Degree  Type  Year  Semester 

4317414 Teacher Training for Secondary Schools, Vocational Training and Language Centres  OB  0  A 
There are no prerequisites
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
Key concepts and problem solving (3 credits)
Key math topics from a historical perspective (4 credits)
Mathematical Modeling (3 credits)
All facetoface 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 facetoface development of the subject. If it were necessary to move to a semifacetoface 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  
Oral presentations  30  1.2  11, 4, 5, 7, 6, 8, 14, 3 
Practical cases  30  1.2  12, 1, 11, 4, 5, 7, 6, 9, 14, 10, 13, 2 
Type: Supervised  
Analysis of modeling situations  30  1.2  12, 11, 4, 5, 7, 8, 9, 14, 10, 13, 2, 3 
Type: Autonomous  
Personal study  50  2  11, 5, 7, 8, 9, 14, 10, 13, 3 
Proposed activities  60  2.4  12, 1, 11, 5, 7, 8, 14, 10, 13, 2, 3 
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
Title  Weighting  Hours  ECTS  Learning Outcomes 

Mathematics history group work  40%  20  0.8  12, 1, 11, 5, 7, 6, 8, 14, 10, 13, 2, 3 
Practical modeling work  30%  15  0.6  12, 1, 11, 4, 5, 7, 6, 9, 14, 10, 13, 2, 3 
Practical problem solving work  30%  15  0.6  12, 11, 5, 7, 14, 10, 13, 2, 3 
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, SpringerVerlag, 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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A specific program is not contemplated. Each teacher will indicate, when necessary, the free software that will be used.