Important notice
The course guide is provisional.
The PDF version of the course guide may take a few days to become available in the DDD.
Teaching Mathematics
Code: 44321Credits: 15
| Degree programme | Type | Course |
|---|---|---|
| Teaching in Secondary Schools, Vocational Training and Language Centres | OP | 1 |
Contact lecturer
- Name :
- Genaro De Gamboa Rojas
- Email :
- genaro.degamboa@uab.cat
Teaching staff
- Lluís Albarracin Gordo
- Edelmira Rosa Badillo Jimenez
- José Abraham de la Fuente Pérez
- David Lobo Sanchiz
- Maria Salo Casajuana
- Daniel Soria Duarte
- Flavio Ricardo Guíñez Abarzúa
- Jordi Deulofeu Piquet
- Edgar Ribot Llobet
Group languages
You can consult this information at the end of the document.
Prerequisites
Mastery of the mathematics that make up the curriculum of Compulsory Secondary Education and the High School/A-level/Baccalaureate.
Objectives
By the end of the Master's, students must be competent in:
Use fundamentals of mathematics didactics to interpret students’ mathematical thinking in a classroom context aimed at making decisions related to the design, management, and assessment of mathematical activity occurring in the classroom.
Know and use the characteristics of mathematics learning to design, manage, and assess mathematical activities in secondary education and baccalaureate.
Know and use didactic resources to design and manage learning situations that foster mathematical thinking.
Know and interpret the curricular elements that determine how mathematics teaching should be (specific competencies, knowledge, and meanings).
Know classroom management resources to foster communication and reasoning in mathematics classes.
Know and use formative and training assessment tools that help students self-regulate their learning.
Learning outcomes
- CA50 (Create exemplary learning situations that promote inclusive competency-based learning in mathematics, including problem-solving activities, mathematical modelling and integration of the history of mathematics as a discipline of knowledge, among others.) Create exemplary learning situations that promote inclusive competency-based learning in mathematics, including problem-solving activities, mathematical modelling and integration of the history of mathematics as a discipline of knowledge, among others.
- CA51 (Apply the key aspects of educational and training assessment integrated into paradigmatic examples of the assessment of mathematics learning.) Apply the key aspects of educational and training assessment integrated into paradigmatic examples of the assessment of mathematics learning.
- CA52 (Demonstrate the digital teaching competence of mathematics teachers, including the appropriate use of dynamic geometry programmes, digital measurement instruments, simulations, real-time sensors, among others.) Demonstrate the digital teaching competence of mathematics teachers, including the appropriate use of dynamic geometry programmes, digital measurement instruments, simulations, real-time sensors, among others.
- KA34 (Describe situations with potential for improvement in the self-observation and co-observation of mathematics teaching and learning situations, whether face-to-face or video, both in real and simulated classrooms, identifying positive and problematic key aspects from the perspective of mathematics teaching.) Describe situations with potential for improvement in the self-observation and co-observation of mathematics teaching and learning situations, whether face-to-face or video, both in real and simulated classrooms, identifying positive and problematic key aspects from the perspective of mathematics teaching.
- KA35 (Remember the curricular contents of mathematics, as well as the body of teaching knowledge around the respective teaching and learning processes.) Remember the curricular contents of mathematics, as well as the body of teaching knowledge around the respective teaching and learning processes.
- SA43 (Base the teaching action of design, implementation and evaluation of competency-based learning activities and situations on the knowledge and strategies of mathematics teaching.) Base the teaching action of design, implementation and evaluation of competency-based learning activities and situations on the knowledge and strategies of mathematics teaching.
- SA44 (Apply the disciplinary contents and the secondary education mathematics curriculum from a literacy and educational vision for society as a whole.) Apply the disciplinary contents and the secondary education mathematics curriculum from a literacy and educational vision for society as a whole.
- SA45 (Evaluate scientific and educational information from the perspective of critical thinking applied to the teaching of mathematics, including the mastery and application of knowledge specific to the area of research in mathematics teaching.) Evaluate scientific and educational information from the perspective of critical thinking applied to the teaching of mathematics, including the mastery and application of knowledge specific to the area of research in mathematics teaching.
