ECTS credits ECTS credits: 5
ECTS Hours Rules/Memories Student's work ECTS: 85 Hours of tutorials: 5 Expository Class: 15 Interactive Classroom: 20 Total: 125
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Mathematics, Statistics, Mathematical Analysis and Optimisation
Areas: Algebra, Geometry and Topology, Mathematical Analysis
Center Faculty of Education Sciences
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
To know and to reflect on the most relevant content of the Mathematics, the subject of education at various levels of the secondary education.
Block 1 (1,5 credits)
1.1 The main concepts and results of the Analysis in secondary education: Historical review, interpretations and various resources.
• Real numbers.
• Sequences of real numbers.
• Real functions of real variable.
• Differential and Integral Calculus.
Block 2 (2 credits)
2.1 Applications of geometry
• The Curvature: Projections in the plane. Maps. Terrestrial planispheres: main representation systems. (Item 43. BOE No. 226 of September 21, 1993, page 27414). A proposal of activities
• Analysis, discussion and resolution of geometric problems for high school exams.
2.2 Analytical Geometry versus Synthetic Geometry in secondary education.
• Critical analysis of textbook exercises and illustrations.
• Discussion on the teaching of geometry in secondary school: synthetic geometry in ESO versus analytical geometry in Baccalaureate. Dynamic geometry, the panacea?
Block 3 (1,5 credits)
3.1 The problems in mathematics. Types of problems. Strategies and tactics for solving problems.
• Problems versus exercises. Types of problems: recreational, contest and open-ended problems.
• Strategies in the solution of problems: draw figures and diagrams, examine special cases, formulate equivalent problems, modify the problem, change the method of reasoning (contradiction).
• Tactics for solving problems: symmetry (geometrical symmetry, algebraic symmetry), the extreme principle, the pigeonhole principle, transformations and invariants (parity, modular arithmetic and coloring, monovariants).
• Use of free mathematical software in problem solving: GeoGebra, Maxima.
BASIC BIBLIOGRAPHY
- Durán Guardeño, A. J. (1996). Historia, con personajes, de los conceptos del Cálculo. Madrid, España: Alianza Editorial, Colección Alianza Universidad.
- Pólya, G. (1989). Cómo plantear y resolver problemas (título original: How To Solve. It?). México: Trillas Editorial (decimoquinta reimpresión).
- Zeitz, P. (2007). The Art and Craft of Problem Solving. Hoboken, NJ: John Wiley & Sons, Inc.
COMPLEMENTARY BIBLIOGRAPHY
BOOKS
- Aleksandrov, A.D., Kolmogorov, A., Laurentiev, M.A. y otros (Edición 2014). La matemática: su contenido, métodos y significado. Madrid, España: Alianza Editorial, Colección Alianza Universidad.
- Edwards Jr., C. H. (1979). The Historical Development of the Calculus. Springer-Verlag.
- Tao, T (2006). Solving Mathematical Problems: A Personal Perspective. New York, EEUU: Oxford University Press.
JOURNALS
- BOLETÍN DAS CIENCIAS. Asociación de Ensinantes de Ciencias de Galicia (ENCIGA).
- NÚMEROS: http://www.sinewton.org/numeros/
- SUMA: http://revistasuma.es/
RESOURCES
- Proyecto Descartes: http://recursostic.educacion.es/descartes/web/
- Archivo “MacTutor” (The MacTutor History of Mathematics archive):
http://www‐history.mcs.st‐andrews.ac.uk/index.html
- GeoGebra: http://www.geogebra.org/
- Lléname: http://geometriadinamica.es/paginas/llename/aplicacion/llename.html
- Wolfram Research: http://www.wolfram.com/ (contiene enlace a Wolfram|Alpha)
- Demonstrations Project: http://demonstrations.wolfram.com/
- Subproyecto ED@D da "Red Educativa Digital Descartes": http://proyectodescartes.org/EDAD/index.htm
- Arránz, J.M., Losada, R., Mora, J.A. y Sada, M.: http://www.geometriadinamica.es/
- Inter2geo. Interoperate Interactive Geometry for Europe. http://inter2geo.eu/
- Máxima: http://maxima.sourceforge.net/ e http://andrejv.github.com/wxmaxima/index.html
GENERAL INFORMATION
- CiUG (Comisión interuniversitaria de Galicia): http://ciug.cesga.es/index.html
- Currículo educativo Galicia: http://www.edu.xunta.gal/portal/guiadalomce
- Materiales curriculares: http://centros.edu.xunta.es/iescarril/matematicas/materiais_matematicas…
- Unidades didácticas ESO: http://proyectodescartes.org/EDAD/
VIDEOS, WEBSITES, COMPLEMENTS AND ASSOCIATIONS
- Sáenz de Cabezón, E., Canal DERIVANDO:
https://www.youtube.com/channel/UCH-Z8ya93m7_RD02WsCSZYA
- Grime, J., Canal SINGINGBANANA
http://www.youtube.com/user/singingbanana?feature=results_main
- Grima, C., http://claragrima.com
- Macho, M., http://www.ehu.eus/~mtwmastm/
- Apuntes Marea Verde: http://www.apuntesmareaverde.org.es/
- Libros de divulgación de Adrián Paenza: http://cms.dm.uba.ar/material/paenza
- Asociación Galega de Profesorado de Educación Matemática: https://www.agapema.org
- Ensinantes de Ciencias de Galicia: http://www.enciga.org
General
(CG1) To know the curriculum contents of the relative subjects to the corresponding educational specialisation.
