ECTS credits ECTS credits: 3
ECTS Hours Rules/Memories Student's work ECTS: 51 Hours of tutorials: 3 Expository Class: 9 Interactive Classroom: 12 Total: 75
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)
To understand the principles, techniques, and didactic resources used to address difficulties associated with the use of different mathematical languages in early childhood and primary education.
To understand the influence of affective components on the teaching-learning process of mathematics in early childhood and primary education.
To acquire the ability to solve practical situations related to difficulties in learning mathematics.
To acquire the ability to write and assess authentic tasks in mathematics.
To acquire the ability to promote metacognitive and self-regulation activities in the mathematics classroom.
1. Mathematical Languages
The importance of the simultaneous use of different languages in mathematical activity.
2. Affective Components
Attitudes towards mathematics
Mathematics anxiety
Influence of affective components
3. Analysis and Study of Practical Cases
Contextualized difficulties
Responding to difficulties
Metacognition in mathematics
Authentic vs. standard tasks
Practical implementation of metacognitive activities in the classroom
Basic Bibliography:
Chamorro, M. C. (Ed.), González, E. F. (Coord.) (2001). Dificultades del aprendizaje de las matemáticas. Spain: Ministerio de Educación, Cultura y Deporte.
Gamboa Araya, R. (2014). Relationship between the affective dimension and mathematics learning. Revista Electrónica Educare, 18(2), 117–139. https://doi.org/10.15359/ree.18-2.6
Gómez-Chacón, I. M. (2000). Matemática emocional. Los afectos en el aprendizaje matemático. Narcea.
Miranda, A., Gil, D. M. (2000). Dificultades del aprendizaje de las matemáticas: un enfoque evolutivo. Archidona (Málaga): Aljibe.
Complementary Bibliography:
Blanco, T. F., Diego-Mantecón, J. M., Sequeiros, P. G. (2018). Truncation of cube vertices. Understanding in mathematics. Uno: Revista de Didáctica de las Matemáticas, 80(2), 27–34.
McLeod, D. B. (1989). Beliefs, Attitudes, and Emotions: New Views of Affect in Mathematics Education. In D. B. McLeod & V. M. Adams (Eds.), Affect and Mathematical Problem Solving: A New Perspective (pp. 245–258). Springer-Verlag.
Munro, J. (1995). SUCCESS in learning mathematics: A learning strategies approach. Hawthorn, VIC: Ed. Assist.
Munro, J. (2003). Dyscalculia: A unifying concept in understanding mathematics learning disabilities. Australian Journal of Learning Difficulties, 8(4), 25–32.
Kramarski, B., Mevarech, Z. R., Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49(2), 225–250.
Naya, M. C., Soneira, C., Mato, M. D., De la Torre, E. (2014). Questionnaire on attitudes towards mathematics among future Primary Education teachers. Revista de Estudios e Investigación en Psicología y Educación, 1(2), 141–149.
Orrantia, J., González, L. B., Vicente, S. (2005). An analysis of arithmetic problems in Primary Education textbooks. Infancia y aprendizaje, 28(4), 429–451.
Orrantia, J., Tarín, J., Vicente, S. (2011). The use of situational information in solving arithmetic problems. Infancia y aprendizaje, 34(1), 81–94.
Phonapichat, P., Wongwanich, S., Sujiva, S. (2014). An analysis of elementary school students’ difficulties in mathematical problem solving. Procedia – Social and Behavioral Sciences, 116, 3169–3174.
Soneira, C., Naya, M. C., Mato, M. D., De la Torre, E. (2015). Mathematical self-concept of Primary Education degree students. In Ramiro-Sánchez, T. & Ramiro, M.T. (2015). Advances in Educational and Developmental Sciences 2015. San Sebastián: University of Granada, pp. 521–526.
Turner, R. (2016). Lessons from PISA 2012 about mathematical literacy: An illustrated essay. PNA, 10(2), 77–94.
Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273–294.
