
Mathematics Learning and Curriculum
Code: 102061Credits: 6
| Degree programme | Type | Course |
|---|---|---|
| Primary Education | OB | 2 |
Contact lecturer
- Name :
- Albert Mallart Solaz
- Email :
- albert.mallart@uab.cat
Teaching staff
- Angel Ramos Jiménez
- Sofía Caviedes Barrera
- Genaro De Gamboa Rojas
Group languages
You can consult this information at the end of the document.
Prerequisites
This course requires a basic level of mathematics equivalent to that achieved in Secondary Education (12-16). Moreover, as we know that mathematics has often been seen as a set of formulas and techniques, it is important that students enrolling in this course have an open and critical attitude with this view, developing a new approach to mathematics from different perspectives. It is strongly recommended that students have passed the course "Mathematics for teachers".
Objectives
The purpose of this course is to acquire a deep knowledge of the mathematical content in the Primary School Curriculum. Several curricular documents will be analyzed in order to show the students different resources that allow them to contextualize the mathematical knowledge in their future teaching. In addition to providing students with educational tools to develop basic mathematical content, this course also aims to provide them with methodological tools that allow them to create rich educational activities that could be applied for teaching other subjects. The specific objectives of this subject are:
- Understanding different frames of reference for mathematics curricula and learn to interpret them.
- Acquiring didactical and professional knowledge of the processes involved in the learning of mathematics, in particular, the connections that exist between mathematical ideas and also between mathematic and other areas. In this regard, it is also important to be aware of the connection between the patterns in our environment and mathematical structures.
- Acquiring didactical knowledge of the appropriate teaching materials to carry out, asses and interpret mathematical tasks in geometry and numbers, encouraging imagination and visual thinking.
Learning outcomes
- Recognising the contributions of mathematical skill to the core skills as a whole.
- Meet all the objectives, content, process and criteria for specific evaluation in the area of mathematics in primary education.
- Establish concrete relations by means of educational proposals in the different areas of the primary education curriculum.
- Have solid knowledge of the teaching of arithmetic and geometry.
- Possess indicators to evaluate and design proposals for mathematics education from the perspective of gender equity and equality.
- Understand and critically evaluate educational software and adequate websites for the teaching and learning of mathematics.
- Recognising the potential of new technologies for attending to the diversity of levels of learning mathematics.
- Identify the social, economic and environmental implications of academic and professional activities within one?s own area of knowledge.
- Propose ways to evaluate projects and actions for improving sustainability.
Contents
1. The mathematics curriculum
1.1 Structure of the current curricular documents in mathematics
1.2 Contrast between different curricular documents
1.3 Analysis of the mathematical content in the curriculum
1.4 Processes in the mathematics curriculum
2. Curriculum’s organization: Numbers and calculation
2.1 Numbers to count and calculate. Decimal numeral system
2.2 Situations and problems of arithmetic: additive thinking. Calculation by counting. Calculation by structuring. Formal calculation
2.3 Situations and problems of arithmetic: multiplicative thinking. Acquiring basic skills and properties
2.4 Use of algorithm and reasoned calculation
2.5 Estimation and approximation. Numerical sense
2.6 Exact calculation, written calculation and calculator
2.7 Analysis of class situations, textbooks and TAC (Technologies for learning and communication) applications
3. Curriculum’s organization: Space and shape
3.1 Knowledge of flat shapes: lines, polygons and puzzles. Classifications using basic elements of geometry
3.2 Relationship 2D-3D. Orientation on the plane and space. Labyrinths, roads and coordinates
3.3 Study of shape. Geometric solids. Construction of polyhedra and 3D puzzles. Curves and generation of solids of revolution
3.4 Use of different materials for the teaching of geometry
3.5 Analysis of class situations, textbooks and TAC (Technologies for learning and communication) applications
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Project development and problem solving | 15 | 0.6 | 1, 2, 3, 5, 6, 7 |
| Masterclass | 15 | 0.6 | 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Classroom practices | 30 | 1.2 | 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Individual work | 75 | 3 | 1, 2, 3, 4, 5, 6 |
| Individual or small group tutorials | 15 | 0.6 | 2, 3, 4, 5, 6, 7 |
The teaching proposal is based on a methodology of active and face-to-face work in the classroom. At the same time, students must complete the proposed tasks punctually in order to adequately follow the teaching of the subject. The student has to 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 specific assessment activities and the criteria for grading them will be the same for everyone enrolled in the course. In Mathematics, the result of each activity or problem can be arrived at in different ways. This premise is what allows us to promote an inclusive vision of mathematics learning.