(CG4) To seek, to obtain, to process and to communicate information (oral, printed, audiovisual, digital or multimedia), to transform it in knowledge and to apply it to the processes of teaching and learning in the matters specific to the specialisation studied.
(CG16) To work as a team with other professionals of the education, enriching its training.
(CG17) To develop habits and attitudes to learn to learn throughout its later professional development.
(CG18) To apply the acquired knowledges and the capacity to problem-solving to educational environments new or unfamiliar.
Specific
(CE-E1) To know the training and cultural value of the matters corresponding to the specialisation.
(CE-E2) To know the contents that take in the respective teachings.
(CE-E3) To know the recent history and developments of the matters and its perspectives in order to transmit a dynamic vision of the same.
(CE-E4) To know contexts and situations in which use or apply the diverse curriculum contents
(CE-E8) To promote a climate that provides the learning and puts in value the contributions of the students.
(CE-E9) To integrate the training in audiovisual and multimedia communication in the process of teaching-learning.
Transversal
(CT-1) To use bibliography and search tools of general and specific library resources, including the access for Internet.
(CT-3) To promote the skills for the work in cooperative and multi-disciplinary environments.
Teaching methodology.
The work in the classroom in the expositive lessons consists, basically, in teaching provided by the teacher. Ordinarily, in the same session will be devoted a time to the exposure or illustration of some theoretical question, and another time to the resolution of problems or exercises. Sometimes, the model will be approached to the one of the masterly lesson, in other cases, it will seek the involvement of all students in the discussion of the matters raised.
In the teaching in the classroom more interactive we seek active participation of students. It will have different formats, sometimes matters prepared by students will be dealt, not explained previously; other times they will be dedicated to the monographic discussion of matters of difficult understanding. General, they will have a more practical orientation that the expository sessions.
Eventually, we will ask the delivery in writing of some activities, or of the summary or comment of some proposed reading.
Tutorships in very reduced groups will be dedicated, individually or in groups, to solve doubts and particular difficulties that they go emerging, and to the customised follow-up of each student.
All the tasks of the student (studies, works, use of platforms, projects, readings, exhibitions, exercises, practical,...) will be guided by the teacher in the classroom and in the tutoring sessions.
CONTINGENCY PLAN in the OBSERVATIONS section
There will be a double method of evaluation: the punctual evaluation and the continuous evaluation,
1. Attitude and work in the classroom. 10%
Attendance, participation and attitude in the lectures and seminar classes.
2. Preparation of a small individual work related to Block 1, in writing, to be discussed later with the teachers. 30%
The elaboration instructions are published in the virtual classroom.
3. Individual participation in the classroom during the debate on secondary education: synthetic geometry in ESO vs. analytical geometry in high school. 10%
Preparation and oral defense of an individual project of complementary activity for a mathematics subject of the ESO. twenty%
Consult the instructions in the work portfolio in the virtual classroom.
4. Individual written and oral presentation of the resolution of two problems raised regarding problem solving techniques from block 3. 30%
Instructions are posted in the virtual classroom.
(2, 3 and 4 EQUIVALENT TO THE EXAMINATION OF THE SUBJECT)
In the case of fraudulent realization of exercises or tests, the one contained in the Regulations for the evaluation of the academic performance of students and review of grades will apply:
Article 16. Fraudulent performance of exercises or tests: The fraudulent performance of any exercise or test required in the evaluation of a subject will imply a failure grade in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. Considering fraudulent, among others, the realization of plagiarized works or obtained from sources accessible to the public without reworking or reinterpretation and without citations to the authors and sources.
CONTINGENCY PLAN in the OBSERVATIONS section
Class meeting:
Expositive lessons in large groups: 15
Interactive lessons in small groups reduced in normal classroom (seminars, debates, exhibitions, ...): 20
Interactive lessons in small groups in specialised classroom (computer science, laboratory, practices of field, ...): --
Tutorships in small groups: --
Tutorships in very small group: 5
Other sessions with the teacher. To specify: --
Work hours total in person: 40
Independent work:
Individual self-study or in group: 50
Writing exercises, conclusions or other derivative works of the subject: 15
Programming / experimentation or other work by technical means (computer, laboratory, data collection, ...): --
Preparation of debates, oral presentations or similar: 5
Library activities, recommended readings, seek bibliographic: 15
Other tasks proposed by the teacher. Specify: --
Total hours working personal: 85
Class attendance and participation in the proposed activities.
