Course guide of Basic Mathematics for Primary Education (2561113)

• Mastery of basic mathematics.

• Proficiency in English (recommended minimum level equivalent to B2 on the CEFR scale).

• Study, analysis and reflection on mathematical concepts and procedures, their ways of representation and modelling, phenomenology and historical aspects, using materials and resources on numbers and operations, measurement, estimation and calculation, geometry (shapes and figures and their properties), data analysis and probability.

• The transversal contents of mathematics in primary education: mathematical sense, problem solving, use of new technologies in mathematics, historical, social and cultural dimension of mathematics.

• Know and relate the main concepts, structures and procedures that make up the topics of Primary School Mathematics.
• Understand and properly employ the facts and properties of mathematical concepts and structures.
• Use mathematical procedures correctly in a written and symbolic way.
• Analyze, reason and effectively communicate mathematical arguments.
• Manage and relate the different ways of representing the mathematical concepts and procedures of Primary Education.
• Model phenomena from different disciplines with notions and basic mathematical tools.
• State, formulate and solve mathematical problems through different strategies in a variety of situations and contexts.
• Use manipulative, graphic, symbolic and technological models to express relationships, properties and mathematical operations.
• Use symbolic language in mathematics and relate it to everyday language.
• Know and manage the basic structure of the Primary Education math curriculum in terms of its contents, and describe it clearly and accurately.
• Perceive mathematical knowledge as part of our culture, with an interdisciplinary and socially useful character.
• Appreciate the educational work in mathematics as a professional, ethical and social commitment

• Unit 1. Numbers and algebra
  1. Numbers. Classification, properties, representations and uses
  2. Interpretation of operations. Approach and resolution of arithmetic word problems
  3. Calculation strategies and algorithms. Properties of numbers and operations
  4. Patterns and relationships. Interpretation and representations

• Unit 2. Geometry
  1. Geometric elements in the plane and in space. Representations and visualization
  2. Properties of plane figures and 3D-shapes: Geometric modeling
  3. Transformations in the plane and regularities
  4. Reasoning and Proof in Geometry

• Unit 3. Measurement
  1. Perception of magnitudes: length, surface, volume, amplitude, mass, capacity, time and money
  2. Units of measurement: types, choice of units and conversion
  3. Direct measurement. Personal strategies
  4. Indirect measurement. Interpretation of school formulas
  5. Measurement estimation

• Unit 4. Statistics and probability
  1. Statistical studies. Collection of information, types of data and variables
  2. Data representation: tables, graphs and statistical measures. Interpretations
  3. Deducing conclusions and statistical inference
  4. Perception of random phenomena and quantification of uncertainty

The practices in small groups are associated with the four basic blocks of content (Arithmetic, Geometry, Magnitudes and their measurement and Statistics and probability) and will be carried out through the use of manipulative materials and/or computing resources. This design of practices pursues a twofold goal.

Firstly, it is intended that students, in groups and autonomously, explore and experience mathematical activities to face the work with new mathematical notions or to deepen the study of notions already introduced in previous sessions. Secondly, these activities contribute to know and use a large number of manipulatives and resources that can be used in the teaching and learning of mathematics in primary education.

Some of the thematic core of the four practice sections are the following:

• Numbers and Algebra: numbering systems; calculation: algorithms and methods; arithmetic problems; fractions and decimals.
• Geometry: polygons: classification and properties; patterns and shapes; polyhedra: classification and basic elements; geometric transformations
• Magnitudes and measurement: direct and indirect measures; measuring instruments; metric system.
• Statistics and probability: organisation of data; interpretation of information in the media; phenomena related to chance.

• CARRILLO, J., CONTRERAS, L. C., CLIMENT, N., MONTES, M. A., ESCUDERO, D. I. Y
  FLORES, E. (2016). Didáctica de las Matemáticas para maestros de Educación Primaria.
  Paraninfo.
• CHAPIN, S. H., & JOHNSON, A. (2006). Math Matters: Understanding the Math You Teach Grades K-8 (2nd Ed.). Math solutions publications.
• SEGOVIA. I. Y RICO, L. (Coord.) (2011). Matemáticas para maestros de educación primaria. Pirámide.

