Complementary Disciplinary Training in Mathematics
Code: 45453 ECTS Credits: 10| 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.
Contact
Name:
Joan Vicenç Gómez i Urgellés
Email:
joan.vicenc.gomez@upc.edu
Teachers
Susana Vásquez
Antoni Gascó
Sergi Muria Maldonado
Joan Carles Naranjo
Joan Vicenç Gómez i Urgellés
Maria Rosa Massa
David Virgili
Contact
- Name:
- Alberto Mallart Solaz
- Email:
- albert.mallart@uab.cat
Teachers
- (External) Antoni Gascó
- (External) David Virgili
- (External) Joan Carles Naranjo
- (External) Joan Vicenç Gomez Urgelles
- (External) Maria Rosa Massa Esteve
- (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
This module aims to provide the most relevant mathematical complements to teach mathematics in secondary school. It is divided into three blocks:
1. Key Concepts and Problem Solving (3 ECTS). The aim of this blog is to use problems to encourage and motivate the learning of mathematics.
2. Key Mathematics Topics from a Historical Perspective (4 ECTS). Teaching mathematics requires a solid knowledge of the subject that goes beyond the strict content that is taught in ESO and baccalaureate. Teachers need to have a training background that gives them a broad and integrated perspective of the mathematical concepts and procedures they need to convey and that they know the origin and its evolution over time.
3. Modeling (3 ECTS). Mathematical modeling is an important part of the High School Mathematics Curriculum. For this reason, examples will be developed for both ESO and Baccalaureate
Learning Outcomes
- CA03 (Competence) To behave in a committed, respectful and ethical manner with society, students, the teaching profession, the educational community and the educational institution, within the framework of the teaching profession's code of conduct.
- CA09 (Competence) To build a mathematical identity supported by professional development and a commitment to education that contributes to the development of a sustainable, equal, diverse and fair society that respects human rights.
- CA10 (Competence) To apply disciplinary and curricular content from the perspective of literacy and education for all.
- CA11 (Competence) To work as a team in a cooperative manner to co-create joint proposals, designs and activities, within the field of teaching in mathematics.
- KA06 (Knowledge) To recognise the basic aspects of the mathematics curriculum and the personal and didactic knowledge of mathematics required to plan learning situations and classroom management and assessment strategies in the field of mathematics.
- SA05 (Skill) To use evidence to analyse teaching actions in the mathematics classroom with a view to enhancing the processes and outcomes of learning mathematics.
- SA06 (Skill) To demonstrate digital competence as a teacher and support students as they use digital tools to learn mathematics.
- SA07 (Skill) To integrate a humanist vision that incorporates mathematical modelling and scientific, social and artistic elements to interpret reality and its relationship with mathematics.
Content
Key concepts and problem solving (3 credits)
Key math topics from a historical perspective (4 credits)
Mathematical Modeling (3 credits)
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Oral presentations | 30 | 1.2 | |
| Practical cases | 30 | 1.2 | |
| Type: Supervised | |||
| Analysis of modeling situations | 30 | 1.2 | |
| Type: Autonomous | |||
| Personal study | 50 | 2 | |
| Proposed activities | 60 | 2.4 |
All face-to-face sessions will be with the whole class group. However, as indicated in the methodology, there will be sessions where small group work will be done in the classroom under the supervision of the teacher.
The methodology will include the following types of activities:
- Teacher exhibition.
- Use of the virtual campus. Discussion forums.
- Cooperative work.
- Student exhibitions.
- Personal work of students.
- Case study and practical work in the classroom.
- Mechanisms of linking the theory and work done with the sessions of the Practicum
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 |
|---|---|---|---|---|
| Mathematics history group work | 40% | 20 | 0.8 | CA03, CA09, CA11, KA06, SA05, SA06 |
| Practical modeling work | 30% | 15 | 0.6 | CA03, CA09, CA10, CA11, KA06, SA05, SA06, SA07 |
| Practical problem solving work | 30% | 15 | 0.6 | CA03, CA09, CA10, CA11, KA06, SA05, SA06 |
The following will be required to be entitled to the final assessment:
Compulsory attendance at a minimum of 80% of class sessions.
The delivery of all the practices and exercises of evaluation within the indicated terms
The set of assessment activities will be as follows:
Key concepts and problem solving (30% of the module)
The evaluation will consist of a final work (which will have a weight of 50% in the final grade) and will be done in groups, as well as the works or activities that are proposed throughout the course (with a weight of 40%) and this case preferably individual. The other 10% will be class attendance and participation.
Mathematical Modeling (30% of the module)
50% of the evaluation will consist of a final work that will be done preferably in groups, and 40% of the works or activities that are proposed throughout the course and in this case individually. The other 10% will be class attendance and participation.
Key mathematics topics from a historical perspective (40% of the module)
The evaluation of this part will consist of individual work with a weight of 40% and group work, with a weight of 50%. 10% corresponds to class attendance and participation.
The works, for any of the groups, must be delivered within the deadlines indicated by the respective teachers of each group.
The final grade is the result of the operation: 0.3 x Note of key concepts and problem solving + 0.3 x Modeling note + 0.4 x Historical perspective note
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
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Conceptes clau i resolució de problemes i modelització Bibliografia bàsica
Bibliografia complementària
Perspectiva histórica de la matemàtica Bibliografia bàsica • BOYER, C. B., Historia de la matemática, Editorial Alianza, Madrid, 1986. • CALINGER, R., (ed.), Vita Mathematica. Historical research and Integration with teaching, The Mathematical Association of America, Washington, 1996. • HILTON, P. i altres, Mathematical reflections. In a Room with Many Mirrors, Springer-Verlag, Nova York, 1997. JAHNKE, H. N.; KNOCHE, N; OTTE, M. History of Mathematics and Education: Ideas and Experiences, Göttingen, Vanderhoeck und Ruprecht. • KATZ, V., (ed.), Using History to Teach Mathematics. An International Perspective, The Mathematical Association of America, Washington, 2000. • STEDALL, J. From Cardano’s Great Art to Lagrange’s Reflections: filling a gap in the history of Algebra, European Mathematical Society Publishing House, 2011. • TOEPLITZ, O., The Calculus. A Genetic Approach. The University of Chicago Press, Chicago, 1963.
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Software
A specific program is not contemplated. Each teacher will indicate, when necessary, the free software that will be used.
Language list
Information on the teaching languages can be checked on the CONTENTS section of the guide.