Course guide of Teaching and Learning of Mathematics in Primary Education (2561127)

• To have completed the subject Basic Mathematics for Primary Education of the Primary Education Teacher Training of the University of Granada.
• The use of artificial inteligence tools in the context of this course will follow the policy of the UGR estated in the following document: "Documento de Recomendaciones para el uso de la Inteligencia Artificial en la Universidad de Granada", aprobado en la sesión ordinaria del Consejo de Gobierno de 16 de diciembre de 2024": https://ceprud.ugr.es/sites/centros/ceprud/public/ficheros/Recomendaciones_IA_en_UGR.pdf
• When preparing written work, it is recommended to follow the guidelines contained in the "Guía del uso no sexista del lenguaje", published by the Vicerrectorado de Igualdad, Inclusión y Sostenibilidad de la Universidad de Granada and available at: https://viics.ugr.es/sites/vic/viics/public/inlinefiles/Guia%20de%20Lenguaje.%20Maquetado.pdf

Foundations of Didactics of Mathematics. Teaching and learning of the different thematic cores of mathematics in Primary Education (Arithmetic, Geometry, Measurement, Statistics and Probability, and Algebra), specified in cognitive aspects (mathematical learning, errors and difficulties) and didactic aspects (tasks and activities, materials and resources), referring to the number sense, algebraic sense, measurement sense, spatial sense and stochastic sense.

The following objectives are proposed for this subject:

• Know and value the social and cultural importance of mathematics as well as its role in the educational system and in the curriculum.
• Characterize the learning of schoolchildren at different ages based on the competencies that they must develop from mathematics in Primary Education.
• Interpret the role of error in learning mathematics and describe the main errors and difficulties that may arise in the process of learning mathematics in Primary Education.
• Pose and solve mathematical problems of different complexity through a variety of ways, contrasting the convenience of each one and analysing the role they can play in teaching.
• Describe and analyse different teaching strategies and techniques that promote the development of mathematical competence in schoolchildren in an environment of equity and respect.
• Know and use appropriate means, materials and resources in the teaching of mathematics, with special attention to information and communication technologies.
• Consolidate specialized knowledge of mathematical content from the specific perspective of teaching and learning in Primary Education.
• Perform queries, searches and reports on the teaching and learning of mathematics with autonomy, clarity, precision and rigor.

• Unit 1. Mathematics, culture and society. The social and cultural importance of mathematics. Mathematics in the educational system. Purposes of mathematics education. Solving mathematical problems.
• Unit 2. Mathematical sense. Number sense. Measurement sense. Spatial and geometric sense. Stochastic sense. Algebraic sense. Features and components.
• Unit 3. Learning of mathematics. Learning expectations, stages of learning, errors and difficulties in learning mathematics. Diagnosis and treatment of difficulties in mathematics.
• Unit 4. The teaching of mathematics. The role of the mathematics teacher, teaching techniques and strategies. Activities and tasks in mathematics, the role of materials and resources. A problem-solving-based methodology for teaching mathematics.

• Problem solving in mathematics.
• Mathematical knowledge in Primary Education.
• Identification, analysis and classification of errors and difficulties in school problems in Primary Education.
• Analysis, selection and design of mathematical tasks, according to components of mathematical sense and knowledge put into play.

• Burgos, M. (2023). Razonamiento algebraico elemental. Implicaciones en la formación de profesores. Universidad de Almería.
• Consejería de Desarrollo Educativo y Formación Profesional, CDEFP. (2023). Orden de 30 de mayo de 2023, por la que se desarrolla el currículo correspondiente a la etapa de Educación Primaria en la Comunidad Autónoma de Andalucía, se regulan determinados aspectos de la atención a la diversidad y a las diferencias individuales, se establece la ordenación de la evaluación del proceso de aprendizaje del alumnado y se determina el proceso de tránsito entre las diferentes etapas educativas. Boletín Oficial de la Junta de Andalucía, núm. 104. Sevilla: Autor.
• Flores, P. y Rico, L. (Eds.) (2015). Enseñanza y aprendizaje de las matemáticas en Educación Primaria. Pirámide.
• Godino, J. D. (Dir.) (2004). Didáctica de las matemáticas para maestros. Departamento de Didáctica de la Matemática. Universidad de Granada. Disponible en: http://www.ugr.es/local/jgodino/.
• Jefatura del Estado. (2020). Ley Orgánica 3/2020, de 29 de diciembre, por la que se modifica la Ley Orgánica 2/2006, de 3 de mayo, de Educación. Madrid: Autor.
• MECD. (2022a). Real Decreto 157/2022, de 1 de marzo, por el que se establecen la ordenación y las enseñanzas mínimas de la Educación Primaria. BOE, 52, 2 de marzo de 2022.
• MECD. (2022b). Orden EFP/279/2022, de 4 de abril, por la que se regulan la evaluación y la promoción en la Educación Primaria, así como la evaluación, la promoción y la titulación en la Educación Secundaria Obligatoria, el Bachillerato y la Formación Profesional en el ámbito de gestión del Ministerio de Educación y Formación Profesional. BOE, 84, 8 de abril de 2022.
• NCTM (2000). Principles and Standards for School Mathematics. NCTM.
• OECD (2018). PISA 2021 Mathematics Framework (Draft). Disponible a través de https://www.oecd.org/pisa/sitedocument/PISA-2021-mathematics-framework.pdf.

