Universidad Pública de Navarra - Nafarroako Univertsitate Publikoa

Module/Subject matter

Obligatory matter / Mathematics and its Didactics.

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Contents

The course develops the arithmetic study, trying to give answer to questions such as: What is a natural number? Which kinds of numbers are there? So, the historical development of different kinds of numbers used in primary education is studied, as well as the properties they verify and the basic operations algorithms. Meanwhile, different situations associated to the number use are worked. 

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General proficiencies

Competencias básicas
CB1 Que los estudiantes hayan demostrado poseer y comprender conocimientos en un área de estudio que parte de la base de la educación secundaria general, y se suele encontrar a un nivel que, si bien se apoya en libros de texto avanzados, incluye también algunos aspectos que implican conocimientos procedentes de la vanguardia de su campo de estudio.
CB2 Que los estudiantes sepan aplicar sus conocimientos a su trabajo o vocación de una forma profesional y posean las competencias que suelen demostrarse por medio de la elaboración y defensa de argumentos y la resolución de problemas dentro de su área de estudio.
CB5 Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía.

Basic Proficiencies

BP1 Students have demonstrated that they possess knowledge of and understand an area of study, based on general secondary education and usually at a level which, albeit with the support of advanced text books, also includes some aspects which imply knowledge of the latest developments in their field of study.

BP2 Students know how to apply their knowledge to their work or vocation in a professional manner and possess skills which are usually demonstrated by developing and defending arguments and resolving problems in their area of study.

specialist and non-specialist audiences.

BP5 Students have developed those learning skills required in order to undertake further studies with a considerable degree of self-reliance.

Competencias generales

CG1 Conocer las áreas curriculares de la Educación Primaria, la relación interdisciplinar entre ellas, los criterios de evaluación, y el cuerpo de conocimientos didácticos en torno a los procedimientos de enseñanza y aprendizaje respectivos.
CG2 Diseñar, planificar y evaluar procesos de enseñanza y aprendizaje, tanto individualmente como en colaboración con otros docentes y profesionales del centro.
CG8 Mantener una relación crítica y autónoma respecto de los saberes, los valores y las instituciones sociales públicas y privadas.
CG9 Valorar la responsabilidad individual y colectiva en la consecución de un futuro sostenible.
CG10 Reflexionar sobre las prácticas de aula para innovar y mejorar la labor docente. Adquirir hábitos y destrezas para el aprendizaje autónomo y cooperativo y promoverlo entre los estudiantes.
CG11 Conocer y aplicar en las aulas las tecnologías de la información y la comunicación. Discernir selectivamente la información audiovisual que contribuya a los aprendizajes, a la formación cívica y a la riqueza cultural.

General proficiencies

GP1 To be familiar with the curricular areas of Primary Education, the interdisciplinary relationship between them, the evaluation criteria and the body of didactic knowledge involved in the respective teaching and learning procedures.

GP2 To design, plan and evaluate teaching and learning processes, both individually and in collaboration with other teachers and school professionals.

GP8 To maintain a critical, independent relationship with respect to knowledge, values and social institutions, both private and public.

GP9 To value both individual and collective responsibility in the achievement of a sustainable future.

GP10 To reflect on classroom practices in order to innovate and improve teaching. To acquire habits and skills for autonomous and cooperative learning, and promote it among schoolchildren.

GP11 To be familiar with Information and Communication Technology, and apply it in the classroom. To distinguish the audiovisual information which contributes to learning, civic education and cultural richness in a selective manner.

Competencia transversal
CT2 Demostrar una competencia lingüística en castellano y, en su caso, en euskera equivalentes a un nivel C1 del "Marco común europeo de referencia para las lenguas: aprendizaje, enseñanza, evaluación" del Consejo de Europa.

Transverse Proficiencies

TP2 To demonstrate a level of competence in Spanish and, where appropriate, Basque equivalent to the C1 level of the Council of Europe¿s Common European Framework of Reference for Languages.

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Specific proficiencies

SP1 To be familiar with the objectives, curricular content, meaning of the areas and organisation, methodology and evaluation criteria of Primary Education.

SP2 To design, plan and evaluate teaching and learning processes with other professionals according to interdisciplinary and disciplinary criteria.

SP3 To encourage reading and the critical commentary of texts from the different scientific and cultural fields. To express themselves correctly both orally and in writing, and to master language learning situations in contexts of diversity.

SP7 To encourage cooperation, the motivation and desire to learn, and to participate actively in the school¿s projects.

SP8 To maintain a critical, independent relationship with respect to knowledge, values and the institutions involved in education.

SP10 To reflect on classroom practices in order to innovate and improve teaching, and associate them with the basic psychological processes, pedagogical models and disciplinary criteria of the stage of education.

SP11 To be familiar with the educational implications of Information and Communication Technology.

SP12 To organise actively the processes of teaching and learning the contents of Primary Education from a perspective of skills development. To be familiar with quality improvement models.

SP14 To contextualise teaching work in the face of political, social and pedagogical changes, and to foster democratic education and the development of active citizenship to achieve a sustainable future.

