This version of the course guide is provisional until the period for editing the new course guides ends.

Logo UAB

Mathematics for Teachers

Code: 102055 ECTS Credits: 6
2025/2026
Degree Type Year
Primary Education OB 1

Contact

Name:
Maria Nuria Gorgorio Sola
Email:
nuria.gorgorio@uab.cat

Teachers

Maria Nuria Gorgorio Sola
Francisco Javier Lucas Rojas Sateler
Lluis Albarracin Gordo
Juan Carlos Tinoco Balongo

Teaching groups languages

You can view this information at the end of this document.


Prerequisites

To follow the course it's required to have a good level in basic mathematics.


Objectives and Contextualisation

It is a basic subject of disciplinary content. Its purpose is to consolidate fundamental mathematical knowledge through various methodologies: problem solving, research and projects, among others. Consolidated progress in this subject should serve as a basis for the construction of of the teaching of mathematics throughout the degree. The fundamental mathematical knowledge built up in this subject is what will enable future teachers to guide Primary Education students towards the achievement of the mathematical competencies of the stage.

The following are specific objectives of the course:

  • Manage the initial mathematical knowledge to bring it closer to the fundamental mathematical knowledge needed to be a teacher.
  • Contextualize mathematical knowledge in the professional work of the mathematics teacher.
  • To counter mechanistic learning of mathematics to construction of knowledge.
  • Establish connections between different mathematical concepts and between mathematical concepts and concepts from other areas of knowledge.
  • Understand math as a valuable problem-solving tool beyond the mathematics classroom.

 

 

 


Competences

  • Acquire basic mathematics skills (numerical skills, calculation, geometry, spatial representations, estimation and measurement, organisation and interpretation of information, etc.).
  • Design and regulate learning spaces in contexts of diversity that take into account gender equality, equity and respect for human rights and observe the values of public education.
  • Incorporate information and communications technology to learn, communicate and share in educational contexts.
  • Know and apply information and communication technologies to classrooms.
  • Know the curricular areas of Primary Education, the interdisciplinary relation between them, the evaluation criteria and the body of didactic knowledge regarding the respective procedures of education and learning.
  • Maintain a critical and autonomous relationship with respect to knowledge, values and public, social and private institutions.
  • Posing and solving problems related to daily life.
  • Reflect on classroom experiences in order to innovate and improve teaching work. Acquire skills and habits for autonomous and cooperative learning and promote it among pupils.
  • Stimulate and value effort, constancy and personal discipline in pupils.
  • Take account of social, economic and environmental impacts when operating within one's own area of knowledge.
  • Value the relationship between mathematics and sciences as one of the pillars of scientific thought.

Learning Outcomes

  1. Being able to solve problems involving the connection between different blocks of content.
  2. Critically analyse mathematical texts, activities and other proposals for education.
  3. Demonstrate knowledge of the fundamental concepts and properties of number systems, plane and space geometry, measurement and data treatment.
  4. Establish concrete relations by means of educational proposals in the different areas of the primary education curriculum.
  5. Exploit situations from a particular scientific field to show the utility of mathematical content.
  6. Find information using technologies for learning and knowledge resources in mathematics.
  7. Identify the social, economic and environmental implications of academic and professional activities within one?s own area of knowledge.
  8. Identifying problem situations drawn from other sciences that can be modelled mathematically.
  9. Posing problems in order to introduce relevant mathematical concepts and results.
  10. Propose ways to evaluate projects and actions for improving sustainability.
  11. Resolving problems independently.
  12. Resolving problems involving names, geometry and measurement in a variety of situations including those from everyday life.
  13. Understand and apply indicators for the evaluation and design of proposals for mathematics education from a perspective of gender equity and equality.
  14. Understand interdisciplinary teaching situations for the teaching and learning of mathematics.
  15. Using software tools and specific maths programs for estimating, demonstrating and communicating mathematical results.

Content

1. Geometry to understand space.

    Elementary geometric constructions. Plain representation of space.

2. Numbers to count and calculate.

    Natural numbers. Decimal numbering system. Divisibility.

3. Measure to know the environment.

    Concept of magnitude. Proportionality.

 4. Data for interpreting reality.

    Organization, interpretation and visualization of data. 

