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Teaching and Learning Mathematics

Code: 43195 ECTS Credits: 12
Degree Type Year Semester
4317414 Teacher Training for Secondary Schools, Vocational Training and Language Centres OB 0 A


Jordi Deulofeu Piquet

Use of Languages

Principal working language:
catalan (cat)


Jordi Deulofeu Piquet
Iolanda Guevara Casanova
José Abraham de la Fuente Pérez
Edelmira Rosa Badillo Jimenez

External teachers

Marta Peña (UPC)
Mireia López
Pere Grima
Salvador Casals (UB)


There are no prerequisites

Objectives and Contextualisation

At the end of the Master, students have to achieve the following objectives:
											1. Acquire the didactic knowledge necessary to start teaching in secondary education.
											2. Apply didactic and problem-solving knowledge to the exercise of teaching as a mathematics teacher in secondary schools.
											3. Integrate the didactic knowledge of mathematics learned in the course, the experiences acquired in the realization of the practicalum in secondary schools and the proposals for innovation and research of the final work of the Master, to face the complexity of the profession as teacher in secondary education.
											4. Communicate their decisions and conclusions as a mathematics specialist clearly and unambiguously to students, their families and other professionals, providing arguments for their own statements based on correct decision-making based on reflection on responsibility social and ethical that implies the exercise of teaching.
											5. Assess the importance of continuous training when teaching mathematics and acquire the necessary skills to be able to carry out this training both independently and in a team with other professionals


  • Analyze and recognize their own socio-emotional skills to develop those needed in their performance and professional development.
  • Communicate and justify conclusions clearly and unambiguously to both specialist and non-specialist audiences.
  • Communicate effectively both verbally and non-verbally.
  • Continue the learning process, to a large extent autonomously.
  • Design and conduct formal and informal activities that help make the center a place of participation and culture in the environment where it is located. Perform the functions of mentoring and guiding students in a collaborative and coordinated manner. Participate in the evaluation, research and innovation of teaching and learning.
  • Design and develop learning spaces with special attention to equity, education and emotional values, equal rights and opportunities for men and women, civic education and respect for human rights that facilitate life in society, decision making and building a sustainable future.
  • Integrate knowledge and use it to make judgements in complex situations, with incomplete information, while keeping in mind social and ethical responsibilities.
  • Know the mathematics curriculum, and the body of didactic knowledge about the teaching and learning of mathematics.
  • Make effective use of integrated information and communications technology.
  • Plan, develop and evaluate the teaching and learning process enhancing educational processes that facilitate the acquisition of the competences of the teaching of mathematics, based on the level and previous training of students as well as the orientation of the same, both individually and in collaboration with other teachers and school professionals.
  • Possess the necessary learning skills to carry out continuous training in both content and teaching of mathematics and general aspects of the teaching profession.
  • Seek out, obtain, process and communicate information (oral, printed, audiovisual, digital or multimedia), transform it into knowledge and apply it in teaching and learning processes in the corresponding areas.
  • Solve problems in new or little-known situations within broader (or multidisciplinary) contexts related to the field of study.
  • Use acquired knowledge as a basis for originality in the application of ideas, often in a research context.