Basic and General Competencies (B/G):
B6. Possess and understand knowledge that provides a basis or opportunity for originality in developing and/or applying ideas, often within a research context.
B7. Apply acquired knowledge and problem-solving skills in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.
B8. Integrate knowledge and handle the complexity of making judgments based on incomplete or limited information, including reflection on social and ethical responsibilities.
B9. Communicate conclusions and the underlying knowledge and reasoning to specialist and non-specialist audiences clearly and unambiguously.
B10. Possess learning skills enabling them to continue studying in a self-directed or autonomous manner.
G1. Communicate effectively, both orally and in writing, in the official languages of the Autonomous Community.
G3. Use basic information and communication technology (ICT) tools necessary for professional practice and lifelong learning.
G4. Act as open, cultured, critical, committed, democratic, and supportive citizens, capable of analyzing reality, diagnosing problems, and formulating and implementing knowledge-based solutions aimed at the common good.
G6. Critically assess knowledge, technology, and available information to solve problems.
G7. Embrace lifelong learning as professionals and citizens.
G8. Value the importance of research, innovation, and technological development in the socio-economic and cultural progress of society.
Transversal Competencies (T):
T1. Ability to analyze and synthesize.
T2. Ability to adapt to new situations.
T3. Work autonomously and with initiative.
T4. Work collaboratively.
T5. Organizational and planning skills in disciplinary and interdisciplinary educational contexts.
T6. Capacity to innovate (creativity) in both school and non-school educational contexts.
T7. Act ethically and with social and environmental responsibility as educators and/or researchers.
T8. Communicate with peers, the educational community, and society in general in their areas of expertise.
T9. Incorporate ICT in research processes, information management, data analysis, and dissemination and communication of results.
T10. Ability to update knowledge, methodologies, and strategies in teaching practice.
Specific Competencies (E):
E1. Understand the theoretical foundations of interdisciplinary work and identify its core interests in both school and non-school contexts.
E2. Critically identify and analyze interdisciplinary proposals in the educational field.
E3. Design, justify, organize, and systematically evaluate interdisciplinary proposals in various educational contexts.
E8. Defend and argue, both orally and in writing, the research and/or innovation work carried out, using audiovisual support resources when necessary.
E9. Test and evaluate disciplinary or interdisciplinary teaching proposals in real educational contexts and promote improvement strategies based on results.
E11. Understand and correctly use scientific language in various forms of expression and communication.
E15. Identify quality and control criteria in both research and teaching practice, fostering a critical, reflective, and innovative spirit.
E16. Design, justify, organize, and evaluate research and innovation proposals in the field of specific didactics.
E17. Select, adapt, and apply ICT and other materials and resources to enhance teaching and learning in different disciplinary areas.
Lectures will primarily involve the teacher presenting the theoretical, conceptual, and methodological framework of the course, allowing students to ask questions and address difficulties. Teachers will use lectures and group discussions to encourage student reflection on specific scenarios related to course content.
Interactive classes will seek greater student involvement through a student-centered teaching methodology based on case studies, project analysis, and problem-solving. All student tasks (studying, assignments, computer use, projects, readings, presentations, exercises, practicals...) will be guided by the teacher both in class and in tutorial sessions, where students can ask specific questions or resolve other difficulties.
In particular, students must develop a research and/or innovation project aimed at achieving practical learning through problem identification, precise formulation, development of relevant procedures, interpretation of results, and drawing conclusions.
If circumstances allow, field trips or Service-Learning experiences with centers and institutions linked to the University of Santiago de Compostela may be considered to reinforce learning.
The virtual classroom will be used to upload the materials used in the sessions and also to send announcements to students through the forums.
Part 1: 50% of the final grade
Part 1 will be assessed using the following:
A) Written and/or oral reports (40%): Individual or group work on a topic of interest, considering methodology, presentation of results, and argumentation of conclusions.
B) Participation (10%): Reasoned participation in activities and group dynamics, provided it is regular and sustained. Mere attendance without active participation will not be graded (per section d) of article 1.2 of the USC’s Class Attendance Regulations, approved on November 25, 2024).
