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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Descriptors

In this subject several notions related with arithmetic are developed. The historical origin and evolution in the representation of natural numbers is closely attached to the evolution of knowledge in children. All the characteristics, basic operations, properties and calculus algorithms in the field of Natural Numbers are worked, as the didactic of all this materia is provided. Arithmetical word-problems solving is also widely treated.

Keywords: arithmetics; natural numbers; basic operations; algorithms.

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General proficiencies

2.1. 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.

2.1 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.

2.2. 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.

2.2. 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.

2.3. 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.

2.3. 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

Estos resultados se concretan en:

RA1 Arithmetical problems resolution and Natural Numbers representation, operations and properties proof.
RA2 Arithmetical exercises and word-problems analysis and formulation.
RA3 Didactic material useful for teaching and learning numerical systems and arithmetic in primary education analysis.

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Methodology

5.1 Teaching methods

5.2 Learning activities

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Evaluation

8.1. Relationship between formative activities and proficiencies

8.2. Evaluation

The global final test will stand for the 90% of the total vote. At least one half of the maximal vote will have to be got for passing it. If it is failed students can make a global test once more in the extraordinary global test.

The vote got in the extraordinary global test will replace the ordinary global test vote in any case. At least one half of the maximal vote will have to be got for passing it. 

In both the global tests (ordinary and extraordinary) some word-problems got from primary mathematics books will have to be solved correctly. Its correct solution will be necessary for passing the subject.

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Agenda

1. Counting and several Numeration Systems.
a. Counting techniques
b. Natural numbers
c. Numeration Systems
d. Didactic of numeration systems
e.Didactic material associated

2. Introduction to Logic and Mathematical Proof.
a. Basic notions on Set Theory
b. Basic Propositional Logic
c. Modus Ponens and Modus Tolens
d. Mathematical proof techniques
e. Polya's word-problems resolution method

3. Addition and Subtraction.
a. Definitions (set and recursive) of these operations
b. Contexts and uses of these operations
c. Word-problems related with these operations classification and resolution techniques
d. Algorithms of these operations

4. Multiplication and exact Division.
a. Definitions (set and recursive) of these operations
b. Contexts and uses of these operations
c. Word-problems related with these operations classification and resolution techniques
d. Algorithms of these operations

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Bibliography

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

11.1. Basic references
Gregory Polya; "How to solve it".
Thomas H. Parker & Scot J. Baldridge "Elementary Mathematics for Techers".
Jana Hazekamp "Why before How".
11.2. 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
Godino, J. D. (2003). Matemáticas para maestros y Didáctica de las Matemáticas para maestro. Edumat-Maestros.
[ www.ugr.es/local/jgodino/edumat-maestros/]]
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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Languages

English / Spanish / Basque

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Location

Campus Arrosadía de la Universidad Pública de Navarra. Para conocer el aula o aulas concretas, consulte en la página Web de la Facultad de Ciencias Humanas y Sociales.

http://www.unavarra.es/fac-humanasysociales/estudios/grado/grado-de-maestro-en-educacion-primaria/presentacion?submenu=yes&languageId=100000

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