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Management and Innovation in the Mathematics Classroom

Code: 102059
Credits: 5
2026/2027
Degree programme Type Course
Primary Education OB 3

Contact lecturer

Name :
Sofía Caviedes Barrera
Email :
sofialuisa.caviedes@uab.cat

Teaching staff

Genaro De Gamboa Rojas
Lluís Albarracin Gordo
Sofía Caviedes Barrera
Francisco Javier Rojas Sateler

Group languages

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

Prerequisites

This course requires basic mathematical knowledge equivalent to that acquired in Compulsory Secondary Education. It is also important that students enrolled in the course show an open, reflective and critical attitude towards mathematics, allowing them to approach the discipline from different perspectives: conceptual, didactic, social, cultural and inclusive. In this context, it is recommended that students have previously taken and passed the first-year course “Mathematics for Teachers” and the second-year course “Mathematics Learning and Curriculum”, as they provide a necessary foundation for the analysis, design and management of mathematical teaching and learning situations in Primary Education.

Throughout the course, an inclusive and gender-sensitive perspective on the teaching and learning of mathematics will be promoted, taking into account student diversity and the design of equitable and accessible teaching proposals. This perspective will be reflected in the use of inclusive and non-sexist language, in the selection of classroom materials and contexts that avoid stereotypes, and in the analysis of teaching situations that foster the participation of all students.

Objectives

This compulsory third-year course focuses on the development of professional competences in didactic and mathematical analysis, based on the study of real situations from the Primary Education mathematics classroom. Its aim is to support the design, management and assessment of innovative, interdisciplinary and inclusive mathematical activities.

The course Management and Innovation in the Mathematics Classroom seeks to strengthen students’ ability to relate and integrate the mathematical, curricular and didactic knowledge required for teaching mathematics in Primary Education. Thus, the course develops practical knowledge and the application of the Primary Mathematics curriculum in the planning, design, management and assessment of teaching and learning tasks and sequences. These processes will be addressed particularly through the following contents:

1. Geometry: geometric transformations, symmetry and similarity.

2. Rational numbers: decimals and operations, representations and concept of fraction.

3. Measure: quantities and units of measurement, measurement procedures. Proportionality.

The following objectives are specified:

1. Knowing theoretical elements to analyze educational situations of teaching and learning mathematics in primary school

2. Acquiring professional skills of didactical and mathematical analysis. In the design, planning, management and evaluation of teaching and learning sequences (involving numbers, measurement and geometry)

3. Understanding and analyzing teaching situations, interdisciplinary and innovative situations, identifying mathematical and other contents.

4. Encouraging innovative aspects of mathematics classroom management and use of educational resources.

5. Designing interventions for teaching mathematics in primary school, based on the curriculum and their theoretical guidelines.

Learning outcomes

  1. Understand interdisciplinary teaching situations for the teaching and learning of mathematics.
  2. Establish concrete relations by means of educational proposals in the different areas of the primary education curriculum.
  3. Identifying and creating good mathematical practices.
  4. Analyse an educational situation for the teaching of mathematics, individually or in groups, to assess its relevance and make innovative alternative proposals.
  5. Using a variety of materials and methodologies for learning mathematics, especially in the contents of numbers, geometry and measurement.
  6. Recognising the contributions of professional skills, mathematical skills and didactic analysis skills to the making of decisions about the design, management and evaluation of learning sequences of innovative mathematics in elementary classes.
  7. Understand and critically evaluate educational software and adequate websites for the teaching and learning of mathematics.
  8. Reflecting on classroom practices based on the use of new information and communication technology in order to innovate and improve the teaching task.
  9. Design and justify didactic situations from their curriculum and theoretical guidelines.
  10. Identifying mathematical aspects in daily life and promoting their use in the design of mathematical activities.
  11. Design innovative didactic sequences for the teaching of mathematics, based on the use of contexts and analysis of phenomena that science provides.
  12. Understand and apply indicators for the evaluation and design of proposals for mathematics education from a perspective of gender equity and equality.
  13. Identify the social, economic and environmental implications of academic and professional activities within one?s own area of knowledge.
  14. Propose ways to evaluate projects and actions for improving sustainability.