A) Books on primary education mathematics and its didactics

• ALSINA, Á. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12 años). Graó.
• BLANCO, L., CLIMENTE, N., GONZÁLEZ, M. T., MORENO, A., SÁNCHEZ-MATAMOROS, G.,
  DE CASTRO, C. Y JIMÉNEZ, C. (Eds.) (2023), Aportaciones al desarrollo del currículo desde
  la investigación en educación matemática. Editorial Universidad de Granada.
• CALVO, C., CARRILLO, A., DE LA FUENTE, A., DE LEÓN, M., GONZÁLEZ, M. J.,
  GORDALIZA, A., GUEVARA, I., LÁZARO, C., MONZÓ, O., MORENO, A. J., RODRÍGUEZ, L. J.,
  RODRÍGUEZ, J. Y SERRADÓ, A. (2021). Bases para la elaboración de un currículo de
  Matemáticas en Educación no Universitaria. Comité Español de Matemáticas.
• CASTRO, E. (Edt) (2001). Didáctica de la matemática en la Educación primaria. Síntesis.
• CHAMORRO, C. (Coord.) (2003). Didáctica de las matemáticas para primaria. Pearson-
  Prentice Hall.
• GODINO, J. D. (Dir.) (2004). Matemáticas para maestros. Departamento de Didáctica de la
  Matemática de la Universidad de Granada. http://www.ugr.es/local/jgodino
• LLINARES, S. Y SANCHEZ, V. (1988). Fracciones. Síntesis.
• MAZA, C. (1991). Enseñanza de la suma y de la resta. Síntesis.
• RESNICK, L. Y FORD, W. (1990). La enseñanza de las matemáticas y sus fundamentos psicológicos. Paidós-MEC.
• VAN DE WALLE, J. A. (2009) Elementary and Middle School Mathematics. Teaching
  Developmentally. Longman, New York.

B1) Focused on numbers and algebra

• BURGOS, M. (2023). Razonamiento algebraico elemental. Implicaciones en la formaciónde profesores. Servicio de publicaciones de la Universidad de Almería.
• CAÑADAS, M. C. (2016). Álgebra escolar: un enfoque funcional. Uno: Revista de didácticade las matemáticas, 73, 7-13.
• CASTRO E., RICO L., CASTRO E. (1988) Números y operaciones. Fundamento para unaaritmética escolar. Síntesis.
• CENTENO, J. (1988). Números decimales. ¿Por qué? ¿Para qué? Síntesis.
• GARCÍA-PEREZ, M. T. Y ADAMUZ-POVEDANO, N. (2019). Del número al sentidonumérico y de las cuentas al cálculo táctico. Fundamentos, recursos y actividades para iniciar el aprendizaje. Octaedro.
• GOMEZ B. (1988). Numeración y Cálculo. Síntesis.

B2) Focused on geometry

• ALSINA, C., BURGUES, C., FORTUNY, J. M. (1987). Invitación a la didáctica de la geometría. Síntesis.
• ALSINA, C., BURGUES, C., FORTUNY, J. M. (1988). Materiales para construir la geometría. Síntesis.
• GUILLEN G. (1991). Poliedros. Síntesis.

B3) Focused on measurement

• CHAMORRO, C., BELMONTE, J. M. (1988) El problema de la medida. Didáctica de las magnitudes lineales. Síntesis.
• OLMO, A., MORENO, F. y GIL, F. (1988) Superficie y volumen. ¿Algo más que el trabajo con
  fórmulas? Síntesis.
• SEGOVIA, I., CASTRO E., CASTRO E. y RICO L. (1989). Estimación en cálculo y medida.
  Síntesis.

B4) Focused on statistics and probability

• BOLOGNA, E. (2013). Estadística para psicología y educación. Editorial Brujas.
• GODINO, J. D., BATANERO, C. y CAÑIZARES, M. J. (1987) Azar y probabilidad. Síntesis.

Other resources

• Primary Education Mathematics textbooks.

• http://nlvm.usu.edu/es/ (Spanish)
• http://recursostic.educacion.es/descartes/web/ (Spanish)
• http://clic.xtec.cat/db/listact_es.jsp (Spanish)
• https://www.geogebra.org/? (English, Spanish, etc.)
• https://es.mathigon.org/ (Spanish)
• https://tuvalabs.com/ (Spanish)
• https://pensamientoalgebraico.es/es/actividades/primaria-6-11-anos (English/Spanish)
• https://nrich.maths.org/ (English)

• 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. 

To pass the course during the ordinary examination diet, lecturers must have observation records of the students for at least the 80% of the workshop sessions. These will focus on students' work habits, and their commitment to their learning, dedication to it, and skills exhibited, among others.

