Teaching and Learning Mathematics
Code: 45452 ECTS Credits: 12| Degree | Type | Year |
|---|---|---|
| 3500318 Teacher Training for Secondary Schools, Vocational Training and Language Centres | OB | 1 |
Errata
Update of the regular teaching staff at the beginning of the academic year.
Teachers
Jose María Alfonso Bañón
Edelmira Badillo
José Abraham de la Fuente Pérez
Albert Mallart Solaz
Mario Ros Carreño
Berta Barquero
Montserrat Alsina Aubach
Pere Grima Cintas
Marta Peña
Vicenç Font
Contact
- Name:
- Alberto Mallart Solaz
- Email:
- albert.mallart@uab.cat
Teachers
- José Abraham Fuente Pérez
- Jose María Alfonso Baņķn
- Edelmira Rosa Badillo Jimenez
- (External) Berta Barquero Farras
- (External) Marta Peņa Carrera
- (External) Montserrat Alsina Aubach
- (External) Pere Grima Cintas
- (External) Sergi Múria
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
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
Learning Outcomes
- CA05 (Competence) To create flexible learning situations in diverse and meaningful contexts through the justified use of a range of strategies and methodologies that promote inclusive learning and the development of mathematics-specific competences.
- CA06 (Competence) To implement activities in the mathematics classroom in the manner in which they were designed and planned, assimilating any unexpected situations generated by the students to achieve and improve on the expected learning outcomes.
- CA07 (Competence) To apply disciplinary and curricular mathematical content from the perspective of literacy and education for all, exploring ways to integrate such content into the classroom.
- CA19 (Competence) To apply an equity and gender perspective when designing mathematics activities.
- KA04 (Knowledge) To recognise the basic aspects of the mathematics curriculum and the personal and didactic knowledge of mathematics required to plan learning situations and action and assessment strategies in the field of mathematics.
- KA05 (Knowledge) To recognise your own socio-emotional competences and personal strengths and weaknesses with a view to self-managing emotions and managing the working atmosphere in the classroom.
- SA02 (Skill) To develop strategies for dealing with critical incidents that occur while teaching and which are related to the processes of teaching and learning mathematics.
- SA03 (Skill) To integrate the various types of assessment into lesson plans, particularly formative assessment and self-assessment, as a tool for checking, regulating and enhancing the processes of teaching and learning mathematics.
- SA04 (Skill) To take the characteristics of the classroom interaction (teacher-student and between students), formative feedback, student competences and the role of the teacher in activating and regulating learning into account when planning lessons.
Content
- 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
Análisis
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Case studies | 12 | 0.48 | |
| Oral presentations | 24 | 0.96 | |
| Problem Solving | 36 | 1.44 | |
| Type: Supervised | |||
| Analysis of didactic situations | 30 | 1.2 | |
| Type: Autonomous | |||
| personal study | 60 | 2.4 | |
| Readings | 36 | 1.44 | |
| Realization of proposals of didactic activities | 42 | 1.68 |
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.
Assessment
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Design of mathematical activities | 23,75% | 15 | 0.6 | CA05, CA06, CA07, CA19 |
| Didactic sequence of calculus | 17,5% | 10 | 0.4 | CA05, CA06, CA07, CA19, KA04, KA05, SA02, SA03, SA04 |
| Interpretation of student productions | 17,5% | 10 | 0.4 | CA06, CA07, CA19, KA04 |
| Practice on the teaching of numbers | 17,5% | 10 | 0.4 | KA04, KA05, SA02, SA03, SA04 |
| Use of materials and resources to teach geometry | 23,75% | 15 | 0.6 | CA05, CA06, CA07, CA19, KA04, KA05, SA02, SA03, SA04 |
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
SINGLE ASSESSMENT
Students who opt for the single assessment must follow the development of the subject, attending class regularly and with the same attendance conditions as continuous assessment students.
They will submit all the assessment activities on a single date at the end of the session and will be required to pass a validation test for each of the activities.
Bibliography
Albarracín, L., & Ärlebäck, J. B. (2022). Esquemas de resolución de problemas de Fermi como herramienta de diseño y gestión para el profesor. Educación Matemática, 34(2), 289-309.
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:
http://www.guiasensenanzasmedias.es/indexESO.asp
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.
López, M., Albarracín, L., Ferrando, I., Montejo, J. Ramos, P., Serradó, A., Thibaut, Mallavibarrena, R. (2020). La Educación Matemática en las enseñanzas obligatorias y el bachillerato. En D. Martín, T. Chacón, G. Curbera, F. Marcellán y M. Siles (Coord.), Libro Blanco de las Matemáticas (pp. 1-94). Madrid: RSME.
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).
http://nrich.maths.org/frontpage
Cada professor indicará bibliografía complementaria para la parte correspondiente a su docencia
Software
Geogebra will be used as well as other free software determined by the teachers of the module.
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (TEmRD) Teoria (māster RD) | 1 | Catalan | annual | morning-mixed |
| (TEmRD) Teoria (māster RD) | 2 | Catalan | annual | afternoon |
| (TEmRD) Teoria (māster RD) | 3 | Catalan | annual | afternoon |
| (TEmRD) Teoria (māster RD) | 4 | Catalan | annual | afternoon |