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

To have completed the subject Mathematical Bases for Primary Education of the Primary Education Teacher Training of the University of Granada.

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, measurement sense, spatial sense, stochastic sense and algebraic sense.

• 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. Teaching and learning of mathematics (arithmetic, measurement, geometry, stochastics and algebra). Learning expectations, learning stages, mistakes and difficulties in learning mathematics. Diagnosis and treatment of difficulties in mathematics. The role of the teacher of mathematics, teaching techniques and strategies. Activities and tasks in mathematics, the role of materials and resources. Methodology for teaching mathematics based on problem solving.

• Mathematical knowledge in Primary Education.
• Problem solving in mathematics.
• 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.

• Consejería de Educación y Deporte (2021). Orden de 15 de enero de 2021, 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, se establece la ordenación de la evaluación del proceso de aprendizaje del alumnado y se determina el proceso de tránsito entre distintas etapas educativas. Consejería de
  Educación y Deporte.
• Flores, P. & 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. Available at
  http://www.ugr.es/local/jgodino.
• Jefatura del Estado (2006). Ley Orgánica 2/2006, de 3 de mayo, de Educación. BOE 106, 4 de mayo de 2006.
• Jefatura del Estado. (2013). Ley Orgánica 8/2013, de 9 de diciembre, para la mejora de la calidad educativa. BOE, 295, 10 de Diciembre de 2013.
• 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. BOE 340, 30 de diciembre de 2020.
• Jefatura del Estado (2022). Real Decreto 157/2022, de 1 de marzo, por el que se establecen la ordenación y las enseñanzas mínimas de la Educación Primaria.
• MECD (2014). Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria. BOE, 52, 1 de Marzo de 2014.
• MECD (2015). Orden ECD/686/2014, de 23 de abril, por la que se establece el currículo de la Educación Primaria para el ámbito de gestión del Ministerio de Educación, Cultura y deporte y se regula su implantación, así como la evaluación y determinados aspectos organizativos de la etapa. BOE, 106, 1 de Mayo de 2014.
• NCTM 2000. Principles and standards for school mathematics. Reston, NCTM.
• OECD (2018). PISA 2021 Mathematics Framework (Draft). Available at https://www.oecd.org/pisa/sitedocument/PISA-2021-mathematics-framework.pdf.
• OECD (2012). PISA 2012 Assessment and Analytical Framework Mathematics, Reading, Science, Problem Solving and Financial Literacy. https://www.oecd.org/pisa/pisaproducts/PISA%202012%20framework%20e-book_final.pdf

• Alsina, Á. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12años). Graó Educación: Barcelona. ISBN 978-84-9980-938-0
• Alsina, C. Burgues, C. & Fortuny, J.M. (1998). Enseñar matemáticas. Barcelona: Grao.
• Bihsop, A. J (1999). Enculturación matemática. La educación matemática desde una perspectiva cultural. Barcelona: Temas de educación. Paidós.
• Carrillo Yáñez, J. (Coord.). (2016). Didáctica de las matemáticas para maestros de Educación primaria. Barcelona: Paraninfo.
• Castro, E. (Ed.) (2001). Didáctica de la matemática en educación primaria. Madrid: Síntesis.
• Chamorro C. (2003). Didáctica de las matemáticas para primaria. Madrid: Pearson-Prentice Hall.
• Jiménez, J. (1997). Evaluación en matemáticas. Una integración de perspectivas. Madrid: Síntesis.
• Martínez Montero, J. y Sánchez Cortés, C. (2017). Resolución de problemas y método ABN. Madrid: Wolters Kluwer.
• Resnick, L. & Ford, W. (1990). La enseñanza de las matemáticas y sus fundamentos psicológicos. Madrid: Paidós-MEC.
• Rico, L., Fortuny, J. M. & Puig, L. (1987-91). Matemáticas, cultura y aprendizaje (colección). Madrid: Síntesis.
• Segovia, I. & Rico, L. (Eds.) (2013). Matemáticas para maestros de Educación Primaria. Madrid: Pirámide.
• Van de Walle, J. A. (2009) Elementary and Middle School Mathematics. Teaching Developmentally. Longman: New York.

• https://es.mathigon.org/polypad (Spanish)
• https://www.geogebra.org (English and Spanish)
• 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)
• http://recursostic.educacion.es/descartes/web (Spanish)
• https://www.ugr.es/~jgodino/edumat-maestros/manual/9_didactica_maestros.pdf (Spanish)
• https://www.ugr.es/~jgodino/edumat-maestros/manual/8_matematicas_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. 

The evaluation of the level of acquisition and development of competencies, in ordinary examination and under the continuos evaluation method, will be continuous and formative, taking into account the aspects of the development of the subject in which individual and group work is valued, and in which the significant learning of the theoretical contents and its practical application can be assessed. For this reason, attendance to practical classes of the subject is considered compulsory in a percentage equal to or greater than 80% of the practical classes taught. The overall grade will correspond to the weighted score of the different aspects and
activities that make up the evaluation system:

• Aspect 1. Assessment of one or more tests (essay, short answer, referring to cases or assumptions or problem solving).
• Aspect 2. Work carried out, individually or in a team, taking into account the presentation, writing and clarity of ideas, structure and scientific level, creativity, justification of what it is discussed, critical thinking, richness of the criticism that is made, and suitability of the bibliography consulted.
• Aspect 3. Assessment of the degree of involvement and attitude of the students manifested in their active participation in the teaching sessions, seminars, consultations, exhibitions and debates, in the preparation of the works (individual or in teams), in the sharing sessions; as well as their attendance to classes, seminars, conferences, tutorials and group sessions.

In order to pass the subject, it is required to pass the different aspects of the evaluation independently. The weight of each of them for the obtention of the final grade is:

• Aspect 1: 50%;
• Aspect 2: 40%;
• Aspect 3: 10%.

In case of not passing any of the previous sections, which make up the ordinary evaluation of the
subject, the student will have to pass a final test, in an extraordinary evaluation call, in order to
pass the subject.

The extraordinary evaluation of the subject aims to assess the significant learning of the students regarding the theoretical contents of the subject as well as its practical application. In this sense, in order to pass the subject in this call the student must pass a theoretical and practical written test with weight in the global qualification corresponding to 30% and 70% respectively.

Those students who have been granted the condition of single final evaluation, for not complying with the continuous evaluation method for the reasons included in the Regulations for Evaluation and Qualification of the students of the University of Granada (http://secretariageneral.ugr.es /pages/regulations/fichasugr/ncg7121/!), in order to pass the subject must pass a theoretical and practical written test, with weight in the global mark corresponding to 30% and 70% respectively, in which the significant learning of the contents of the subject is assessed.

• Link to request for single final evaluation: 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.

• The importance of 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".