Mathematics for Understanding the World
Code: 102056Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Primary Education | OP | 4 |
Contact lecturer
- Name :
- Lluís Albarracin Gordo
- Email :
- lluis.albarracin@uab.cat
Teaching staff
- Brenda Lorena García Triana
Group languages
You can consult this information at the end of the document.
Prerequisites
It is suggested that the students that enroll in this subject have studied and passed the first year subject "Mathematics for teachers", the second course subject: "Learning mathematics and curriculum" and the third course subject "Management and innovation In the classroom of mathematics ".
To pass this subject, the student must show, in the activities proposed, good general communicative competence, both orally and in writing, and a good command of the language or the vehicular languages that appear in the teaching guide.
Objectives
This is an optional fourth year subject that is focused on the development of professional competencies around mathematics and its ability to understand the world around us. This subject should provide tools and strategies for teachers who want to study in depth the mathematics teaching and their relationship with the world, from the perspective of the application of mathematics to the physical or natural world and sociocultural as well as from The perspective of inspiration in both worlds to inspire / create mathematics and design, manage and evaluate interventions in the classroom of primary math according to these references.
It is taught when the students have already completed the compulsory subjects: Mathematics for teachers, Mathematics and curriculum development, and Management and innovation in the classroom of mathematics, and who wish to study or study as a free-choice subject, or Well to get the mention in didactics of mathematics. For this reason, from the subject Mathematics to understand the world, we want to focus on the knowledge of the world that surrounds us (both physical and natural and social) from the point of view of mathematics, to provide tools to offer Resources and strategies that allow future teachers to present a mathematics meaningful, useful and meaningful in primary.
This course develops the practical knowledge and application of the primary mathematical curriculum in the planning, design and evaluation of tasks and sequences of teaching and learning of mathematical contents. It works on numbering and calculations, relations and change, space and form, measurement, and statistics and chance to understand the world around us and have didactic tools to design interventions in the classroom of primary math. However, this does not mean that the mathematical processes and contents that work should be limited solely to those of the primary curriculum, but that the teacher should achieve the mathematical competences necessary to interpret Part of the world that surrounds itand to know how to limit itself and adapt to the level of primary when it comes to taking them to the classroom. The teacher must know more about what pupils need to learn.
The following specific objectives are specified:
1. To know different applications of mathematics from the point of view of the socio-cultural environment as well as physical / natural.
2. Design interventions for the teaching of mathematics in primary school based on these applications.
3. To design, plan, manage and evaluate teaching and learning activities of mathematics based on the criteria set by the primary curriculum.
4. Work on the mathematical contents of the environment using efficient didactic methodologies.
5. Understand the role of the world that surrounds us (natural and sociocultural) in order to create mathematics in a way that is opposite to that of the aforementioned application.
6. Knowing mathematical ideas from other cultural worlds present in primary classrooms.
Learning outcomes
- Gaining a deeper knowledge of school mathematics at a level of level connections, contexts and skills.
- Adapt teaching and learning programs and activities to pupil diversity.
- Understand recreational didactic situations involving mathematics, both inside and outside the classroom, to promote independent learning and cooperative work.
- Assessing the value of, and applying professional cases relating to, the teaching of mathematics.
- Design innovative teaching sequences from contexts that provide recreational mathematics.
- Identifying, designing and communicating concepts, facts and phenomena of different sciences capable of being modelled using mathematical concepts.
- Analyse social and historical facts and collect various interpretations of the relationship between mathematics and other sciences. Understand the positive or distorting role of the media in the use of these relationships.
- Understand and critically evaluate educational software and related web-based resources in the gaming world that are suitable for teaching and learning mathematics.
- Analyse the goals of mathematics education at different stages of primary education.
- Design teaching and learning sequences that connect different mathematical topics.
- Identify the social, economic and environmental implications of academic and professional activities within one?s own area of knowledge.
- Analyse the indicators of sustainability of academic and professional activities in the areas of knowledge, integrating social, economic and environmental dimensions.
- Propose viable projects and actions to boost social, economic and environmental benefits.
- Propose ways to evaluate projects and actions for improving sustainability.
Contents
The teacher's mathematical competence must not be reduced to what his students must achieve, but rather must go further. The contents of the subject are determined by two aspects.
On the one hand, by the desire to understand some current phenomena in contemporary life and environment. On the other, the desire to bring some in the classroom, turning them into mathematical education and learning activities so that primary school students learn mathematics and understand better the world in which they live.
From the point of view of the teaching methodologies for the Primary School, the course aims to integrate mathematical work into the work dynamics of projects, focusing on the competence of solving contextualized problems and mathematical modeling.
There are various conceptions of mathematical modeling but it is widely shared to consider mathematical modeling as a problem-solving process that links the real world and mathematics.
Modeling involves mathematizing real-world situations and elaborating mathematical models to describe the phenomena studied, often conceptualized as the result of having engaged in a complex modeling process. The phenomena that will be studied and will conform the contents of the subject will be:
Count to know
How are we?, how are they? How are I?
Identification and creation of numerical and geometric patterns
Unreacheable magnitudes
Living the measurement
What does it mean to measure?
Walk in space and in time
Measure of uncertainty
How many ways can you do it?
Group yourself
QR codes
Go from one place to another
Mathematics to everyday contexts
Video games
Tiles the plan
Mosaics: a universal cultural phenomenon
Mathematical photography
Images that are not understood without mathematics
Mathematics for ...
Get Informed (media)
Get to know the city (mathematical itineraries)
Enjoy (games and sports)
Bringing a healthy life (health and consumption)
Work (workplace)
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Autonomous | 75 | 3 | |
| Big group | 45 | 1.8 | |
| Supervised | 30 | 1.2 |
The main character in the teaching-learning process is the student and under this premise.