 

The following are considered transversal contents relevant to all the content mentioned before:

 
5. Visualisation and representation of ideas and mathematical concepts.

6. Problem solving.

7. Patterns and relationships.

 

 

 

 

 


Activities and Methodology

Title Hours ECTS Learning Outcomes
Type: Directed      
Classrom practice 30 1.2 2, 6, 8, 1, 15
Master class 45 1.8 2, 5, 8, 9
Projects development and problem solving 75 3 2, 5, 3, 8, 9, 11, 12, 1

The teaching proposal is based on a methodology of active, face-to-face classroom work. In parallel, the student must carry out the proposed tasks on time in order to properly follow the teaching of the subject. The student must work bearing in mind that learning mathematics requires daily practice and that mathematics is not learnt by watching or seeing how someone else does mathematics. Learning is based on DOING mathematics, showing a pro-active attitude.

The student is expected to autonomously take responsibility for extending his or her basic mathematical knowledge. The inclusion of different learning paces will be facilitated with voluntary, non-assessable activities. The specific assessment activities and the criteria for marking them will be the same for all those enrolled on the course.

The inclusion of different learning paces will be facilitated with proposals for non-assessable voluntary activities. The specific assessment activities and the criteria for marking them will be the same for all those enrolled on the course. In mathematics, the result of each activity or problem can be reached by different routes. This premise is what allows us to promote an inclusive vision of mathematics learning.

Activity analysis and Problem solving

Working sessions in small or large groups where problems are solved and situations are analysed in relation to the mathematical contents involved in the subject. The students responsible for the assignment will present their work orally and the teacher will validate the mathematical knowledge that is involved with the active participation of the rest of the students.

Master classes

Presentation by the teacher of the main contents of the course in which students are expected to actively participate.

Practices or investigations

Group work sessions where research activities are proposed that students solve under the guidance of their teacher.

 

NOTE: The proposed teaching methodology and assessment may be modified if health authorities impose restrictions on public gatherings.  

Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.


Assessment

Continous Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Individual written tests 77,50 0 0 3, 11, 12, 1
Plannning, solving and reporting of problems and/or activities 11,25 0 0 6, 3, 9, 11, 12, 1, 15
Projects or investigations 11,25 0 0 2, 5, 6, 13, 14, 4, 7, 8, 10

The student must work bearing in mind that learning mathematics requires daily practice and that mathematics is not learned by watching or listening to how someone does mathematics. Learning is based on DOING mathematics, showing a proactive attitude. Students are expected to autonomously take responsibility for extending and consolidating their basic mathematical knowledge.

The specification of some of the assessment activities will depend on whether the student chooses continuous assessment or single assessment. The assessment criteria will be the same for all those enrolled on the course.

TEST OF BASIC MATHEMATICAL KNOWLEDGE AS A REQUIREMENT FOR ASSESSMENT

During the course the student must obtain a minimum mark of 7 out of 10 in a Basic Mathematical Knowledge (BMK) test in which he/she must demonstrate that he/she has mastered the mathematical knowledge proper to compulsory education.

  • On the first day of the course (10/02/2026 or 12/02/2026 as appropriate) ALL students may sit this test on the first day of the course: BMK 1. Those students who obtain a mark equal to or higher than 7/10 will be considered to have passed the BMK.
  • In the middle of the semester, there will be a new opportunity to take this test: BMK 2. Students who have not obtained a 7/10 in the BMK 1 test will be able to take this test, whether they are in continuous or single assessment. It will take place in the middle of the semester - dates to be specified by the teacher depending on the organisation of the content blocks. Each teacher will publish the date of BMK 2 when they publish the course syllabus.
  • There will be a CMF make-up exam (CMF3) (23/06/2026 or 25/06/2026, as applicable) for those students, both continuous assessment and single assessment, who have not obtained a 7 in previous CMF exam sessions. A minimum grade of 7/10 is required to pass.

The BMK test is intended that the studenthas reached a good level of basic mathematics, in particular the mathematics of compulsory education, which is a prerequisite for the evaluation of the subject. In the event that the student does not pass the minimum grade in any of the three examinations, the final grade for the subject will be a 3.

TYPOLOGY AND WEIGHTING OF EVALUATION ACTIVITIES

For each of the different blocks into which the subject is organised (organisation of data; numbers and proportionality; geometry and measurement) there will be a follow-up assessment activity for the block, which will take one form or another depending on whether the student chooses continuous assessment or single assessment.