The criteria and assessment tools to be used are as follows:

• EV-C1. Mastery of the theoretical and practical content, and critical analysis of that content (65%). This will be assessed through:
  • EV-I1. Written exams: essay questions, short-answer questions, multiple-choice questions, case studies, and problem-solving (45%).
  • EV-I4. Portfolios, reports, students' notebooks (20%)
• EV-C2. Valuation of work completed, individually or in teams, based on presentation, writing style, clarity of ideas, structure, scientific rigor, creativity, justification of arguments, the quality and depth of the analysis provided, and the currency of the references cited (25%). It will be evaluated using:
  • EV-I3. Observation scales (25%).
• EV-C3. Level of engagement and attitude demonstrated by students through their participation in consultations, presentations, and debates; as well as in the preparation of assignments, whether individual or in groups, and in group discussion sessions (5%). This will be assessed using:
  • EV-I3. Observation scales (5%).
• EV-C4. Attendance at classes, seminars, lectures, tutorials, and group sessions (5%).
  • EV-I3. Observation scales (5%).

Students' work will be evaluated based on presentation, writing, or oral expression, as well as the clarity of ideas, the structure and scientific rigor of the written work or speech, creativity, the adequate justification of arguments, the depth and richness of the analysis provided, and, where applicable, the suitability and currency of the references cited. Grammatical and spelling errors, as well as the improper use of artificial intelligence tools in the preparation of any assignment that forms part of the evaluation, will negatively impact
the grade for the corresponding assignment.

To pass the course, students must achieve a minimum score of 5 out of 10 (or itsequivalent, if a different scale is used) on all assessment tools. The student’s final grade will be:

• If observation records for the student are available for at least 80% of the practical classes taught:
  • If grades are available for assessment instruments whose combined weight exceeds 50%:
    • The weighted average of the scores obtained on those instruments, provided that all scores are equal to or greater than 5 points out of 10.
    • The lowest score obtained on those assessment instruments, when at least one of the assessment instruments yields a score lower than 5 out of 10.
  • If grades are available for assessment instruments whose combined weight is less than or equal to 50%: Not presented
• If there are no observation records for the student covering at least 80% of the practical classes taught: Not presented

If a student receives a grade lower than 5 out of 10 on any of the assessment tools that make up the course’s regular evaluation, he or she must pass a final exam during the make-up exam period.

In departmental sections where the course does not have small groups, the evaluation will adhere to these guidelines as closely as possible.

During the extraordinary examination diet, special exam period, students may choose to retain grades of 5 or higher out of 10 obtained on the assessment instruments administered during the ordinary diet, if they and indicate this. Consequently, they will only be required to pass the exams corresponding to the assessment instruments they did not pass, provided they choose to retain those grades. However, if the student has not passed any of the assessment components during the regular exam period, they must take one or more written exams consisting of a theoretical and a practical section, the combined grade of which will account for 100% of the final grade for the course.

To pass the course, students must achieve a minimum score of 5 out of 10 (or its equivalent, if another grading scale is used) on each of the theoretical and practical parts of the written exam or exams.

The student’s final grade will be:

• The weighted average of the scores on the theoretical and practical sections, provided that the score on both is greater than or equal to 5 out of 10.
• The lowest of the grades below 5 points, when the grade in at least one of the sections is below 5 points out of 10.
• Not presented, when the activities and tests in the assessment process completed by the student account for up to 50% of the total weight of the assessment.

Students who, after request to the department, are granted the single final assessment format must take one or more written exams consisting of a theoretical section and a practical section, the combined grade of which will account for 100% of the final grade for the course. The exams will have a level of rigor and difficulty equivalent to that of the assessment activities conducted during the regular assessment period.
To pass the course, students must achieve a minimum score of 5 out of 10 (or its equivalent, if another grading scale is used) on each of the theoretical and practical parts of the written exam or exams.
The student’s final grade will be:

• The weighted average of the scores on the theoretical and practical sections, provided that the score on both is greater than or equal to 5 out of 10.
• The lowest of the grades below 5 points, when the grade in at least one of the sections is below 5 points out of 10.
• Not presented, when the activities and tests in the assessment process completed by the student account for up to 50% of the total weight of the assessment.

In those evaluation tests that require or plan to use audio and/or video during its development, this use will be done in accordance with the guidelines established in the instructions and recommendations for the application of data protection, personal or home privacy regulations established by the General Secretary or competent body of the University of Granada.

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

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.

If AI tools are used in the course, students must use them ethically and responsibly. Students must follow the recommendations
contained in the document “Recommendations for the Use of Artificial Intelligence at the
UGR,” published at this link: https://ceprud.ugr.es/sites/centros/ceprud/public/ficheros/Recomendaciones_IA_en_UGR.pdf

This syllabus is subject to possible adaptations for students with recognised specific educational support needs (SESN) in accordance with the reports provided by their corresponding SESN 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.

Useful information for student with SESN (Service and suport): https://ve.ugr.es/servicios/atencion-
social/estudiantes-con-discapacidad

Geogebra: https://www.geogebra.org/classic?lang=es