With regard to the gender perspective, and in line with the proposals of the Observatory for Equality of the UAB, this subject works explicitly with materials and knowledge produced by women scientists.
Development of projects and problem solving
Work sessions in small or large groups where problems are solved and projects are developed related to the mathematical contents involved in the course. The students responsible for the task will present their work orally and the teacher will validate the mathematical knowledge involved with the active participation of the rest of the students.
Master classes
Presentation by the lecturer of the main contents of the course with the active participation of the students.
Practical or research work
Small group work sessions in which research activities are proposed and students complete them under the guidance of the lecturer.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Planning, resolution and reporting of activities | 15% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Project planning, development and reporting | 15% | 0 | 0 | 1, 2, 3, 4, 5, 7, 9 |
| Individual written test on the curriculum and numbering | 20% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Individual final exam | 50% | 0 | 0 | 1, 2, 3, 4, 5, 6, 7 |
The student must work taking into account that learning mathematics requires daily practice. Learning is based on DOING mathematics, showing a proactive attitude. It is expected that the student, autonomously, assumes responsibility for expanding and consolidating their foundational mathematical knowledge.
The specification of some of the assessment activities will depend on whether the student opts for continuous assessment or single assessment. The evaluation criteria will be the same for all students enrolled in the course.
When it is considered that the student has not been able to provide sufficient assessment evidence, the course will be graded as not assessable. This will occur when the student does not participate in all of the assessment tasks proposed in the course.
TYPE AND WEIGHT OF THE ASSESSMENT ACTIVITIES:
The assessment activities have various types, and the period for providing feedback, returns or grades will not exceed 20 working days of the academic calendar:
- Planning, resolution and report of activities: A series of interrelated mathematical activities will be proposed to be developed in small groups, which will be presented and discussed in seminars (15% of the course grade).
- Planning, development and project report: Students, organized in small groups, will be required to plan and develop a geometry project that they will have to present to the rest of their classmates (15% of the course grade).
- Individual problem-solving test: For the first two blocks of the course (Block I: Curriculum; Block II: Numeration and calculation), students must complete an individual monitoring test (20% of the course grade).
CALCULATION OF THE COURSE GRADE
The final course grade is the weighted average of the marks of the assessment activities of the monitoring of the first two blocks (20%), the Planning, resolution and report of activities (15%), the Planning, development and report of the geometry project (15%), and the mark obtained in the final exam or the resit exam (with a weight of 50%), under the following conditions:
- In order to be able to calculate the weighted average with the rest of the course marks, the student must have obtained at least 5 in the final exam or the resit exam. If the student does not obtain at least 5 in the final exam or the resit, the course is not passed and the final grade will be 3.
- Late submission of assessment activities results in a 0.
- Absence from the monitoring test of the first two blocks results in a 0.
- Assessment activities are not recoverable under any circumstances, except for the final written exam.
- Even if the student has passed the final exam or, where applicable, the resit, if the weighted average does not reach 5, the student does not pass the course and the final grade recorded will be 3.
OTHER CONSIDERATIONS REGARDING ASSESSMENT
The student must take into account the following regulatory considerations:
- Calculators are not allowed in individual written tests, unless indicated by the lecturer.
- The use of Artificial Intelligence tools in assessment activities is not allowed. In this course, the use of AI technologies is not permitted at any stage. Any work containing AI-generated fragments will be considered a breach of academic integrity and will result in a penalty of 0 for the activity, or more severe sanctions in serious cases.
- All assessment activities are compulsory for all students.
- The grade of group work is not necessarily the individual grade of each student in that group.
- Students who do not attend seminar sessions during the development of monitored assessment activities will receive a maximum grade of 5 in those activities.