The follow-up assessment activities for each block have different typologies and are defined based on the content bloc:

  • Data Organization Block – The follow-up assessment for this block accounts for 15% of the course grade and is comprised of two components: a) Project Planning, Development, and Reporting: For the data organization block, students will be asked to plan and develop a statistical research project in small groups; and b) individual completion of three exercises related to the concepts covered in class, which will take place on the final day of the block. The individual grade for the data organization block is obtained by weighting the project grade resulting from the group work (75%) and the grade for the three exercises (25%). The total grade for the data organization block accounts for 15% of the course grade.
  • Geometry and Measurement Block – The follow-up assessment for the geometry and measurement block has two components: a) Planning, solving, and reporting on activities: For the geometry and measurement block, a practical exercise will be proposed consisting of a set of interlinked mathematical activities to be developed in small groups and discussed in seminars; and b) individual completion of three exercises linked to the concepts worked on in class, which will take place on the last day of the block. The individual grade for the geometry and measurement block is obtained by weighting the grade for the practical exercise resulting from the group work (75%) and the grade for the individual exercises (25%). The grade for the geometry and measurement block corresponds to 15% of the course grade.
  • Numbers and proportionality block – For the numbers and proportionality block, students must take an individual follow-up test (20% of the course grade)

At the beginning of each block, the follow-up assessment activities for the block will be presented and specified.

  • Continuous assessment students will submit their group work for blog monitoring one week after the end of the block. Instructors will publish the dates of the submissions and the numerical test for blog monitoring when publishing the program, as the dates depend on the timing of the blocks.
  • Students who opt for a single assessment for the geometry and measurement and data organization sections will be required to submit a written report for the activity and/or project and complete a written validation activity for their submitted report. The reports and validation tests and the test for the block numbers and proportionality will take place on 16/06/2026 or 8/06/2026, as appropriate.

FINAL TEST

Two weeks after finishing the subject there will be an individual final test of the entire course content (50% of the course grade). The date of the final exam is 16/06/2026 or 18/06/2026 depending on the day of the week that the group teaches this subject.

CMF MAKE-UP TEST 

Those students, whether taking continuous assessment or single assessment, who have not obtained a 7 in both previous CMF sessions may take a make-up CMF test on 06/23/2026 or 06/25/2026, depending on the day of the week the group has a class. A minimum grade of 7/10 is required to pass.

MAKE-UP TEST

Those students who do not achieve a 5 in the final exam, if the weighted average of their marks (block follow-up and final exam) is higher than or equal to 3.5, they can take the make-up exam (weighted 50% - in substitution of the mark in the final exam). The make-up test is not a test to improve the grade of the final test in the case of students who have passed it. The make-up test will be held two weeks after the final test, on 30/06/2026 or 02/07/2026 depending on the day of the week that the group teaches this subject. When a student has had to take the make-up test and has passed it, the maximum mark that will be considered for the weighting of the course marks will be a 5, regardless of whether the student has obtained a higher mark in the make-up test.

CALCULATION OF THE COURSE GRADE

The final grade of the course is the weighted average of the marks of the three evaluation activities of the monitoring of the blocks (geometry and measurement = 15%; number and proportionality = 20%; organisation of data = 15%) and the mark obtained in the final test or the make-up test (with a weight of 50%), with the following conditions:

  • In order to be eligible for the weighted average of the course marks, the student must have obtained a minimum of 7 out of 10 in the Fundamental Mathematical Knowledge test. If the student has not reached this minimum in any of the opportunities given, the final grade for the course will be a 3.
  • In order to be eligible for the weighted average with the rest of the marks of the course, the student must have obtained a minimum of 5 in the final exam or in the make-up exam. If the student does not obtain a minimum of 5 in the final exam or in the make-up exam, he/she does not pass the course and the final grade for the subject will be a 3.
  • Late submission of the block assessment activities will result in a 0 in the block assessment. Likewise, failure to attend the problem-solving test will result in a 0 in the evaluation of that block.
  • The block follow-up assessment activities are not recoverable in any case.
  • Despite having passed the final exam or, where appropriate, the recovery, if the weighted average of the marks does not reach 5, the student does not pass the subject and the final grade on their transcript will be a 3.

OTHER ASSESSMENT CONSIDERATIONS

The student should take into account the following normative considerations on assessment:

• The dates established for the CMF exams, final assessment, and resits are non-changeable unless the student suffers from a serious illness or any other justified exceptional situation. Individual changes to the dates of submissions or tests will not be made, except for justified reasons. A driver's license exam, a pre-arranged trip, or a family celebration are examples of situations that DO NOT generate changes to the dates of the subject assessment activities.

• Block follow-up assessment activities cannot be made up. The CMF test and the final test can be made up under the conditions set out above.