Contents

1. Mathematical and didactic analysis of school mathematics contents of primary education

1.1. Geometry: geometric transformations, symmetry and similarity.

1.2. Rational numbers: decimal numbers and operations, representations and conceptof fractions.

1.3. Measure: quantities and units of measurement, measurement procedures. Proportionality.


2. Design, planning and analysis of work in primary mathematics classrooms

2.1. To design activities for the mathematics classroom.

2.2. To analyse the pedagogy and mathematics of primary classroom situations.

2.3. To design didactic sequences to promote mathematics competences in the primary school classroom


3. Management and innovation in the mathematics classroom primary

3.1. Methodologies for the work in the classroom: projects, problem solving and collaborative work environments.

3.2. Resources for the work in mathematics classroom: technologies, languages, manipulatives and games.


4. Evaluation of mathematical activity in the primary classroom

4.1. Mathematics assessment: concepts, processes, skills.

4.2. Methodes to evaluate mathematical practices: assessment, correction, rating.

4.3. Moments of assessment in learning mathematics: initial, continuing, summative, final.

Learning activities and methodology

Title Hours ECTS Learning outcomes
Student work on the preparation of written reports, assignments, and oral presentations 62 2.48 1, 3, 4, 6, 10, 12, 13, 14
In-person. Large group 12.5 0.5 1, 4, 8
Tutoring 20 0.8 6, 10, 12, 13
Presentation seminars. Small groups. 4 0.16 6, 10
Technology seminars. Small group 4 0.16 6, 10, 13
Seminars. Small group 17.5 0.7 2, 4, 5, 8, 11
Preparation final assessment 5 0.2 2, 3, 4, 8, 10, 12

There will be weekly large-group sessions and small-group seminars. The large-group sessions, led by the teaching staff, will focus on the analysis and discussion of real situations involving the teaching and learning of mathematics in Primary Education classrooms, as well as on the clarification of the mathematical and didactic concepts and ideas arising from these situations. In order to foster the development of professional competences in didactic and mathematical analysis, the small-group seminars will focus on the study of real situations from Primary Education mathematics classrooms, or on moments of transition between educational stages, linked to mathematical contents of the curriculum. These situations will serve as a starting point for the design, management and assessment of mathematical activities. In addition, the seminars will promote oral presentations, collective discussion and critical reflection on the processes of designing, implementing and analysing mathematics teaching sequences for Primary Education.

Note: Fifteen minutes of one session, within the established schedule, will be reserved for students to complete the surveys on teaching performance and on the course.

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

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Individual work: assessment exam 50% 0 0 3, 4, 5, 6, 7, 8, 10, 12, 13, 14
Pair work: proposal and justification of a sequence of activities within the framework of a learning situation 30% 0 0 3, 4, 6, 7, 10, 13
Group work: oral presentation, implementation of mathematical activities, and subsequent analysis (microteaching) 20% 0 0 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Attendance at a minimum of 80% of the course sessions is compulsory.

This course does not include the single-assessment system.

Assessment will take place throughout the academic semester through the following activities:

  • Oral presentation, implementation and analysis of mathematical activities: Presentations will take place two weeks after the corresponding contents have been worked on in class, linked to geometric transformations or rational numbers.
  • Design of a learning situation: This activity must be submitted three weeks after the end of the content block to which the sequence of activities refers, either geometric transformations or rational numbers.
  • Final written exam: This will take place during the week of 21/12/2026, corresponding to the last teaching week of December.

All assignments must be submitted within the established deadline. In the event of late submission, an additional period of one week may be enabled, during which the maximum grade for the activity will be 5 out of 10. The deadlines for submission and for the return of corrections will be specified in the course programme; under no circumstances may feedback be returned later than 20 working days after submission.

Resit: Students who have not passed the final exam, but have an average grade equal to or higher than 3.5, may sit a resit exam. This exam will have a weight of 50% and will replace the grade of the final exam. It will take place during the week of 18/01/2027, according to the teaching day assigned to each group. Group and pair assignments may also be resubmitted, with a maximum grade of 5 out of 10, and must be submitted on the same day as the resit exam.

In order to calculate the final grade for the course, students must obtain a minimum grade of 5 both in the final exam and in the average of the formative activities: group work and pair work.

Students will receive a grade of not assessable if they do not submit any of the required assignments or if they do not sit the individual exams in December.

Correct use of language is essential in all submissions and assessment activities. Linguistic accuracy will be taken into account in the assessment of all assignments.