Contents
Contents
1. Introduction to mathematics didactics
1.1 Mathematics education
1.2 Learning mathematics
1.3 Competency-based mathematics and the new curriculum
1.4 Teaching mathematics
2. Mathematical and didactic analysis of primary education curriculum mathematical content
2.1 Plane and spatial geometry
2.2 Real and complex numbers
2.3 Measurement
2.4 Algebra: functions, equations, and inequalities
2.5 Probability and statistics
3. Design, planning, and analysis of classroom work in secondary and baccalaureate mathematics
3.1 Designing activities in the mathematics classroom
3.2 Didactic and mathematical analysis of secondary classroom situations
3.3 Designing competency-based didactic sequences in secondary mathematics classrooms
4. Problem solving
4.1 Problems and rich mathematical activities
4.2 Problem-solving heuristics
4.3 The role of communication in problem solving
4.4 Problem solving as a historical driver of the development of mathematical knowledge
5. Assessment of mathematical activity in secondary and baccalaureate classrooms
5.1 Assessment content in mathematics: concepts, processes, competencies
5.2 Forms of assessment of mathematical practices: assessment, correction, grading
5.3 Assessment moments in mathematics learning: initial, continuous, summative, final
6. Management of the mathematics classroom in secondary and baccalaureate
6.1 Classroom working methodologies to promote mathematical communication and reasoning
6.2 Resources for mathematics classroom work: technological, linguistic, manipulative, and playful
6.3 Contributions from mathematics didactics research to the design of mathematical didactic sequences
Learning activities and methodology
| Title | Hours | ECTS | Learning outcomes |
|---|---|---|---|
| Directed activities - Attendance and participation in lectures, laboratory practices, outings, etc., and the completion and assessment of proposed activities. | 97.5 | 3.9 | CA50, CA51, CA52, KA34, KA35, SA43, SA44, SA45 |
| Autonomous activities - Analysis of readings and innovative didactic proposals, report writing, activity design, and analysis and resolution of cases. | 202.5 | 8.1 | CA50, CA51, CA52, KA34, KA35, SA43, SA44, SA45 |
| Supervised activities - Completion, revision, and assessment of proposed tasks (reports, case studies, problem solving, presentations). | 75 | 3 | CA50, CA51, CA52, KA34, KA35, SA43, SA44, SA45 |
The methodology combines directed, supervised, and autonomous activities. Students will have an active role, participating in secondary class simulations.
- Directed activities (25%)
Attendance and participation in lectures, laboratory practices, outings, etc., and the completion and assessment of proposed activities. - Supervised activities (5%)
Completion, revision, and assessment of proposed tasks (reports, case studies, problem solving, presentations). - Autonomous activities (70%)
Analysis of readings and innovative didactic proposals, report writing, activity design, and analysis and resolution of cases.
Note: 15 minutes of one class will be reserved, within the calendar established by the institution/program, for students to complete surveys evaluating teaching performance and the course/module.
In this course, activities are proposed to develop students' DTC. In particular, the appropriate use of dynamic geometry software, digital measuring instruments, simulations, and real-time sensors, among others, will be addressed.
Assessment
Continuous assessment activities
| Title | Weight | Hours | ECTS | Learning outcomes |
|---|---|---|---|---|
| Design and implementation of rich activities in the classroom | 50% | 0 | 0 | CA50, CA51, CA52, SA43, SA45 |
| Mathematical and didactic analysis of materials and student productions | 40% | 0 | 0 | KA34, KA35, SA43, SA44 |
| Introductory didactics assessment activity | 10% | 0 | 0 | KA34, KA35, SA43, SA44 |
All assessment tasks must be submitted by the established deadline. If a task is not submitted on time, an additional one-week submission period will be granted; however, the maximum grade for that activity will be capped at 5 out of 10.
Assessment will be carried out continuously throughout the academic year through the following activities:
- Introduction to Mathematics Education Activity (10%): This activity is completed in pairs and must be submitted at the end of the first introductory block on mathematics education.
- Mathematical and Didactic Analysis of Teaching Materials and Student Work (40%): These activities are completed individually, are linked to the curriculum content blocks, and must be submitted at the end of the corresponding block.
- Design and Implementation of Rich Classroom Activities (50%): This component involves the design, implementation, and analysis of rich mathematical activities. These activities are completed in groups, are linked to the curriculum content blocks, and must be submitted and presented at the end of the corresponding block.
To pass the course, students must submit all assessment activities and obtain a minimum grade of 5 out of 10 in each of them. If a student fails any assessment activity, a resubmission period of 10 working days will be provided, starting from the date on which the grade is communicated. If the Design and Implementation of Rich Classroom Activities component must be retaken, a 10-working-day period will be provided for the in-person resubmission, beginning on the last day of teaching for the course.
Feedback on assignments and tests will be provided within a maximum of 20 working days after the submission or completion date.
Plagiarism is considered a serious academic offence. If plagiarism is detected in an assignment, the assignment will be declared invalid, must be redone, and the maximum possible grade will be 5 out of 10.
Correct and appropriate use of language is essential in all submitted work. Linguistic accuracy will be taken into account in the assessment of all assignments.