  • Any student who has not been assessed in a set of activities whose weight is equivalent to at least two-thirds of the total grade for the subject will be considered unassessable.
  • The use of a calculator is not allowed in individual written tests, unless indicated by the teacher.
  • The use of Artificial Intelligence tools in assessment activities is not allowed.
  • All assessment activities are compulsory for all students.
  • The mark for a group assignment is not necessarily the individual mark for each student in that group.
  • The copying or plagiarism of material or the use of AI in assessment activities when not explicitly recommended by the teacher will be considered a lack of honesty in assessment and may result in a 0 in the overall mark for the subject.
  •  The lecturer will publish the marks for the assessment activities within a period of no more than 20 working days of the academic calendar and will make the relevant returns for the different assessment activities.

 

ATTENDANCE AND ASSESSMENT

The course has a face-to-face character.

CONTINUOUS ASSESSMENT

Specific dates for the specific assessment activities for students takingpart in continuous assessment:

  • The student can take the two opportunities to pass the CMF, and the retake test until the required mark of 7/10 is achieved. The dates have been defined above (see test of fundamental mathematical knowledge as a requirement for assessment).
  • Follow-up deliveries of the blocks will be made one week after closing the block, as established above (typology and weight of the evaluation activities).

     

     

  • The dates set for the final test, the CMF make-up test and the make-up test are those established for all students enrolled in the course.

SINGLE ASSESSMENT

Students who take the single assessment must follow the development of the subject, attending classregularly. However, they WILL NOT SUBMIT THE FOLLOW-UP ASSESSMENT ACTIVITIES OF THE BLOCK UNTIL THE SAME DAY OF THE FINAL ASSESSMENT. For this reason, they WILL NOT HAVE A RETURN of the individualised follow-up assessment activities of the blocks during the course of the subject. In any case, they will be able to access the general feedback, either that which is done during the feedback sessions for the whole class group or that which may be published on the virtual campus for the whole group.

The date of collection of the assessment evidence and the requirement for a validation test of the evidence collected is specific to students who take the single assessment. The teaching team of the subject considers it necessary to carry out a validation test of the collected evidences because the students will have had access to the process of returning the activities and the project and the corrected evidences of their classmates.

The date for the delivery for the evaluation of the blocks and for the tests for their validation and the test of the block of numbers and proportionality is the same established for the final exam, 16/06/2026 or 18/06/2026 depending on the day of the week that the group has teaching of this subject.

Therefore, on 16/06/2026 or 18/06/2026, as appropriate, students taking the single assessment must:

-          Take the same final test at the same time as the rest of the students in the course.

-          Take an individual written test to evaluate the follow-up of the block of numbers and proportionality.

-          Hand in the evaluation activities of the geometry and measurement block and take their validation tests.

Students with a mark of 3.5 or more but less than 5 can take a recovery test, which will be the same for allstudents of the subject and will be held on the same day (on 30/06/2026 or 02/07/2026 as appropriate). Therefore, it is essential that students taking a single assessment reserve the FULL DAY of the final assessment, 30/06/2026 or 02/07/2026 as appropriate, in order to have time to carry out all the tests that will constitute the evidence of their assessment.

Likewise, students with a single evaluation who must make up the CMF will do so on the same day (23/06/2026 or 25/06/2026 depending on the day they have the course) under the same conditions as the rest of the students enrolled in the course.

The grade for the geometry and measurement and data organisation blocks will be that of the corresponding validation test. The weighting of the assessment of the different blocks and of the final exam (or, if applicable, the recovery) and the calculation of the final mark for the course are the same for all students on the course, even if they have taken a single assessment. The other specific assessment considerations also apply to both continuous assessment and single assessment students.

 

ATTENTION NOTE FOR STUDENTS WHO DID NOT PASS THE COURSE IN PREVIOUS ACADEMIC YEARS

From the academic year 2023-24, there is NO SYNTHESIS EXAMINATION for this subject.

Therefore, those enrolling for thesecond time will be able to choose between continuous assessment or single assessment. In both cases, the conditions regarding attendance will be the same as for the rest of the students enrolled in the subject. Therefore, we recommend that students repeating the subject ensure that they are available in time to follow it regularly, if necessary, avoiding enrolling in other subjects of other courses that are taught on the same day in the same time slot.

NOTE: In order to pass this subject, it is necessary to show a good general communicative competence, both orally and in writing, and a good command of the vehicular language or languages listed in the teaching guide. In all activities (individual and group), linguistic correctness, writing and formal aspects of presentation will therefore be taken into account. It is necessary to be able to express oneself fluently and correctly and to show a high degree of understanding of academic texts. An activity may be returned (not assessed) or failed if it is deemed not to meet these requirements.