Total or partial plagiarism in any activity, as well as copying in an assessment test, will result in a grade of 0 for the corresponding activity and may lead to failing the course, in accordance with current academic regulations.

The use of artificial intelligence tools is restricted to those activities in which the teaching staff explicitly authorise their use. In such cases, students must clearly indicate which parts have been generated or assisted by AI, specify the tools used, and include a critical and ethical reflection on their influence on the work process and on the final result. Lack of transparency in the use of these tools will be considered a breach of academic integrity and will result in a grade of 0 for the activity.

Each student is responsible for demonstrating mastery of the contents assessed in the activities submitted. The teaching staff may request additional oral or written justifications whenever they consider it necessary in order to properly assess the evidence of learning.

In group assignments, the collective grade does not necessarily imply an identical individual grade for all group members. Individual assessment will be determined on the basis of the evidence of learning and each student’s participation in the process and in the final product.

Repeating students: This course does not provide for synthesis exams for repeating students.

Bibliography

  • Alsina, À. (2019). Itinerarios didácticos para la enseñanza de las matemáticas de 6 a 12 años. Graó.
  • Castelnuovo, E. (1981). La matemática: La geometría. Ketres Editora.
  • Chamorro, M. C. (2003). Didáctica de las Matemáticas para Primaria. Pearson Educación.
  • De Keersmaeker, K., Van Hoof, J. y Verschaffel, L. (2023). The relationship between primary school children’s inhibition and the processing of rational numbers. European Journal of Psychology of Education, 38, 1703–1724. https://doi.org/10.1007/s10212-022-00669-y
  • Generalitat de Catalunya. (2022). Decret 175/2022, de 27 de setembre, d’ordenació dels ensenyaments de l’educació bàsica. Diari Oficial de la Generalitat de Catalunya, núm. 8762, 29 de setembre de 2022. https://dogc.gencat.cat/ca/document-del-dogc/?documentId=938401
  • Kuzle, A. (2023). Geometry teaching in transition: An investigation on the importance of school geometry in primary education. Center for Educational Policy Studies Journal, 13(3), 31–56. https://doi.org/10.26529/cepsj.1267
  • NCTM. (2003). Principios y estándares para la educación matemática. Sociedad Andaluza de Profesores de Matemáticas.
  • Pereda Loriente, Á., González-Calero, J.A., Tirado-Olivares, S. y Del Olmo-Muñoz, J. (2025). Enhancing mathematics performance in primary education: The impact of personalized learning on fractions and decimal numbers. Educ Inf Technol 30, 15961–15991. https://doi.org/10.1007/s10639-025-13428-5
  • Rodrigo David , M. G., Chang Dávila, C. F., Wilson Damian, C. O., Guamán Guerrero, M. I. y Granda Chamba, B. D. (2025). Estrategias Activas para Enseñar Fracciones en Primaria: Una Revisión Sistemática. Ciencia Latina Revista Científica Multidisciplinar, 9(5), 6340-6354. https://doi.org/10.37811/cl_rcm.v9i5.19993
  • Segovia, I. y Rico, L. (2011). Matemáticas para maestros de Educación Primaria. Ediciones Pirámide.
  • Smith, M. S., Yurekli, B., y Stein, M. K. (2024). Coaching the 5 practices: Supporting mathematics teachers in orchestrating productive discussions. Corwin.
  • Van den Heuvel-Panhuizen, M. (2008). Children learn mathematics: A learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school (Vol. 1). Brill.
  • Van den Heuvel-Panhuizen, M. y Buys, K. (2008). Young children learn measurement and geometry: A learning-teaching trajectory with intermediate attainment targets for the lower grades in primary school (Vol. 2). Brill.


Web references


Software

To be decided

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 first semester morning-mixed
(TE) Theory 31 Catalan first semester morning-mixed
(TE) Theory 41 Catalan first semester afternoon
(TE) Theory 71 English first semester afternoon
(SEM) Seminars 211 Catalan first semester morning-mixed
(SEM) Seminars 212 Catalan first semester morning-mixed
(SEM) Seminars 311 Catalan first semester morning-mixed
(SEM) Seminars 312 Catalan first semester morning-mixed
(SEM) Seminars 411 Catalan first semester afternoon
(SEM) Seminars 412 Catalan first semester afternoon
(SEM) Seminars 711 English first semester afternoon
(SEM) Seminars 712 English first semester afternoon