• Alsina, Á. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12 años). Graó Educación. ISBN 978-84-9980-938-0.
• Alsina, Á., Burgués, C. y Fortuny, J.M. (1998). Enseñar matemáticas. Graó.
• Bihsop, A. J (1999). Enculturación matemática. La educación matemática desde una perspectiva cultural. Temas de educación. Paidós.
• Carrillo Yáñez, J. (Coord.). (2016). Didáctica de las matemáticas para maestros de Educación primaria. Paraninfo.
• Castro, E. (Ed.) (2001). Didáctica de la matemática en educación primaria. Síntesis.
• Chamorro C. (2003). Didáctica de las matemáticas para primaria. Pearson-Prentice Hall.
• Godino, J. D. (2004). Matemáticas para maestros. Departamento de Didáctica de la Matemática. Universidad de Granada.
• Jiménez, J. (1997). Evaluación en matemáticas. Una integración de perspectivas. Síntesis.
• Martínez Montero, J. y Sánchez Cortés, C. y de la Rosa-Sánchez, J. M. (2020). Enseñar matemáticas con el método ABN. En 4º, 5º y 6º y preparación para la ESO. Wolters Kluwer.
• Resnick, L. y Ford, W. (1990). La enseñanza de las matemáticas y sus fundamentos psicológicos. Paidós-MEC.
• Rico, L., Fortuny, J. M. y Puig, L. (1987-91). Matemáticas, cultura y aprendizaje (colección). Síntesis.
• Segovia, I. y Rico, L. (Eds.) (2013). Matemáticas para maestros de Educación Primaria. Pirámide.
• Van de Walle, J. A. (2009) Elementary and Middle School Mathematics. Teaching Developmentally. Pearson

This bibliography will be completed with documents and articles from specialized journals, as well as mathematics textbooks for Primary Education from various publishers and their corresponding teacher's guides.

Other resources:

• Mathematics textbooks for Primary Education.
• Materials and resources for the teaching of mathematics in Primary Education.

Examples of websites with virtual educational resources or teaching units:

• http://clic.xtec.cat/db/listact_es.jsp (Spanish)
• https://es.mathigon.org/polypad (Spanish)
• https://www.geogebra.org (English, Spanish, etc.)
• http://illuminations.nctm.org (English)
• https://intef.es (Spanish)
• https://intef.es/recursos-educativos/situaciones-aprendizaje (Spanish)
• https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Algebra (English)
• https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Geometry (English)
• https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Measurement (English)
• https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/Number-and-Operations (English)
• http://nlvm.usu.edu/es (Spanish)
• https://nrich.maths.org (English)
• https://pensamientoalgebraico.es/es/actividades/primaria-6-11-anos (Spanish)
• https://tuvalabs.com (Spanish)
• https://www.ugr.es/~jgodino/edumat-maestros/manual/8_matematicas_maestros.pdf (Spanish)
• https://www.ugr.es/~jgodino/edumat-maestros/manual/9_didactica_maestros.pdf (Spanish)

• MD01. Aprendizaje cooperativo. Desarrollar aprendizajes activos y significativos de forma cooperativa. 
• MD02. Aprendizaje por proyectos. Realización de proyectos para la resolución de un problema, aplicando habilidades y conocimientos adquiridos. 
• MD03. Estudio de casos. Adquisición de aprendizajes mediante el análisis de casos reales o simulados. 
• MD04. Aprendizaje basado en problemas. Desarrollar aprendizajes activos a través de la resolución de problemas. 

Article 18 of the Regulations for the Evaluation and Grading of Students at the University of Granada establishes that the regular examination session will be based preferably on the continuous assessment of students, except for those who have been granted the right to Final Single Assessment.

The evaluation of the level of acquisition and development of the competencies, in ordinary examination and under the continuous evaluation method, will be continuous and formative, taking into account the aspects of the development of the subject, in which individual and group work and the significant learning of the theoretical contents and its practical application can be assessed. The assessment of the development of competencies and the degree of involvement and attitude of the students will be carried out using observation instruments. To issue these evaluations, it will be essential that the teacher has observations of each student about their way of working (individual or in group), their commitment to the subject, their dedication to it or the skills they manifest, among other things, in a percentage equal to or greater than 80% of the practical sessions taught.