Bibliography

ALEKSANDROV, A.D. i altres. (1973) La matemática: su contenido, métodos y significado Vol 1. Madrid: Alianza. 

BAEZA, M.A., ARNAL, M.,CLAROS, F.J., RODRÍGUEZ, M.I. (2024) Nociones matemáticas elementales: aritmética, magnitudes, geometría, probabilidad y estadística. Paraninfo

CASTELNUOVO, E. (1981) La geometria. Barcelona: Ketres. 

CASTRO, A., MENGUAL, E., PRAT, M., ALBARRACÍN, L., GORGORIÓ, N. (2014). Conocimiento matemático fundamental para el grado de educación primaria: inicio de una línea de investigación. En M. T. González, M. Codes, D. Arnau y T. Ortega (Eds.), Investigación en Educación Matemática XVIII (pp. 227-236). 

COURANT, R. i ROBBINS, H. (1955) ¿Qué es la matemática? Madrid: Aguilar.

DEULOFEU, J. (2001) Una recreación matemática: Historias, juegos y problemas. Barcelona: Planeta. 

FISHER, R. VINCE, A. (1988) Investigando las Matemáticas. Madrid: Akal.

GARDNER, M. (1983) ¡Ajá! Paradojas. Barcelona: Labor. 

GODINO, J. D. i RUÍZ, F. (2003). Geometría y su didáctica para maestros. Granada: Departamento de Didáctica de las Matemáticas.  (http://www.ugr.es/local/jgodino/)

GORGORIÓ, N., ALBARRACÍN, L., & VILLAREAL, A. (2017). Examen de competència logicomatemàtica en la nova prova d'accés als graus de mestre. Noubiaix: revista de la FEEMCAT i la SCM, (pp. 58-64).

KLINE, M. (1974) La naturaleza de las matemáticas. Introducció de Matemáticas en el mundo moderno. Selecció de M. Kline. Barcelona: Blume.

MASON, J., BURTON, L. i STACEY, K. (1988) Pensar matemáticamente. Barcelona: Labor-MEC. 

MENGUAL, E., GORGORIÓ, N. ALBARRACÍN, L. (2017) Análisis de las actividades propuestas por un libro de texto: El caso de la medida. REDIMAT, 6(2), 136-163

NCTM (2003) Principios y estándares para laeducación matemática.  Sevilla: SAEM Thales.

PIZARRO, N., GORGORIÓ, N., ALBARRACÍN, L. (2014). Aproximación al conocimiento para la enseñanza de la estimación de medida de los maestros de primaria. En M. T. González, M. Codes, D. Arnau y T. Ortega (Eds.), Investigación en Educación Matemática XVIII (pp. 523-532). Salamanca: SEIEM.

PIZARRO, N., GORGORIÓ, N., ALBARRACÍN, L. (2016) Caracterización de las tareas de estimación y medición de magnitudes. Números, (91), 91-103.

PONCARÉ, H. (1974) La creación matemática, extret de Matemáticas en el mundo moderno. Selecció de M. Kline. Barcelona: Blume. 

POLYA, G. (1982) Cómo plantear y resolver problemas. México: Trillas.

RICO, L. (2011) Matemáticas para maestros de educación primaria. Madrid: Pirámide.

 


Software

We plan to use the usual programmes for editing texts or oral presentations, a spreadsheet, or GeoGebra, a free interactive programme that combines geometry, algebra and calculus.


Groups and Languages

Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.

Name Group Language Semester Turn
(SEM) Seminars 211 Catalan second semester morning-mixed
(SEM) Seminars 212 Catalan second semester morning-mixed
(SEM) Seminars 311 Catalan second semester morning-mixed
(SEM) Seminars 312 Catalan second semester morning-mixed
(SEM) Seminars 411 Catalan second semester afternoon
(SEM) Seminars 412 Catalan second semester afternoon
(SEM) Seminars 413 Catalan second semester afternoon
(SEM) Seminars 712 English second semester afternoon
(SEM) Seminars 713 English second semester afternoon
(SEM) Seminars 721 English second semester afternoon
(TE) Theory 21 Catalan second semester morning-mixed
(TE) Theory 31 Catalan second semester morning-mixed
(TE) Theory 41 Catalan second semester afternoon
(TE) Theory 71 English second semester afternoon
(TE) Theory 72 English second semester afternoon