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Learning outcomes

Los resultados de aprendizaje son la concreción de las competencias que el estudiante adquirirá en la materia. Se establecen tres niveles:
- Óptimo: adquisición del 100% de las competencias y maestría en al menos el 75% de ellas.
- Medio: adquisición de la mayoría de las competencias pretendidas en la materia y maestría en aquellos aspectos que contribuyen a las competencias específicas del título.
- Deficiente: insuficiente adquisición de los aspectos que contribuyen a las competencias específicas del título.
Un estudiante obtiene una calificación de APTO si el nivel de aprendizaje es óptimo o medio.

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The learning outcomes refer to the proficiencies that the student will adquire in the subject. There are three levels:

- Optimum: Adquisition of 100% of proficiencies, dominating at least 75% of them

- Medium: Adquisition of most of the proficiencies, dominating those skills that contribute to the specific proficiencies of the grade

- Deficient: Poor adquisition of skills that contribute to the specific proficiencies of the grade

A student will get a pass ("APTO") grade if the learning level is optimum or medium

Concrete learning outcomes:

LO1 Arithmetical problems resolution and Natural Numbers representation, operations and properties proof.
LO2 Arithmetical exercises and word-problems analysis and formulation.
LO3 Didactic material useful for teaching and learning numerical systems and arithmetic in primary education analysis.

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Methodology

Teaching methods

Learning activities

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Languages

English / Spanish / Basque

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Evaluation

ES1: Class participation will be measured through the interventions carried out in it and the tasks that arise and resolve in it.

ES3: Practical work will be proposed and resolved in the classroom or proposed as tasks and works associated with autonomous work. They can be practical work to be carried out both individually and in group and must be delivered at a specific date.

ES4: Two tests will be conducted: partial (40%) and final (40%). In both cases the qualification of APT must be obtained. If 5 or more were obtained in the partial test, the part corresponding to the partial test will not be required in the final test. If a score of less than 5 is obtained in the partial test, the final test will be that of the whole agenda.

In all ES4 tests and their recovery, the student must solve a problem extracted from the textbooks of Primary Education. Correct resolution of this problem will be essential to qualify the rest of the test.

If the APT score is NOT obtained in the ES4 result, the maximum achievable final score is 4.5. Thus, the note to be assigned in the minutes will be the lowest of the following two: 4.5 and the average of all evaluation tools.

* Tools to use in recoveries:

a) ES3 (practical work). If the overall note of these works does not obtain the APT rating, the ES4 test must be answered individually to a practical question in order to recover the ES3.
b) ES4 (oral or written evidence). In the extraordinary evaluation, another test will be conducted that maintains a format similar to that of the test conducted during the ordinary evaluation period.

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Agenda

1 Counting and several Numeration Systems

1. Counting techniques and counting principles.
2. Natural numbers.
3. Numeration Systems.
4. Didactic of numeration systems.
5. Resources: physical materials, pencil and paper, software.

2 Introduction to logic and mathematical proof

1. Introduction to Set Theory.
2. Mathematical proof techniques.
3. Extensive (particular) / intensive (general) duality and algebraic levels.

3 Addition and subtraction

1. Set and recursive definitions of addition and subtraction.
2. Classification of contexts and uses of addition and subtraction.
3. Techniques and algorithms.

4 Multiplication and division.

1. Set and recursive definition of multiplication, Euclidean Division.
2. Classification of contexts and uses of addition and subtraction.
3. Divisibility on the set of natural numbers.
4. Techniques and algorithms.
5. Contextualized problems on combinatorial problems.

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Bibliography

Access the bibliography that your professor has requested from the Library.

Basic references
Gregory Polya; "How to solve it".
Thomas H. Parker & Scot J. Baldridge "Elementary Mathematics for Techers".
Jana Hazekamp "Why before How".

Electronic bibliography

Godino, J. D. (Coor.) (2003).  Monografías Edumat-Maestros (Matemáticas y su didáctica). Granada: Universidad de Granada. Disponible en: https://www.ugr.es/~jgodino/edumat-maestros/

Other references
Castro, E.; Castro, Enr. "Didáctica de la Matemática en Educación Primaria". Madrid Síntesis.
Castro, E.; Rico L.; Castro E. "Números y operaciones". Madrid Síntesis.
Gómez, B. "Numeración y cálculo". Madrid Síntesis
Gimena, J.; Girondo, L. "Cálculo en la escuela". Edit. Graó
Gómez B. y Jaime A. "El cálculo aritmético" Albastros Ediciones.
Ifrah G. "Las cifras". Edit. Alianza.
Maurin C. ; Johsua A. : "Les structures numériques à l'école primaire" Ellipses.
Segovia, I. ; Rico, L. : "Matemáticas para maestros de Educación Primaria" Pirámide

Wilhelmi, M.R.; Pascual, J. R.:"Matemáticas para maestros".

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Location

Arrosadia Campus of the Public University of Navarra. For specific classroom, see the website of the Faculty of Humanities, Social and Educational Sciences.

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