Students will receive a grade of Not Assessed (NA) if they fail to submit assessment activities whose combined weighting exceeds one-third of the final course grade.
This course does not offer a comprehensive final assessment (prova de síntesi) for students enrolling in the course for a second time.
For this course, the use of Artificial Intelligence (AI) technologies is permitted only for those tasks explicitly authorized by the course instructor. Students must clearly identify which parts of their work have been generated using AI, specify the tools used, and include a critical reflection on how these tools influenced both the process and the final outcome of the activity. Failure to disclose the use of AI in an assessed activity will be considered a breach of academic integrity and will result in a grade of zero for that activity.
SINGLE ASSESSMENT
Students who choose the single assessment option must follow the course throughout the semester, attending classes regularly under the same attendance requirements as students following continuous assessment. They must submit all assessment activities individually on a single date at the end of the teaching period and must also pass a validation assessment for each activity. All assessment activities must be submitted during the last two weeks of the course timetable.
Bibliography
Albarracín, L., i 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., i Gorgorió, N. (2014). Devising a plan to solve Fermi problems involving large numbers. Educational Studies in Mathematics, 86(1), 79–96.
Alsina, C., Burgués, C., i Fortuny, J. (2001). Ensenyar matemàtiques. Graó.
Ascher, M. (1991). Ethnomathematics. Wadsworth.
Azcárate, C., i Deulofeu, J. (1998–2004). Guías Praxis para el profesorado. Matemáticas. ESO. Wolters Kluwer.
Bishop, A. J. (1999). Enculturación matemática. Paidós Ibérica.
Calvo, C., Deulofeu, J., Jareño, J. i Morera, L. (2017). Aprender a enseñar matemáticas en laeducación secundaria obligatoria. Síntesis.
Cockcroft, W. H. (1985). Las matemáticas sí cuentan. Informe Cockcroft. Ministerio de Educación y Ciencia. (Treball original publicat el 1982)
Corbalán, F. (1998). Juegos matemáticos para secundaria y bachillerato. Síntesis.
Courant, R., i Robbins, H. (1979). ¿Qué es la matemática? Aguilar.
Generalitat de Catalunya. (2022). Decret 175/2022, de 27 de setembre, d'ordenació dels ensenyaments de l'educació bàsica (DOGC núm. 8762). https://projectes.xtec.cat/nou-curriculum/educacio-basica/decret-educacio-basica/
Gardner, M. (2009). ¡Ajá! Inspiración. RBA.
Goñi, J. M. (Ed.). (2010a). Matemáticas. Complementos de formación disciplinar. Graó.
Goñi, J. M. (Ed.). (2010b). Didáctica de las matemáticas. Graó.
Goñi, J. M. (Ed.). (2010c). Matemáticas. Investigación, innovación y buenas prácticas. Graó.
López, M., Albarracín, L., Ferrando, I., Montejo, J., Ramos, P., Serradó, A., Thibaut, R. i Mallavibarrena, R. (2020). La Educación Matemática en las enseñanzas obligatorias y el bachillerato. A D. Martín, T. Chacón, G. Curbera, F. Marcellán i M. Siles (Coords.), Libro Blanco de las Matemáticas (pp. 1–94). Real Sociedad Matemática Española.
Mason, J., Burton, L., i Stacey, K. (1988). Pensar matemáticamente. Labor-MEC.
National Council of Teachers of Mathematics. (2004). Principios y estándares para la educación matemática. Sociedad Andaluza de Educación Matemática Thales.
Palmer, M. (2018). Las matemáticas de la vida cotidiana. La realidad como recurso de aprendizaje y las matemáticas como medio de comprensión. Miradas Matemáticas, Madrid España.
Pérez, A., i Sánchez, M. (Eds.). (2009). Matemáticas para estimular el talento: Actividades del proyecto Estalmat. Sociedad Andaluza de Educación Matemática Thales.
Pólya, G. (1965). Cómo plantear y resolver problemas. Trillas.
Pólya, G. (1981). Mathematical discovery. John Wiley & Sons.
Diversos autors. (2011). Col·lecció El mundo es matemático. RBA.
Recursos web d'interès
CREAMAT. Centre de Recursos per Ensenyar i Aprendre Matemàtiques. https://phobos.xtec.cat/creamat/joomla/
DivulgaMAT. Centro Virtual de Divulgación de las Matemáticas. https://www.divulgamat.net/
Software
In this course, activities are proposed to develop students' DTC.
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 |
|---|---|---|---|---|
| (TEmRD) Teoria (màster RD) | 1 | Catalan | annual | morning-mixed |