Public University of Navarre

Academic year: 2024/2025 | Previous academic years:  2023/2024 
Bachelor's degree in Primary Education at the Universidad Pública de Navarra
Course code: 312503 Subject title: MATHEMATICS AND TEACHING II
Credits: 6 Type of subject: Mandatory Year: 3 Period: 1º S
Department: Estadística, Informática y Matemáticas

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Module/Subject matter

Didactic and disciplinary / Mathematics and its didactics



Decimal numbers; fractions, rational numbers and irrational numbers, the Q set of rational numbers and their didactics; proportionality, magnitudes and measurement; the Z set of integers; problem solving. Combinatorics and probability.

In the introduction of these contents, aspects related to the teaching and learning processes of mathematics will be highlighted. A distinction will also be made between the mathematical contents of teacher training and their school presentation.


General proficiencies

Core competencies
CB1 Students have demonstrated knowledge and understanding in an area of study that starts at the base of general secondary education, and is usually found at a level that, while supported by advanced textbooks, also includes some aspects that involve knowledge from the forefront of their field of study
CB2 Students know how to apply their knowledge to their work or vocation in a professional way and possess the competencies that are usually demonstrated through the elaboration and defense of arguments and problem solving within their area of study
CB5 Students have developed the learning skills needed to undertake further studies with a high degree of autonomy
General competence
CG1 Know the curriculum areas of Primary Education, the interdisciplinary relationship between them, the assessment criteria, and the body of didactic knowledge related to the respective teaching and learning procedures.
CG2 Design, plan and evaluate teaching and learning processes, both individually and in collaboration with other teachers and professionals at the centreCG8 Maintain a critical and autonomous relationship with knowledge, values and public and private social institutions.
CG9 - Valuing individual and collective responsibility for achieving a sustainable future.

CG10 - Reflect on classroom practices to innovate and improve teaching work. Acquire habits and skills for autonomous and cooperative learning and promote it among students.

CG11 - Know and apply information and communication technologies in classrooms. Selectively distinguish audiovisual information that contributes to learning, civic education and cultural richness.

Transversal competences
CT2 Demonstrate linguistic competence in Spanish and, where appropriate, Basque equivalent to a level C1 of the "Common European Framework of Reference for Languages: Learning, Teaching, Assessment" of the Council of Europe.


Specific proficiencies

CE1 Know the objectives, curriculum contents, the meaning of the areas and the organization, methodology and evaluation criteria of Primary Education.
CE2 Design, plan and evaluate teaching and learning processes according to interdisciplinary and disciplinary criteria with other professionals.
CE3 Encourage the reading and critical commentary of texts from the various scientific and cultural domains. Proper oral and written expression, and mastering language learning situations in diverse contexts.

CE7 - Foster cooperation, motivation and desire to learn, and actively participate in center projects.
CE8 Maintain a critical and autonomous relationship with respect to the knowledge, values and institutions involved in education.
CE10 Reflect on classroom practices to innovate and improve teaching work, and refer them to the functioning of basic psychological processes, pedagogical models and disciplinary criteria of the stage.
CE11 - Understanding the educational implications of information and communication technologies.
CE12 Actively organise the teaching and learning processes of the contents of primary education from a competence development perspective. Knowing quality improvement models.
CE14 - Contextualize teaching action in the face of political, social and pedagogical changes, promote democratic education and the development of active citizenship for the achievement of a sustainable future.


Learning outcomes

A student earns an APTO grade if the learning level is optimal or medium.

These results are reflected in the following processes:

- R1 Solve arithmetic problems and demonstrate properties relating to numbers, their representation and their operations.

- R2 Analyze and formulate statements of exercises and arithmetic problems.

- R3 To analyse teaching materials for the teaching and learning of numerical systems and arithmetic in primary education.



Teaching methodologies
Code / Description
MD1 / Master presentation in plenary
MD2 / Large group interaction
MD3 / Interaction in medium group
MD5 / Individualized Interaction: Tasks and Guidelines for Autonomous Study

Training activities
Code / Description / Hours / Presence
AF1 / Theoretical classes (foundations, examples, verified applications and developments) / 45 / 100
AF2 / Practical classes or, where appropriate, external practices / 15 / 100
AF3 / Preparation of papers and, where appropriate, oral defence / 30 / 10
AF4 / Self-study of the student / 50 / 0
AF5 / Tutoring 5 / 100
AF6 / Oral or written examinations / 5 / 100




Learning outcome   Assessment system   Weight (%) Recoverable character  (%)* Minimum grade required  
RA1, RA2, RA3 SE3: Practical work: observation, proposal and, where appropriate, evaluation 30 30  
RA1, RA2, RA3 SE4: Oral or written tests, partial or combined 70 70 QUALIFIED  (5)
   TOTAL 100 100  


SE3: Practical work that will consist of tasks posed and solved in class or associated with independent work that will have to be delivered on a certain date. Individual and group work may be proposed

SE4: Two tests will be performed: partial (30%) and final (40%). In both, you will need to have an APTO rating. If the partial test has a grade of 5 or higher, the corresponding part need not be taken in the final test. If the grade on the partial test is less than 5, the complete final test will be taken.

In all SE4 tests and in the recovery tests, the student will have to solve some problem extracted from primary school textbooks. Your correct answer will be a prerequisite for the qualification of the rest of the test.
If an APTO grade is NOT obtained on the SE4, the maximum final grade that will be obtained is 4. 5. Thus, the lowest score between 4. 5 and the average for all assessment instruments will be recorded in the minutes.
Tools used in recovery:
(a) SE3 (practical work). If an APTO rating has not been achieved in the overall work, an individual practical question included in the SE4 test will be performed as a recovery of the SE3.
(b) SE4 (oral or written tests). A standard test will be conducted in a format similar to that carried out in the regular period.





1. Fractions and rational numbers

Fractions and their meaning
Equivalence of fractions
Rational numbers and school curriculum
Operations with Rationals
Teaching materials and resources for your study in Primary

2. Decimal numbers

Decimals in the Primary Curriculum
Extended decimal numbering system
Decimal division and generating fraction
Order and operations with decimals
Non-periodic decimals

3. Whole numbers

Historical contextualization
Classes of equivalence and formalizing the integer
Contexts of using the integer

4. The irrational number

Examples: pi, e, non-integer roots
Conceptual development of the irrational number

5. Proportionality between magnitudes

Basic concepts
Contexts for the use of proportionality
Proportionality between magnitudes
Geometric proportionality

6. Probability

Introduction to probability. Contexts of use. Problems

7. Problem-solving

8. Fundamentals of teaching and learning mathematics

Primary Education Curriculum.
Characteristic features of mathematics.
Implications of learning theories in the teaching of mathematics.


Experimental practice program




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

POLYA, George. How to solve it: A new aspect of mathematical method. Princeton university press, 2004.

RAMOS ALONSO, Pedro. ARITMÉTICA PARA MAESTROS. + pensar - cuentas. ISBN13 978-0244513320. (2019).