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Teaching Innovation and Introduction to Educational Research on Teaching Mathematics

Code: 45584
Credits: 10
2026/2027
Degree programme Type Course
Teaching in Secondary Schools, Vocational Training and Language Centres OP 1

Contact lecturer

Name :
Lluís Albarracin Gordo
Email :
lluis.albarracin@uab.cat

Teaching staff

Juan Carlos Tinoco Balongo
Genaro De Gamboa Rojas
Flavio Ricardo Guíñez Abarzúa
Lluís Albarracin Gordo

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 Baccalaureate.

Objectives

By the end of this course, students should be competent in:

Use educational innovation to diagnose problematic aspects related to student learning, identify relevant elements, design innovation proposals, and assess their impact on improving student learning.

Identify and interpret the role of the resources available for teaching and learning mathematics in Compulsory Secondary Education and Baccalaureate, justifying the suitability of their use in specific contexts.

Interpret the meaning of the specific mathematical competences defined in the curriculum, for the design and implementation of learning situations that promote deep learning of mathematics. Particular emphasis will be placed on mathematical modelling, mathematical connections, and classroom mathematical communication.

To ground teaching practices—specifically the design, implementation, and evaluation of competency-based learning activities and situations—in the knowledge and strategies of mathematics education, using tools specific to research in mathematics education

Learning outcomes

  • CA53 (Manage the teaching action in the school and the classroom, taking into account the characteristics of dialogic interaction, the intentionality of the questions and the role of teachers in activating and regulating mathematics learning.) Manage the teaching action in the school and the classroom, taking into account the characteristics of dialogic interaction, the intentionality of the questions and the role of teachers in activating and regulating mathematics learning.
  • CA54 (Integrate the values and professional commitment towards an education that contributes to the development of a sustainable, egalitarian, diverse and just society that respects human rights into the planning, design, adaptation, implementation and evaluation of sciences.) Integrate the values and professional commitment towards an education that contributes to the development of a sustainable, egalitarian, diverse and just society that respects human rights into the planning, design, adaptation, implementation and evaluation of sciences.
  • KA36 (Select the basic aspects of the curriculum and the professional and teaching knowledge of the content to plan learning situations, action strategies and evaluation strategies suitable for the teaching of mathematics from the perspective of the Universal Design of Learning.) Select the basic aspects of the curriculum and the professional and teaching knowledge of the content to plan learning situations, action strategies and evaluation strategies suitable for the teaching of mathematics from the perspective of the Universal Design of Learning.
  • KA37 (Identify the scientific, social and artistic knowledge necessary to analyse and design interdisciplinary classroom projects that integrate the mathematics curriculum with other subjects.) Identify the scientific, social and artistic knowledge necessary to analyse and design interdisciplinary classroom projects that integrate the mathematics curriculum with other subjects.
  • SA46 (Apply the gender equity perspective to educational action in the mathematics classroom, through an intersectional lens, recognising the problems of the scientific-technological field.) Apply the gender equity perspective to educational action in the mathematics classroom, through an intersectional lens, recognising the problems of the scientific-technological field.
  • SA47 (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.

Contents

1. Mathematical modelling



1.1. The concept of mathematical modelling

1.2. Mathematical models in Secondary Education

1.3. Mathematical modelling and learning situations



2. Resources for teaching mathematics



2.1. Manipulatives for teaching mathematics

2.2. Digital resources for teaching mathematics

2.3. The role of mathematics in project-based learning



3. Teaching innovation in mathematics education



3.1. The concept of innovation in mathematics education

3.2. The use of contexts in teaching mathematics

3.3. Extra- and intra-mathematical connections



4. Introduction to research in mathematics education



4.1. Research questions in mathematics education

4.2. Data analysis and use of evidence in mathematics education

Learning activities and methodology

Title Hours ECTS Learning outcomes
Attendance and participation in lectures, lab practices, field trips, etc., and the completion and assessment of proposed activities. 65 2.6 CA53, CA54, KA36, KA37, SA46, SA47
Completion, review, and evaluation of proposed tasks (reports, case studies, problem solving, presentations). 15 0.6 CA53, CA54, KA36, KA37, SA46, SA47
Analysis of readings and didactic innovation proposals, writing reports, designing activities, analyzing and solving cases. 170 6.8 CA53, CA54, KA36, KA37, SA46, SA47

The methodology combines guided, supervised, and autonomous activities. Students will take an active role.

Guided activities (25%)

Attendance and participation in lectures, lab practices, field trips, etc., and the completion and assessment of proposed activities.

Supervised activities (5%)

Completion, review, and evaluation of proposed tasks (reports, case studies, problem solving, presentations)

Autonomous activities (70%)

Analysis of readings and didactic innovation proposals, writing reports, designing activities, analyzing and solving cases.

Note: 15 minutes of one class will be reserved, within the schedule established by the institution/degree program, for students to complete surveys evaluating teaching performance and the course/module itself.