The assessment criteria that will be applied to determine the final grade, through observation scales, portfolios, reports, or journals, together with their corresponding weighting for calculating the final grade, are as follows:

• EV-C1. Demonstration of mastery of theoretical and practical content, and critical analysis thereof: 35%
• EV-C2. Assessment of work completed, individually or in teams, taking into account presentation, writing quality and clarity of ideas, structure and academic/scientific level, creativity, justification of arguments, the depth and richness of critical analysis, and the relevance and currency of the bibliography consulted: 45%
• EV-C3. Degree of student engagement and attitude, as demonstrated through participation in consultations, presentations, and debates, as well as in the preparation of individual or group assignments and collaborative discussion sessions: 15%
• EV-C4. Attendance at classes, seminars, conferences, tutorials, and group sessions: 5%

In students’ work, the following aspects will be assessed: presentation; written or oral expression and clarity of exposition; structure and academic/scientific quality of the written work or presentation; creativity; appropriate justification of arguments; the ability to provide insightful and substantial critical analysis; and, where applicable, the suitability and currency of the bibliography consulted. Poor grammar and spelling, as well as the unauthorized, undeclared, or improper use of artificial intelligence tools in the preparation of any activity that forms part of the assessment, will have a negative impact on the grade awarded for the corresponding activity.

Grading

To pass the course through continuous assessment, it will be necessary to meet the minimum attendance requirement of 80% of the practical sessions taught and to achieve a final weighted average grade of 5 out of 10 or higher (or its equivalent if another grading scale is used), obtaining a grade of 5 out of 10 or higher (or its equivalent if another grading scale is used) in each assessment criterion.

In the event that the grade obtained in at least one of the assessment criteria is lower than 5 out of 10 points (or its equivalent if another grading scale is used), the final grade will be the lowest grade obtained among the assessment criteria indicated above.

If no evidence is recorded for any of the assessment criteria, the final grade will be: “No show.”

Any adjustments or clarifications required when applying the weighting of the criteria to determine the final grade will be made by the corresponding teaching staff.

In departmental sections where the course does not have small-group classes, assessment will be adapted as closely as possible to these guidelines.

The extraordinary evaluation of the subject aims to assess the significant learning of the students regarding the theoretical contents of the subject and its practical application, as well as the development of the expected competencies. In this evaluation call students will be evaluated through a report or examination that includes both theoretical and practical components, which will account for 30% and 70% of the final grade, respectively.

Grading

The final grade obtained by each student in the extraordinary assessment session for the course is determined as follows.

If the report or examination has been completed:

• If the grade obtained in each part is 5 out of 10 or higher (or its equivalent if another grading scale is used), the final grade will be the weighted average of those grades.
• If the grade obtained in at least one part is below 5 out of 10 (or its equivalent if another grading scale is used), the final grade will be the lowest of those grades.

If the report or examination has not been completed, the final grade will be “No Show.”

Any ambiguities arising from the application of the weighting criteria in determining the final grade will, where necessary, be resolved by the corresponding teaching staff.

Those students who have been granted the single final evaluation according to the corresponding regulations (https://www.ugr.es/universidad/normativa/texto-consolidado-normativa-evaluacion-calificacion-estudiantes-universidad-granada) will be evaluated through a report or examination including both theoretical and practical parts, with weights in the final grade of 30% and 70% respectively.

Grading

The final grade obtained in the course by each student under the single final assessment system is determined as follows.

If the report or examination has been completed:

• If the grade obtained in each part is 5 out of 10 or higher (or the equivalent if another grading scale is used), the final grade will be the weighted average of those grades.
• If the grade obtained in at least one part is below 5 out of 10 (or the equivalent if another grading scale is used), the final grade will be the lowest of those grades.

If the report or examination has not been completed, the final grade will be "No Show."

Any ambiguities arising when applying the weighting of the assessment criteria to determine the final grade will, where necessary, be resolved by the corresponding teaching staff.

The content of the article 15 on the originality of the works and production in tests, included in the Regulations for Evaluation and Qualification of the students of the University of Granada (https://www.ugr.es/universidad/normativa/texto-consolidado-normativa-evaluacion-calificacion-estudiantes-universidad-granada), is highlighted:

1. The University of Granada will promote respect for intellectual property and will transmit to students that plagiarism is a practice contrary to the principles that govern the University education. For this, it will proceed to recognise the authorship of the works and their protection in accordance with intellectual property as established by current legislation.
2. Plagiarism, understood as the presentation of a work or work done by another person as one's own or the copying of texts without citing their origin and giving them as one's own elaboration, will automatically lead to a numerical grade of zero in the subject in which it was detected, regardless of the rest of the grades that the student would have obtained. This consequence must be understood without prejudice to the disciplinary responsibilities that students who plagiarize may incur.
3. The work and materials submitted by students must be signed with an explicit declaration that the work is original, meaning that no sources have been used without proper citation.

Link to single final assessment request: https://sede.ugr.es/procs/Gestion-Academica-Solicitud-de-evaluacion-unica-final.

Link to request for evaluation due to incidents: https://sede.ugr.es/procs/Gestion-Academica-Solicitud-de-evaluacion-por-incidencias.

This syllabus is subject to possible adaptations for students with recognised specific educational support needs (NEAE) in accordance with the reports provided by their corresponding NEAE tutors at the University of Granada and the regulations of the University of Granada: https://www.ugr.es/sites/default/files/2017-09/NCG1114.pdf.

Information of interest for students with disabilities and/or Specific Educational Support Needs (NEAE): Management of services and support (https://ve.ugr.es/servicios/atencion-social/estudiantes-con-discapacidad).