TThere will be an e-learning platform to support the teaching of this subject at USC.
ENVIRONMENTAL RESPONSIBILITY
In relation to the individual or group assignments to be done for this course, please note the following recommendations, which will improve environmental responsibility in the use of resources: Avoid plastic covers or other unnecessary outer packaging; whenever possible, use staples rather than comb binding; use duplex printing in mode "ink saving"; do not use blank pages as chapters or parts separator, and avoid annexes not having direct reference to the topics covered.
GENDER PERSPECTIVE
In regard to criteria of gender equality in the university field, it is recommended to use non-sexist language both in everyday classroom work as well as in recommended academic work. You can obtain information on the link in the link:
http://www.usc.es/export/sites/default/gl/servizos/oix/descargas/lingua…
CONTINGENCY PLAN
In general, in scenarios 2 and 3, as far as possible, the programming will be respected, except in regard to face-to-face activities (classes, tutorials, possible student presentations, ...) that, When presence is not possible, they will be developed virtually, either synchronously or asynchronously, as appropriate (through the Virtual Classroom, TEAMS, etc.) as long as the appropriate means are available for this.
ADAPTATION OF THE METHODOLOGY TO SCENARIOS 2 AND 3
SCENARIO 2 (distancing): Partially virtual teaching, according to the distribution organized by the Faculty. For this, the means provided for synchronous telematic teaching and the virtual classroom of the course will be used.
SCENARIO 3 (closing of the facilities): Teaching totally remotely using the means provided for this purpose and the virtual classroom of the subject. In either of these two scenarios, the tutorials will be attended electronically. At the same time, student participation in classrooms will be replaced (partially or totally, as appropriate) by “participation in virtual classrooms”, synchronous or asynchronous, depending on the needs and available means (for example, through participation in thematic forums expressly created for some activity; debates through a virtual platform, etc.)
ADAPTATION OF THE ASSESSMENT SYSTEM TO SCENARIOS 2 AND 3
SCENARIO 2 (distancing): Same procedure as described in the evaluation system, with the only difference that the activities that will be carried out throughout the course will be telematic. The individual expositions of the substitutive works of the exam will be carried out in person, at the teaching staff's center of origin.
SCENARIO 3 (closure of the facilities): Same procedure as described in the evaluation system, with the only difference that the individual presentations of the substitute works of the exam will be telematic.
STUDENTS WITH DISPENSE OF ATTENDANCE
TEACHING METHODOLOGY Partially virtual tutoring, according to student availability. For this, the means provided for synchronous and/or asynchronous telematic teaching and the virtual classroom of the course will be used.
EVALUATION SYSTEM
1. Attitude and personal work. 10%
The students will deliver in the virtual classroom the tasks proposed in the classroom.
2. Preparation of a small individual work related to Block 1, in writing, to be discussed later with the teachers. 30%
The elaboration instructions are published in the virtual classroom.
3. Individual delivery in the virtual classroom of the answers to the questions posed in the debate on secondary education: synthetic geometry in ESO vs. analytical geometry in high school. 10%
Delivery in the virtual classroom and oral defense of an individual project of complementary activity for a mathematics subject of the ESO. twenty%
Consult the instructions in the work portfolio in the virtual classroom.
4. Individual written and oral presentation of the resolution of two problems raised regarding problem solving techniques from block 3. 30%
Instructions are posted in the virtual classroom.
(2, 3 and 4 EQUIVALENT TO THE EXAMINATION OF THE SUBJECT)
Javier Barja Perez
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813150
- ja.barja [at] usc.es
- Category
- Professor: University Lecturer
María Elena Vázquez Abal
Coordinador/a- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813143
- elena.vazquez.abal [at] usc.es
- Category
- Professor: University Professor
Rosa Mª Trinchet Soria
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Mathematical Analysis
- Phone
- 881813205
- rosam.trinchet [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 18:00-21:00 | Grupo /CLE_01 | Galician, Spanish | (NORTH CAMPUS) - CLASSROOM 23 |
| Tuesday | |||
| 17:00-20:00 | Grupo /CLIS_01 | Galician, Spanish | (NORTH CAMPUS) - CLASSROOM 23 |
| Wednesday | |||
| 17:30-20:00 | Grupo /CLIS_01 | Galician, Spanish | (NORTH CAMPUS) - CLASSROOM 23 |
| 01.19.2022 18:00-20:00 | Grupo /CLE_01 | (NORTH CAMPUS) - CLASSROOM 21 |
| 07.04.2022 18:00-20:00 | Grupo /CLE_01 | (NORTH CAMPUS) - CLASSROOM 21 |