Exhibitions on basic themes of the syllabus (31 hours): it is done with the entire class group through an open and active participation by students.
When a return is needed, it will begin with an introduction where the lessons of the previous seminar will be shared. It will end with the presentation of the tasks that must be developed at the seminar and individually.
Work spaces in small groups within the classroom supervised by the teacher where through the analysis of documents or activities of research and use of manipulatives, it approaches the contents and topics worked in the large group and prepare the projects (14 hours).
Criteria of inclusion and respect for the different diversities always represented in any classroom, including the university classroom, will be considered.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| 3. Research on a real world phenomenon and the paper of mathematics in its resolution and interpretation: Individual work | 30% | 0 | 0 | 1, 2, 6, 7, 8, 9, 10, 11, 12, 13, 14 |
| 1. Design of contextualized mathematical problems and analysis of the students' solution strategies: Individual work | 30% | 0 | 0 | 1, 2, 3, 4, 5, 6, 10 |
| 2. Group project of mathematical modeling in a real environment: Working in groups | 40% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 |
The evaluation of the subject will be carried out throughout the academic year through the activities shown in the previous table. The deliveries of each of the works are scheduled for March 8th (individual), May 24th (in small group) and June 7th (individual) 2027. Refunds will be made in the first 20 working days after the evaluations. No synthesis test is offered.
If a student does not submit a set of activities whose weight is equivalent to a minimum of two-thirds of the total grade for the subject, he will be classified as Not assessable.
To pass the evaluation it is necessary that the student fulfills the following two requirements: i) obtain a minimum qualification of 5 in the global evaluation; ii) obtain an average higher than 5 in the two individual papers. There will only be recovery for individual jobs. If the qualification of an individual work is lower than 5, the students will have to redo it so that it can be evaluated again. The recovery delivery date for individual assignments is June 21th, 2027.
According to UAB regulations, plagiarism or copying of a work, as well as the abusive and/or improperly declared use of artificial intelligence tools will be penalized with a 0, with no possibility of recovery. In the case of group work, the penalty will affect the entire group.
To pass this subject, it is essential to show an attitude compatible with the teaching profession.
To pass this subject, the student must show good general communication skills, both orally and in writing, and a good command of the language or vehicular languages that appear in the teaching guide.
In all activities (individual and in groups), linguistic correction, writing and formal aspects of presentation will therefore be taken into account. Students must be able to express themselves fluently and correctly and must show a high degree of understanding of academic texts. An activity can be returned (not evaluated) or suspended if the teacher considers that it does not meet these requirements.
Unique evaluation
Students who take the single assessment must follow the development of the subject, attending class regularly. The assessable activities are the same as in continuous assessment.
1. Design of contextualized mathematical problems and analysis of students' resolution strategies. Individual. Evaluation weight: 30%
2. Group project of mathematical modeling in a real environment. Individual. Evaluation weight: 40%
3. Research on a real-world phenomenon and the role of mathematics in its resolution and interpretation. Individual. Evaluation weight: 30%
However, THE FOLLOW-UP EVALUATION ACTIVITIES OF THE BLOCK WILL NOT BE SUBMITTED UNTIL THE SAME DAY OF THE FINAL EVALUATION. That's why they will NOT have individualized RETURN of the monitoring evaluation activities of the blocks during the development of the subject. In any case, they will be able to access the general return, whether that is made during the return sessions to the whole class group or those that can be published on the virtual campus that is made by the group.
The same evidence will be collected as for the continuous evaluation, except that for this modality the three works will be individual and will have to be delivered through the virtual campus space coinciding on June 7th, 2027). The recovery system will be the same as for the continuous evaluation.
Dates to consider
Single assessment delivery: June 7th, 2027
Continuous and unique evaluation recovery delivery: June 21th, 2027
Bibliography
Albarracín, L., & Ärlebäck, J. B. (2022). Esquemas de resolución de problemas de Fermi como herramienta de diseño y gestión para el profesor. Educación Matemática, 34(2), 289-309.
Albarracín, L., & Ärlebäck, J. B. (2025). Exploring the role of assumptions in mathematical modeling teacher training using Fermi problems. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-025-01677-0
Albarracín, L., Badillo, E., Giménez, J., Vanegas, Y. & Vilella, X. (2018). Aprender a enseñar matemáticas en la educación primaria. Editorial Síntesis.
Albarracín, L., Gorba, A., & Gorgorió, N. (2022). Un proyecto de modelización matemática para aprender a ir seguros a la escuela. UNO-Revista de Didáctica de las Matemáticas, 95, 64-69.
Barquero, B. (2023). La modelización matemática en la formación del profesorado: experiencias con los REI-FP para educación primaria. Revista Interuniversitaria de Formación del profesorado, 37(2).
Brunet Biarnes, M. (2026). Propuesta para utilizar los problemas de Fermi como actividad de modelización matemática en educación primaria. Epsilon, (122), 73-90.
Fernández, J. M. M., & Montejo-Gámez, J. (2023). Modelización para el desarrollo de la competencia matemática en Educación Primaria: una experiencia de aula. Unión, 19(68).
Trelles, C., Toalongo, X., & Alsina, Á. (2022). Una actividad de modelización matemática en primaria con datos auténticos de la COVID-19. Enseñanza de las ciencias: revista de investigación y experiencias didácticas, 40(2), 193-213.
Software
No specific software is used.
Course groups and languages
The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE
| Type of teaching | Group | Language | Semester | Shift |
|---|---|---|---|---|
| (TE) Theory | 20 | Catalan | second semester | morning-mixed |