- Copying or plagiarism in any assessment activity results in a 0 in the course.
ATTENDANCE AND ASSESSMENT
The course is face-to-face. Students who do not attend seminar sessions during assessment activities will receive a maximum grade of 5 in those activities. This applies to both continuous and single assessment students.
CONTINUOUS ASSESSMENT
Students under continuous assessment will complete the individual problem-solving test one week after the end of Block II (Numeration and calculation), as well as submit the activities. Lecturers will publish the dates when releasing the syllabus, as they depend on the timing of the blocks. In principle, this will be the ninth session of each group, provided conditions allow it (G21 on 21/4/27, G31 and G41 on 22/4/27, G71 on 30/4/27).
FINAL EXAM: After completing the course, there will be an individual final exam covering all course content (50%). Dates:
- G21: 9/6/27
- G31 and G41: 27/5/27
- G71: 4/6/27
RESIT EXAM: Students with an average above 3.5 but below 5 may take a resit exam (50%, replacing the final exam mark). It will take place two weeks after the final exam, depending on the group’s schedule.
Note: Only the final exam can be resat. The test of the first two blocks and group work cannot.
The submissions and test for the first two blocks will take place one week after each block ends, as described above.
The dates for the final and resit exams are the same for all students enrolled.
SINGLE ASSESSMENT
Students opting for single assessment must follow the course regularly, attending classes. However, they will NOT SUBMIT MONITORING ASSESSMENT ACTIVITIES UNTIL THE DAY OF THE FINAL ASSESSMENT. Therefore, they will NOT receive individualized feedback during the course. They may, however, access general feedback provided in class or on the virtual campus.
Students under single assessment must submit all evidence and complete a validation test of that evidence. This is required because they will have had access to feedback processes and corrected materials from peers.
Submission and validation will take place on the same dates as the final exam:
- G21: 9/6/27
- G31 and G41: 27/5/27
- G71: 4/6/27
Students must submit written reports and complete a validation activity; the weight of these validation tasks is included in the same percentages (15% activities, 15% project).
On that day, they must:
- Take the final exam (same conditions as others; same applies to the resit if needed)
- Take the individual monitoring test for the first two blocks
- Submit activities and complete validation
- Submit the geometry project and complete validation
Students with an average between 3.5 and 5 may take the resit, under the same conditions.
The weighting and grading system are identical for all students.
It is essential that single-assessment students reserve THE ENTIRE DAY for the final assessment.
REPEATING STUDENTS
From the 2023–24 academic year, THERE WILL BE NO SYNTHESIS EXAM in this course. Students retaking the course may choose between continuous or single assessment under the same conditions. It is recommended they ensure full availability.
NOTE
To pass this course, students must demonstrate good communicative competence, both oral and written, and a strong command of the language(s) used. Linguistic accuracy, writing quality, and presentation will be assessed. Work may be returned (not graded) or failed if it does not meet these requirements.
Bibliography
Books of reference
Burgués, C. (2013). Competències bàsiques de l'àmbit matemàtic. Identificació i desplegament a l'educació primària. Generalitat de Catalunya. Departament d'Ensenyament.
Cil, O., & Akçay, A. O. (2025). A mixed‑method quasi‑experimental study on transforming preservice teachers’ mathematics anxiety and teaching self‑efficacy beliefs. Journal of Mathematics Teacher Education, 28(1), 179–209.
NCTM. (2003). Principios y estándares para la educación matemática. Granada: Sociedad Andaluza de Profesores de Matemáticas.
TAL Team (2001). Children learn mathematics. Utrecht: Freudenthal Institute and National Institute for Curriculum Development.
TAL Team (2005). Young children learn measurement and geometry. Utrecht: Freudenthal Institute and National Institute for Curriculum Development.
Software
In this subject it is necessari to have access to a basic text processor, a presentation tool, spreadsheets and a pdf reader. Some free software (e.g. Geogebra) can be used under teacher's judegement. It is no necessary to buy or get any particular license.
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 | 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 |
| (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 | 711 | English | second semester | afternoon |
| (SEM) Seminars | 712 | English | second semester | afternoon |