Academic management

The course "Mathematics and its education III" belongs to subject  “Teaching and learning mathematics",  which is within the disciplinary and educational module of the degree

Those required to get access to the degree. It is  recommended, but not mandatory, to have passed Mathematics I and II

The subject will work on the development of the following basic, general and specific competences of the degree: CB1, CB2, CB3, CB4, and CB5; CG1, CG2, CG3, CG4, CG5, CG6; CE1, CE2, CE4, CE5, CE8, CE10, CE11. In addition, regarding the Specific Competences of the Subject (CEM), work will be done on the development of:

CEM6.1. Acquire basic mathematical skills (numerical, calculation, geometric, spatial representations, estimation and measurement, organization and interpretation) that allow the teaching profession to be carried out properly.

CEM6.2. Know the school curriculum for mathematics, reflecting on the teaching-learning process, classroom organization, attention to diversity, interdisciplinarity,...

CEM6.3. Develop and evaluate curriculum content through teaching resources (general and mathematical computer programs, information and communication technology, and teaching materials) to manage the teaching-learning process.

CEM6.4. Analyze, reason, and communicate mathematical teaching proposals.

CEM6.5. Pose and solve problems related to everyday life.

CEM6.6. Value the relationship between mathematics and science as one of the pillars of scientific thought.

The above competencies must be translated into the following learning outcomes (RA):

RA6.1. Acquire and consolidate the stochastic sense and competence in problem-solving that allow the teaching function in Primary Education to be carried out safely.

RA6.2. Know the definitions, phenomenology, properties, representation registers, and procedures related to statistics, probability and problem-solving in Primary Education.

RA6.3. Properly manage the mathematical processes and mathematical practice necessary for the teaching function in Primary Education.

RA6.4. Complete a structured view of mathematical concepts and their relationships in the field of statistics, probability, and problem-solving, connecting them with other mathematical fields.

RA6.5. Know the school curriculum of statistics, probability, and problem-solving at its different levels (autonomous, national, international) and distinguish its different forms (intended, implemented, achieved).

RA6.6. Manage the organization of the mathematics classroom, with special attention to the diversity of the student body.

RA6.7. Select teaching materials and resources (including technological ones) suitable for teaching statistics, probability and problem solving and integrate them into classroom practice.

RA6.8. Design mathematical tasks for the classroom that involve the processes of problem-solving, communication, reasoning and proof, and representation linked to the contents of statistics and probability and their intra- and extra-mathematical connections.

RA6.9. Design and evaluate rich tasks that allow addressing the diversity of mathematics students.

RA6.10. Know and manage in the classroom the most common difficulties, obstacles, and errors of Primary students in statistics, probability and problem-solving.

RA6.11.Identify affective characteristics in students regarding their perception and learning of statistics, probability and problem-solving.

RA6.12.Know and apply different teaching methodologies in mathematics that contribute both to personal development and to the integration of students.

RA6.13. Design, develop and evaluate didactic units in the statistics and probability block, and in other areas, using problem-solving as the axis of the activity and keeping coherence with the curriculum.

RA6.14. Develop a positive attitude towards mathematics and an open one regarding its learning and teaching, as an active process, socially constructed and in which error is conceived as a fundamental part of learning.

1. Statistics and information processing. Historical evolution, types of statistical variables, collection, classification, and organization of data, manipulative and graphic representations, measures of centralization and dispersion. Statistical research cycle, reading levels of statistical graphs, transnumeration processes, constructions of centralization and spread measures in the CPA sequence, errors and difficulties in learning statistical graphs and dispersion and centralization measures, materials and resources for the teaching of descriptive statistics, analysis of textbooks, beliefs and attitudes towards statistics, knowledge of the Primary Statistics curriculum, curricular designs, elaboration and evaluation of didactic units of statistics.
2. Chance and probability. Historical evolution, random experiments, definitions of probability, simple and composed experiments, determination and calculation of probabilities, tree diagrams and contingency tables, connections between statistics and probability. Language of probability, meanings of probability, probability as a measure, conditional probability in Primary, the CPA sequence in probability, errors and difficulties in learning probability, materials and resources for teaching probability, analysis of books of text, beliefs, attitudes, and biases towards probability, knowledge of the probability curriculum of Primary, curricular designs, elaboration and evaluation of didactic units of probability.
3. Problem-solving. Historical evolution, problem definition, types of mathematical problems, Pólya problem-solving stages, heuristics, sources and resources to pose problems, computational thinking and educational robotics in solving mathematical problems. IMMPS model, approach and resolution of problems, affective domain in problem resolution, methodologies in teaching problem resolution, errors and difficulties in problem resolution, materials and resources for problem resolution, materials and resources for thinking computing and educational robotics, analysis of textbooks, knowledge of the Primary problem-solving curriculum, curricular designs, elaboration and evaluation of problem-solving didactic units.