Learning Outcomes

  1. Choose, use and develop materials for teaching mathematics.
  2. Communicate and justify conclusions clearly and unambiguously to both specialist and non-specialist audiences.
  3. Continue the learning process, to a large extent autonomously.
  4. Critically analyse one's own performance in the classroom in relation to one's emotional competences.
  5. Demonstrate knowledge and use of resources and strategies for providing information and academic and professional guidance.
  6. Demonstrate knowledge of contexts in which use is made of the different areas of mathematics in the secondary school curriculum, underlining the functional nature of mathematics.
  7. Demonstrate knowledge of the different types of continuing education.
  8. Demonstrate knowledge of the educational and cultural value of the mathematics content taught in secondary school and integrate it into the framework of science and culture.
  9. Demonstrate knowledge of the secondary school mathematics curricula.
  10. Demonstrate knowledge of the theoretical and practical developments in mathematics teaching and learning.
  11. Design learning activities taking into account the diversity of the pupils.
  12. Gain experience in planning, teaching and assessing the subject areas that correspond to the mathematics discipline.
  13. Identify the problems in mathematics teaching and learning and put forward possible alternatives and solutions.
  14. Integrate knowledge and use it to make judgements in complex situations, with incomplete information, while keeping in mind social and ethical responsibilities.
  15. Know and use internet resources and software to teach mathematics in secondary school.
  16. Obtain and select audiovisual, digital or multimedia information and use it to design learning activities.
  17. Show mastery of oral and written expression in teaching.
  18. Solve problems in new or little-known situations within broader (or multidisciplinary) contexts related to the field of study.
  19. Tie education to its context and understand the educational function of the family and the community, both in imparting knowledge and competences and in teaching respect for rights and freedoms, equality of rights and opportunities between men and women, and equal treatment and non-discrimination of persons with a disability.
  20. Transform the mathematics curricula into sequenced learning activities and work programmes.
  21. Use acquired knowledge as a basis for originality in the application of ideas, often in a research context.


- Introducción a la didáctica de las matemáticas: currículum, competencies, aprendizaje y enseñanza

- Recursos, propuestas de enseñanza y conocimiento didáctico en relación a los bloques temáticos del currículum de matemáticas, así como a la conexión entre ellos y a su inclusión en el mundo que nos rodea:

Números e iniciación al álgebra                 

Geometría y medida

Estadística i probabilidad                                        



The methodology combines presentations by the teacher, solving didactic problems and practical proposals.
											Readings of articles and texts that are discussed in class are commissioned.
											In relation to the autonomous activity, the student must carry out the proposed readings, solve the practices commissioned and study what is proposed by the teaching staff of the module.

The proposed teaching methodology and assessment may undergo some modification depending on the attendance restrictions imposed by the health authorities. 
"The proposed methodology involves a face-to-face development of the subject. If it were necessary to move to a semi-face-to-face development,
the theoretical part it would be done by videoconference (through teams) and the practical part would be done in person, but dividing the group into two subgroups.
If it were necessary to return to a confinement everything would be done through teams and the virtual campus.In any case it would always be synchronously according to the timeline of the subject

Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.


Title Hours ECTS Learning Outcomes
Type: Directed      
Case studies 12 0.48 4, 15, 6, 8, 10, 7, 5, 11, 13, 21, 14, 18, 2, 20
Oral presentations 24 0.96 17, 4, 15, 6, 9, 10, 5, 13, 16, 14, 18, 2, 1
Problem Solving 36 1.44 17, 4, 15, 6, 8, 11, 16, 21, 14, 18, 2, 3, 1, 20
Type: Supervised      
Analysis of didactic situations 30 1.2 17, 12, 4, 15, 6, 9, 10, 5, 11, 13, 21, 14, 18, 2, 19, 1, 20
Type: Autonomous      
Readings 36 1.44 17, 4, 15, 6, 8, 9, 10, 5, 16, 21, 14
Realization of proposals of didactic activities 42 1.68 17, 12, 15, 6, 8, 9, 5, 11, 16, 14, 18, 2, 3, 1, 20
personal study 60 2.4 12, 6, 8, 9, 10, 7, 5, 11, 13, 21, 14, 18, 2, 3, 19, 1, 20


											The following will be required to be entitled to the final assessment: 
Attendance at a minimum of 80% of class sessions. The delivery of all practices and exercises within the indicated deadlines.
The mastery of mathematics that make up the curriculum of Compulsory Secondary Education and Baccalaureate
The delivery of all assessment activities and a minimum grade of 5 points out of 10 in each of them.
The return of the works and controls will be made no later than 30 working days after the date of delivery and / or completion.