C) Completion of tasks: Various theoretical-practical tasks will be assigned during class. If a student misses a session for justified reasons, tasks may be completed via the Virtual Campus. These tasks are mandatory to pass Part 1 but are not graded.
Part 2: 50% of the final grade
D) Final assessment: Students must present and defend a project. Assessment criteria include clarity, synthesis, communication skills, accuracy, reasoning, and adequacy of responses.
Both parts must be passed to pass the course. Otherwise, students must take a final exam in the resit session covering the theoretical and practical content.
Academic Dishonesty
Fraudulent completion of any assessment task (as per the Regulations on Academic Performance Assessment and Grade Review – Approved June 15, 2011, and amended April 5, 2017) will result in a fail grade for the exam session, independently of any disciplinary action. Plagiarized work or those sourced from publicly accessible content without proper citation or reworking will be considered fraudulent.
Students Exempt from Attendance
Students must meet deadlines and other course requirements. Regular contact with the instructor through tutorials is recommended. Within seven days of the semester start, they must contact the instructor to arrange alternative assessment for part B if applicable.
Repeating students must contact the course instructor within 7 days from the beginning of the term, and may keep the grades of the parts previously passed (1 or 2) in the previous academic year, if the instructor considers it appropriate.
Classroom hours: 21
Independent work: 53
Total: 74 hours
The active methodology requires students to take charge of their learning. Attending and engaging in class supports skill acquisition and information gathering. Familiarity with the recommended bibliography will aid and consolidate learning.
Submitted work must meet academic standards of quality, form, and correctness. Guidelines for Master's Thesis (TFM) preparation may be used as a reference, as well as the instructor's specific guidance.
Students must preferably submit their work through the virtual classroom; in any case, the instructor may request submission through other means.
Environmental responsibility. If the instructor requires submission in paper format, the following requirements must be met:
* Avoid plastic covers or other unnecessary external packaging.
* Whenever possible, use staples instead of binding.
* Use both sides of the paper and, if printed, use "ink-saving" quality.
* Do not use blank sheets as dividers between chapters or sections.
* Avoid including appendices not directly related to the content developed.
Gender perspective. The use of non-sexist language is recommended, both in everyday classroom work and in academic assignments. Further information is available at:
https://www.usc.gal/cdn/ff/QKcBDjOX5QgeJQkeVe81BaV8Ho1…
Mandatory use of the institutional “rai” email account.
Mandatory use of institutional technological tools: Virtual Campus, Microsoft Office 365, and other tools provided by the faculty and authorized by the university as institutional tools.
The use of mobile phones is not allowed, except when used as a working tool under the teacher's instructions. Students are responsible for any legal or academic consequences resulting from improper use.
The teaching-learning process (classes / tutorials) is a private process, and therefore the communication and exchange of information between the instructor and the students enrolled in the course must be understood as such.
Compliance with data protection regulations is mandatory: https://www.usc.gal/es/politica-privacidad-proteccion-datos
Gonzalo Castiñeira Veiga
Coordinador/a- Department
- Applied Didactics
- Area
- Didactics of Mathematics
- gonzalo.castineira.veiga [at] usc.es
- Category
- PROFESOR/A PERMANENTE LABORAL
| Tuesday | |||
|---|---|---|---|
| 16:00-17:00 | Grupo /CLE_01 | Galician | (NORTH CAMPUS) - CLASSROOM 52 |
| 17:00-18:30 | Grupo /CLIL_01 | Galician | (NORTH CAMPUS) - CLASSROOM 52 |
| 05.21.2026 16:00-17:30 | Grupo /CLE_01 | (NORTH CAMPUS) - BOARDROOM (MARÍA BARBEITO CLASSROOM) |
| 07.07.2026 18:00-19:30 | Grupo /CLE_01 | (NORTH CAMPUS) - BOARDROOM (MARÍA BARBEITO CLASSROOM) |