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 (2 credits)
1.1 The curvature.
• Projections on the plane. Maps. Planispheres: systems of representation. (Tema 43. BOE Nº226 del 21 de Septiembre de 1993, pag 27414).
1.2 Synthetic Geometry versus Analytic Geometry on secondary education.
• Discussion on the teaching of geometry in high school: synthetic geometry in ESO versus analytic geometry in high school.
• The dynamic geometry, the panacea?
Block 2 (1,5 credits)
2.1 Real numbers. Proportions.
2.2 Progressions. Sequences of real numbers. Their presence in the real world.
2.3 Real functions of real variable: Representation, interpretation, approximation, transformations, problems solving and applications in the Science. Tools for his manipulation.
2.4 Differential and Integral Calculus in the secondary education: historical Review, applications to the resolution of problems, interpretation of the definite integral, interactive resources.
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.
BOOKS
- ALEKSANDROV, A.D., KOLMOGOROV, A., LAURENTIEV, M.A. e outros (1976). La matemática: Su contenido, métodos y significado (tres tomos). Madrid, España: Alianza Editorial, Colección Alianza Universidad.
- DURÁN GUARDEÑO, A. J. (1996). Historia, con personajes, de los conceptos del Cálculo. Madrid, España: Alianza Editorial, Colección Alianza Universidad.
- EDWARDS Jr., C. H. (1979). The Historical Development of the Calculus. Springer-Verlag.
- PÓLYA, G. (1989). Cómo plantear y resolver problemas (título original: How To Solve. It?). México: Trillas Editorial (decimoquinta reimpresión).
- TAO, T (2006). Solving Mathematical Problems: A Personal Perspective. New York, EEUU: Oxford University Press.
- Zeitz, P. (1998). The Art and Craft of Problem Solving. Hoboken, NJ: John Wiley & Sons, Inc.
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/
- Arquivo “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/ (contén ligazón ó Wolfram|Alpha)
- Demonstrations Project Project: http://demonstrations.wolfram.com/
- Subproxecto ED@D da "Red Educativa Digital Descartes": http://proyectodescartes.org/EDAD/index.htm
- ARRÁNZ, J.M., LOSADA, R.,MORA,J.A., MORA, J.A. e 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
- Materiais curriculares: http://centros.edu.xunta.es/iescarril/matematicas/materiais_matematicas…
- Unidades didácticas ESO: http://proyectodescartes.org/EDAD/
VIDEOS, WEBSITES, COMPLEMENTS AND ASSOCIATIONS
- Eduardo Sáenz de Cabezón, Canal DERIVANDO:
https://www.youtube.com/channel/UCH-Z8ya93m7_RD02WsCSZYA
- James Grime, Canal SINGINGBANANA
http://www.youtube.com/user/singingbanana?feature=results_main
- Clara Grima: http://claragrima.com
- Marta Macho: 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.
There will be a double evaluation method: the punctual evaluation and the continuous evaluation,
1. Attitude and work in the classroom. 10%
Attendance, participation and attitude in the lecture and seminar classes.
2. Active participation in the classroom in the debate on the teaching of geometry in secondary school:
Synthetic geometry in ESO versus Analytical Geometry in High school. 10%
Oral preparation and defense of a complementary activity project for one math subject of ESO. 20%
Consult the instructions in the work folder in the virtual course.
3. Preparation of a small individual work related to Block 2, in writing, to discuss it later with the teaching staff. 30%
The preparation instructions are published in the virtual course.
4. Written and oral presentation of the resolution of the problems raised. 30%
Delivery and defense of the solution of the problems raised regarding problem-solving techniques.
The instructions are published in the virtual course.
(2, 3 and 4 EQUIVALENCE TO THE EXAMINATION OF THE MATTER)
Students with a teaching exemption (Instruction Nº 1/2017 of the General Secretariat of the USC) will propose an alternative plan of work and evaluation that covers the set of the objectives and contents of the subject.
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.
EN VIRONMENTAL 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:
Javier Barja Perez
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813150
- ja.barja [at] usc.es
- Category
- Professor: University Lecturer
María Elena Vázquez Abal
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813143
- elena.vazquez.abal [at] usc.es
- Category
- Professor: University Professor
Rosa Mª Trinchet Soria
Coordinador/a- 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 | Spanish, Galician | (NORTH CAMPUS) - CLASSROOM 25 |
| Wednesday | |||
| 17:30-20:00 | Grupo /CLIS_01 | Galician, Spanish | (NORTH CAMPUS) - CLASSROOM 23 |
| 01.21.2021 18:00-20:00 | Grupo /CLE_01 | (NORTH CAMPUS) - CLASSROOM 21 |
| 07.01.2021 18:00-20:00 | Grupo /CLE_01 | (NORTH CAMPUS) - CLASSROOM 21 |