Plagiarism is considered a major infraction, if a plagiarism is detected in a job it will be invalidated, it must be repeated and the student will only be able to take the test on the day of recovery.
For a definition of plagiarism you can consult: http://wuster.uab.es/web_argumenta_obert/unit_20/sot_2_01.html

Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Design of mathematical activities 23,75% 15 0.6 17, 12, 4, 15, 6, 8, 9, 10, 5, 11, 13, 16, 21, 14, 18, 2, 19, 1, 20
Didactic sequence of calculus 17,5% 10 0.4 17, 12, 15, 6, 8, 9, 11, 16, 21, 14, 18, 2, 1, 20
Interpretation of student productions 17,5% 10 0.4 12, 15, 8, 9, 10, 7, 5, 13, 21, 14, 18, 2, 3, 19
Practice on the teaching of numbers 17,5% 10 0.4 17, 12, 15, 6, 8, 9, 10, 7, 11, 13, 16, 21, 14, 18, 2, 1, 20
Use of materials and resources to teach geometry 23,75% 15 0.6 17, 12, 15, 6, 8, 9, 10, 5, 11, 13, 16, 21, 14, 18, 2, 3, 1, 20


Alsina,C. Burgués,C. Fortuny. 2001.“Ensenyar Matemàtiques”. Graó.

Azcarate, C., Deulofeu, J. (1998-2004) Guías Praxis para el profesorado. Matemáticas.ESO. Madrid: Wolters Kluver. On-line (articles) a:


Ascher, M. (1991) Ethnomathematics. Belmont, California: Wadsworth

Bishop, A. (1999) Enculturación matemática. Barcelona: Paidos Ibérica

Cockroft, W.H. (1985) Las matemáticas sí cuentan. Informe Cockroft. Madrid. MEC

(Versión original en inglés: Mathematics Counts. Crown. 1982).

Corbalán, F. (1998) Juegos matemáticos para secundaria y bachillerato. Madrid: Síntesis

Courant, R., Robbins, H. (1979) ¿Qué es la matemática? Madrid: Aguilar

DOGC (2007). “Competencies Matemàtiques infantil, primaria i secundaria”: Decret 142/2007 DOGC núm. 4915. pàg. 21873 i 21927

Gardner, M. (2009) ¡Ajá! Inspiración. Barcelona: RBA

Goñi, J.Ma (Editor) (2010a) Matemáticas. Complementos de Formación disciplinar. Barcelona: Graó.

Goñi, J.Ma (Editor) (2010b) Didáctica de las Matemáticas. Barcelona: Graó.

Goñi, J.Ma (Editor) (2010c) Matemáticas. Investigación, innovación y buenas prácticas. Barcelona: Graó.

Mason, Burton, Stacey (1988) Pensar matemáticamente. Barcelona: Labor-MEC.

NCTM (2004) Principios y Estándares para la Educación Matemática. Sevilla: Sociedad Andaluza de Educación Matemática "Thales". Versió original en anglès a: http://www.nctm.org/

Moore, D. (1995) Estadística aplicada básica. Antoni Bosch editor, Barcelona

Pérez, A., Sánchez, M. (Editores) (2009) Matemáticas para estimular el talento: actividades del proyecto Estalmat. Sevilla: Sociedad Andaluza de Educación Matemática "Thales".

Pólya, G. (1965) Como plantear y resolver problemas. Mexico: Ed. Trillas.

Pólya, G. (1981) Mathematical Discovery. New York: J. Wiley and Sons

Steen, L.A. i altres (2006) Las matemáticas en la vida cotidiana. Madrid: Addison-Wesley/ Universidad Autonoma de Madrid.

Varis autors (2011).Col.lecció de RBA “el mundo es matemático”.Qualsevol llibre pot ser útil

Webs d’ interès:

http://phobos.xtec.cat/creamat/joomla/  (CREAMAT. Centre de Recursos per ensenyar i aprendre matemàtiques. Generalitat de Catalunya. Departament d’Educació)

http://www.divulgamat.net/  (Divulgamat: Centro Virtual de Divulgación de las matemáticas).


Cada professor indicará bibliografía complementaria para la parte correspondiente a su docencia



Geogebra will be used as well as other free software determined by the teachers of the module.