Lectures will be as interactive as possible, also using ICT resources. Interaction is an essential component.

Practical classes will consist in expositions performed by students, knowledge and handling of different classroom material resources, problem solving, simulation of didactical situations, and different classroom resources. 

Group tutorships will be perfomed by following students' demands.

The distirbution is the following:

Exceptionally, depending on health conditions, non-classroom teaching activities can be programmed. In that case, the students will keep informed about the possible changes.

Tutorial action plan

During the course, statistical analysis of environmental data will be performed, in order to make students conscious about necesity of taking care of our planet.

Regarding professional orientation, group tasks will improve positive attitudes towards real working environments. Moreover, students will be informed about different job opportunties for graduates related to mathematics.

a) The following evaluation instruments will be used, with the weight that each of them will have in the final grade:

    Written exam on topics 1, 2, and 3: 60%
    Practical tasks: 25%
    Elaboration and defense of group work: 15%

All assessment instruments will be related to all learning outcomes. In addition, since the evaluation has a necessarily subjective component that goes beyond quantification, the qualification may be nuanced by the observation of the students' work and the global consideration of the learning results.

b) A written exam will be carried out, on the contents of units 1, 2, and 3, in the ordinary and extraordinary calls. In addition, another exam may be proposed on a date prior to that of the ordinary call, with the authorization of the dean and, in that case, it will serve as an exclusive alternative to that of the ordinary call.

c) To pass the subject it will be necessary to obtain at least 5 out of 10 in the written test. In the event that said minimum is not obtained, the final numerical grade will be the weighted average --calculated as established in section a)-- whenever it is less than 5, or a 4.9 if said weighted average is greater than 5.

d) Regarding the extraordinary call, the qualification of the ordinary in the written exam will be kept if it is higher than 5 (and the weighted average of all the qualifications does not reach 5), and alternative practical tasks will be proposed to those carried out during the course. Group work, due to its nature and characteristics, is not likely to be carried out again in the extraordinary call, so the qualification obtained in the ordinary call will be maintained.

e) Regarding the extraordinary advanced call (held in December/January for repeating students), it will be evaluated as follows: the exam will have a weight of 60% and the remaining 40% will correspond to the practical tasks that have been carried out in the course until the time of the exam (since the subject is annual when this call is held it is impossible to have done the group work, so, in order not to harm the students, its weight is added to that of the practical tasks) and an additional task to be done along with the exam.

f) With regard to written expression, both in assignments and exams, the existence of three or more misspellings in any one of them may result in a failure, in the corresponding instrument, for the affected student.

g) Regarding the differentiated evaluation, non-attendance alternatives will be offered for the tasks carried out in person, not being compulsory to attend the rest of the sessions. In any case, the evaluation will be adapted to the circumstances of the student, in accordance with the provisions of the resolution that grants said evaluation and group work and tasks may be carried out individually if there is no possibility for the student to collaborate with other people.

h) Exceptionally, if health conditions require it, remote evaluation methods may be included. In which case, the student body will be informed of the changes made

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Alsina, Á. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12 años). Barcelona: Graó.

Batanero, C., Díaz. D. (Eds.) (2011). Estadística con proyectos. Universidad de Granada, Granada.

Blanco Nieto, L., Cárdenas Lizarazu, J.A., Caballero Carrasco, A. (2015). La resolución de problemas de matemáticas en la formación inicial de Profesorado de Primaria. Universidad de Extremadura, Cáceres.

Carrillo. J., Contreras, L.C., Climent, N., Montes, M.A., Escudero, D., Flores, E. (Eds.) (2016).  Didáctica de las matemáticas para maestros de Educación Primaria. Paraninfo, Madrid

Echenique Urdiain, Isabel (2006): Matemáticas resolución de problemas, Fondo de Publicaciones del Gobierno de Navarra, Pamplona, accesible en http://recursos.cepindalo.es/file.php/185/Adjuntos/matematicas_navarra.pdf

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Godino, J. D. ( Dir.) (2004): Didáctica de las matemáticas para maestros, U. Granada, accesible en http://www.ugr.es/local/jgodino/ 

Godino, J. D. ( Dir.) (2004): Matemáticas para maestros, U. Granada, accesible en http://www.ugr.es/local/jgodino/

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Nrich: enriching mathematics. https://nrich.maths.org/

Varios. Libros de texto, para Educación Primaria y para Educación Secundaria, de diversas editoriales: Anaya, Edebé, Santillana, SM,... y sus correspondientes recursos web.