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
Research Assessment Activity in the Secondary School Classroom - Data Coding 30% 0 0 CA53, CA54, KA36, KA37, SA46, SA47
Evaluation activity: analysis of teaching resources for mathematics education 20% 0 0 CA53, CA54, KA36, KA37, SA46, SA47
Research Assessment Activity in the Secondary School Classroom - Research Question and Objectives 20% 0 0 CA53, CA54, KA36, KA37, SA46, SA47
Evaluation activity: mathematical modelling 30% 0 0 CA53, CA54, KA36, KA37, SA46, SA47

To pass this course, students must demonstrate strong general communication skills, both oral and written, and a good command of the Catalan language.

All tasks must be submitted within the established deadlines. If tasks are not submitted on time, an additional one-week period will be granted, but the maximum grade for each activity will be 5 out of 10.


Evaluation activity: mathematical modelling (30%): This task is carried out in small groups and must be submitted by mid-December.

Evaluation activity: analysis of teaching resources for mathematics education (20%): This task is carried out in pairs and must be submitted by the end of January.

Research Assessment Activity in the Secondary School Classroom - Research Question and Objectives (20%): This task is carried out individually and must be submitted before the start of the second teaching placement.

Research Assessment Activity in the Secondary School Classroom - Data Coding (30%): This task is carried out individually and must be submitted at the end of the course.


To pass the module, students must submit all evaluation activities and obtain a minimum grade of 5 out of 10 in each. If an activity is failed, students will have 10 working days to resubmit it, starting from the day the grade is communicated. If the activity on the design and implementation of rich classroom activities must be resubmitted, a 10-day period for in-person resubmission will be granted, starting from the end of the course.

Feedback on assignments and tests will be provided within 20 working days after submission and/or completion.

Plagiarism is considered a serious offense: if plagiarism is detected in an assignment, it will be invalidated, must be redone, and the maximum grade will be 5.

Correct and appropriate language use is essential in all submissions. Linguistic accuracy will be considered in the evaluation of all work.

A student will be graded as not assessable if they fail to submit assignments that account for more than one third of the final grade.

This course does not allow a synthesis exam in the case of a second enrollment.

For this course, the use of Artificial Intelligence (AI) technologies is permitted exclusively for tasks authorized by the instructor. Students must clearly identify which parts were generated with this technology, specify the tools used, and include a critical reflection on how these influenced the process and the final result of the activity. Failure to disclose the use of AI in any assessable activity will be considered academic dishonesty and will result in a total penalty (zero) for that activity.


Single assessment

Students who opt for the single assessment must follow the course development, attending classes regularly under the same attendance conditions as students in continuous assessment. They will submit all evaluation activities individually on a single date at the end of the teaching period and must pass a validation test for each activity. The activities must be submitted during the last two weeks of the course’s teaching schedule.

Bibliography

Albarracín, L. (2021). Una secuencia de actividades para desarrollar la visualización usando un videojuego. Enseñanza de las Ciencias, 39(2), 181-199.

Albarracín, L., & Ärlebäck, J. B. (2025). Exploring the role of assumptions in mathematical modeling teacher training using Fermi problems. ZDM – Mathematics Education 57(2-3), 213–228.

Alsina, C., Nelsen, R. B. (2006). Math Made Visual. Creating images for understanding Mathematics. MAA, Washington.

Alsina, C., Burgués, C., Fortuny, J.M. (1991). Materiales para construir la geometria. Col·lecció Matemáticas: cultura y aprendizaje, número 11. Síntesis.

Badillo, E.; García, L.; Marbà, A. y Briceño, M. (2012). El desarrollo de competencias en las clases de ciencias y matemáticas. Universidad de los Andes.

Caviedes, S., De Gamboa, G., & Badillo, E. (2024). Mathematical connections involved in area measurement processes. Research in Mathematics Education, 26(2), 237-257.

CREAMAT Centre de Recursos per Ensenyar i Aprendre Matemàtiques (Departament d'Educació): http://phobos.xtec.cat/creamat/joomla/.

Font, V. (2005). Reflexión en la clase de Didáctica de las Matemáticas sobre una "situación rica", en Badillo, E. Couso, D., Perafrán, G., Adúriz-Bravo, A. (eds) Unidades didácticas en Ciencias y Matemáticas (pp. 59-91). Magisterio: Bogotá.

Font, V.; Giménez, J.; Larios, V. y Zorrilla, J. F. (2012). Competencias profesionales del profesor de matemáticas de secundaria y bachillerato. Barcelona: Publicacions i Edicions de la Universitat de Barcelona.

Goñi, J. M. (2012) Didáctica de las matemáticas. Formación del profesorado de secundaria en matemáticas. Barcelona: Editorial Graó/Ministerio de Educación.

Guiñez, F., & Ferrando, I. (2025). Desafío Internacional de Modelización Matemática (IMMC): Experiencias en Chile y España. Uno: Revista de didáctica de las matematicas, (107), 37-42.

Hernán, F., Carrillo, E. (1991). Recursos en el aula de Matemáticas. Col·lecció Matemáticas: cultura y aprendizaje, número 34. Ed. Síntesis, Madrid.

Software

In this course, activities are proposed to develop the students’ DDC.

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