, G3, OSC1, OSC2
Students will also have a virtual classroom, through which official communications will be carried out, and all the necessary material will be provided to carry out the proposed tasks that will be delivered on the campus or virtual classroom itself.
If the situation allows it, didactic outings and / or practical experiences of SL will be carried out with centers and institutions that maintain links with the University of Santiago de Compostela.
LEARNING ASSESSMENT SYSTEM
ORDINARY CALL:
- PRESENTIAL STUDENTS:
The competences will be evaluated: G1, G2, G3, OSC1, OSC2 based on the following scheme:
PART 1 (CONTINUOUS EVALUATION): 50% of the final grade.
The following aspects can be assessed:
A) PARTICIPATION IN THE PRESENTIAL SESSIONS OR VIDEOCONFERENCE (10%) (four individual and optional challenges)
B) REPORTS AND OTHER WRITTEN OR ORAL PRODUCTIONS (30%) (eight tasks of a collective and compulsory nature)
C) ORAL OR DIGITAL PRESENTATIONS (10%) (two productions of a collective and compulsory nature)
PART 2 (FINAL EVALUATION): 50% of the final grade
D) SPECIFIC TESTS in which the students will put into practice the skills worked on throughout the course and their acquisition will be assessed (1 individual and compulsory test).
To pass the subject it will be necessary to pass both parts: PART 1 (CONTINUOUS ASSESSMENT) and PART 2 (FINAL ASSESSMENT).
The SPECIFIC TESTS, of PART 2, will consist of a test on the knowledge of didactics of mathematics in secondary education reflected in the program.
IMPORTANT NOTE:
Students who do not have an exemption must attend class as an essential condition to be evaluated.
- STUDENTS WITH EXEMPTION OR WITH WAIVER:
Students with exemption or waiver must contact the teachers to discuss the details of the assessment. In any case, it will be similar to the presential one.
EXTRAORDINARY OPPORTUNITY
Students that do not pass the subject in the ordinary opportunity must elaborate the tasks and pass the specific tests required. The tasks have as a deadline the date of the exam of the second opportunity.
WORK SESSIONS AND NUMBER OF ACTIVITIES:
PRESENCE HOURS (45 hours) depending on:
1. ACTIVITIES IN THE EXHIBITION GROUP (four tasks of a collective and compulsory nature) (18 hours)
- Brief expository activities: curriculum, learning difficulties, methodologies, resources, evaluation, projects, ...
- Practice on topics exposed in group class.
- Presentations and expositions of work plan, tasks and projects.
- Carrying out tests.
2. ACTIVITIES IN INTERACTIVE GROUP (six tasks of a collective and compulsory nature) (24 hours)
- Teaching-learning situations
- Didactic challenges.
- Learning through tasks and projects.
- Learning through problems
- Gamification in the classroom.
- Inverted classes.
- Meetings and discussions from small to large groups.
3. INDIVIDUAL ACTIVITIES (four individual challenges and optional 3 hours)
- Group work reflection
- Project discussion
HOURS OF SELF-EMPLOYED WORK (90 hours) depending on:
4. ACTIVITIES IN EXHIBITION GROUP (25 hours)
- Reading and viewing of materials.
- Preparation of presentations and exhibitions.
- Preparation of tests.
5. ACTIVITIES IN INTERACTIVE GROUP (45 hours)
- Reading and viewing documents
- Collaboration on platforms in the preparation of tasks.
- Resolution of challenges.
- Design of teaching-learning situations.
- Planning of tasks and projects.
- Elaboration of learning through problems.
- Creation of gamified proposals.
- Production of inverted classes.
- Search for complementary information.
- Reflection in small groups.
6. INDIVIDUAL ACTIVITIES (20 hours)
- Resolution of doubts
- Discussion of projects and small group work
- Self-assessment activities
TOTAL HOURS: 135 hours.
RECOMMENDATIONS:
Attendance at classes and working in them will favor the acquisition of skills and the collection of information.
The immersion in the resources provided in digital format will help the student to advance in their learning and consolidate them.
Students who present any type of functional diversity or difficulty for a normal daily follow-up of the subject, be that permanent or temporary difficulty, must justify their situation through a document issued by the service accredited by the USC for these purposes (Promotion Service and University Integration) and inform the teacher of their case within the first two weeks of the corresponding semester, so that they can agree as soon as possible on the work plan of the student in the matter and, if necessary, the curricular and / or evaluative adaptations that were pertinent to address each particular situation.
REMARKS:
Students who are excused from attending classes must respect the deadlines for handing in assignments and other established requirements, and it is recommended and necessary that they maintain contact with the teaching staff of the subject through tutorials and the virtual platform, in order to guarantee the excellent development of the subject and the passing of the same.
IMPORTANT NOTE:
THE RESOURCES NECESSARY FOR STUDENT LEARNING WILL BE PROVIDED IN DIGITAL FORMAT THROUGH THE VIRTUAL CAMPUS.
The tasks elaborated by the students must be delivered via virtual campus.
ENVIRONMENTAL RESPONSIBILITY
In relation to personal or group work carried out for the subject, the following indications must be taken into account:
- Avoid plastic lids or other unnecessary external packaging.
- Whenever possible, use staples instead of binding.
- Print on both sides in "ink-saving" quality.
- Do not use blank sheets of paper as chapter or part dividers.
- Avoid annexes that do not have direct reference to the topics developed.
GENDER PERSPECTIVE:
In attention to gender equality criteria in the university environment:
- It is recommended to use non-sexist language both in classroom work and in academic assignments.
OBLIGATORY USE OF THE RAI ACCOUNT.
OBLIGATORY USE OF INSTITUTIONAL TECHNOLOGICAL TOOLS: Virtual Campus, Microsoft Office 365, and other tools provided by the faculty and authorised as institutional tools by the university (Lifesize, etc.).
MOBILE TELEPHONES MAY NOT BE USED, except when used as a work tool following the instructions given by the teacher, and students are responsible for the legal and academic consequences that may arise from inappropriate use of the same.
BE AWARE THAT TEACHING - LEARNING (CLASSES / TUTORIALS) IS A PRIVATE PROCESS, private being understood as a process of communication and exchange between the teacher and the students enrolled in the subject.
OBLIGATORY COMPLIANCE WITH DATA PROTECTION REGULATIONS: https://www.usc.gal/es/politica-privacidad-proteccion-datos
Ana Belen Rodriguez Raposo
Coordinador/a- Department
- Applied Didactics
- Area
- Didactics of Mathematics
- Phone
- 881812124
- anabelen.rodriguez.raposo [at] usc.es
- Category
- Professor: Temporary PhD professor
| Tuesday | |||
|---|---|---|---|
| 16:00-19:00 | Grupo /CLE_01 | Galician | (NORTH CAMPUS) - CLASSROOM 33 |
| Thursday | |||
| 16:00-19:00 | Grupo /CLIS_01 | Galician | (NORTH CAMPUS) - CLASSROOM 33 |
| 05.20.2025 16:00-18:00 | Grupo /CLE_01 | (NORTH CAMPUS) - CLASSROOM 33 |
| 06.26.2025 18:00-20:00 | Grupo /CLE_01 | (NORTH CAMPUS) - CLASSROOM 21 |