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Bachelor's Degree in Primary Education Teaching
GMEDPR01-2-006
Mathematics and Associated Teaching Methods II
General description and schedule Teaching Guide

Coordinator/s:

Itziar García Honrado
garciaitziaruniovi.es

Faculty:

Marlén Alonso Castaño
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(English Group)
Pablo Giadas Álvarez
giadaspablouniovi.es
Juan José Santa Engracia de Pedro
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Itziar García Honrado
garciaitziaruniovi.es

Contextualization:

The subject "Matemáticas y su didáctica II" is englobed in the mathematics teaching and it is related to the matter of how it can be learned which is a part of the module in the Degree of disciplinary knowledge and didactics. The subject is developed along the 2nd semester of the 2nd course of the Degree for Teacher in Primary Education. It is carried out by the Department of Statistics, Operational Research and Mathematics Didactics, specifically by the Area of Mathematics Didactics.

 

 

 

 

Requirements:

-

Competences and learning results:

The course will work on the development of the following Basic Competences (CB) of the degree:

CB1. That students have demonstrated to possess and understand knowledge in the area of didactics of mathematics that starts from the basis of general secondary education, and is usually found at a level that, although it is supported by advanced textbooks, also includes some aspects that involve knowledge from the forefront of their field of study.

CB2. Students are able to apply their knowledge to their work or vocation in a professional way and possess the competences that are usually demonstrated through the elaboration and defence of arguments and the resolution of problems within the area of didactics of mathematics.

CB3. Students have the capacity to gather and interpret relevant data (usually within the area of didactics of mathematics) in order to make judgements that include reflection on relevant social, scientific or ethical issues.

CB4. Students are able to communicate information, ideas, problems and solutions to both specialist and non-specialist audiences.

CB5. That students have developed those learning skills necessary to undertake further studies with a high degree of autonomy.

 

In turn, and with regard to the Specific Competences (CE) of the degree, this subject aims for students to be able to:

CE1. Know the curricular areas of Primary Education, the interdisciplinary relationship between them, the assessment criteria and the didactic knowledge around the respective teaching and learning procedures.

CE2. Design, plan, develop and evaluate teaching and learning processes, both individually and in collaboration with other teachers and professionals at the centre.

CE3. Deal effectively with language learning situations in multicultural and plurilingual contexts. Encourage the reading and critical commentary of texts from the different scientific and cultural domains contained in the academic curriculum.

CE4. Design and regulate learning spaces in contexts of diversity that attend to gender equality, equity and respect for human rights that constitute the values of citizenship education.

CE5. Encourage coexistence in the classroom and outside it, solve discipline problems and contribute to the peaceful resolution of conflicts. Encourage and value effort, perseverance and personal discipline in students.

CE6. Know the organisation of Primary Education schools and the diversity of actions that comprise their operation. Carry out the functions of tutoring and guidance with students and their families, attending to the unique educational needs of the students. Assume that the exercise of the teaching function must be perfected and adapted to scientific, pedagogical and social changes throughout life.

CE7. Collaborate with the different sectors of the educational community and the social environment. Assume the educational dimension of the teaching function and promote democratic education for active citizenship.

CE8. Keep a critical and autonomous relationship with regard to knowledge, values and public and private social institutions.

CE9. Value individual and collective responsibility in achieving a sustainable future.

CE10. Reflect on classroom practices in order to innovate and improve teaching work. Acquire habits and skills for autonomous and cooperative learning and promote it among students.

CE11. Know and apply information and communication technologies in the classroom. Selectively discern audiovisual information that contributes to learning, civic education and cultural wealth.

CE12. Understand the function, possibilities and limits of education in today's society and the fundamental competences that affect Primary Education schools and their professionals. Know models of quality improvement with application to educational centres.

 

With regard to the Subject Specific Competences (CEM), this subject aims for the student to be able to:

CEM6.1. Achieve basic mathematical competences (numerical, calculation, geometric, spatial representations, estimation and measurement, organisation and interpretation) that allow them to carry out the teaching function with confidence.

CEM6.2. Know the school mathematics curriculum, reflecting on the teaching-learning process, classroom organisation, attention to diversity, interdisciplinarity, ...

CEM6.3. Develop and evaluate curriculum content using teaching resources (general and mathematical computer programmes, information and communication technology and teaching materials) to manage the teaching-learning process.

CEM6.4. Analyse, reason and communicate mathematical proposals.

CEM6.5. Propose and solve problems related to everyday life.

CEM6.6. Value the relationship between mathematics and science as one of the pillars of scientific thought.

 

From the General Competences (CG), this subject aims for the student to be able to:

CG1. Work in a team, disciplinary and interdisciplinary, in a cooperative and collaborative way, respecting diversity.

CG2. Use interpersonal communication means and strategies in different social and educational contexts.

CG6. Incorporate information and communication technologies into their training and professional activity.

CG7. Know how to adapt to new situations, developing a creative spirit and leadership attitude.

CG8. That students develop an ethical commitment to respect fundamental rights, guaranteeing the effective equality of men and women, equal opportunities, non-discrimination and universal accessibility for people with disabilities, as well as the values of a culture of peace and democratic values.

 

The above competences are expressed in the following Learning Outcomes (RA):

RA6.1. Know and apply basic mathematical skills (numerical, calculation, geometric, spatial representations, estimation and measurement, organisation and interpretation of information).

RA6.2. Handle the mathematical contents that enable him/her to work confidently as a teacher in Primary Education.

RA6.3. Select or create mathematical learning environments that encourage pupils to solve complex tasks, seeking to develop their basic mathematical competences.

RA6.4. Design classroom activities within multifaceted contexts, interrelating mathematical competences with other basic competences.

RA6.5. Select and implement in the classroom diverse resources and materials (computational, audiovisual, manuals, bibliographic, etc.) that promote the development of basic mathematical competences.

RA6.6. Fully integrate students, making appropriate use of TICs, in our information society, transforming it in knowledge.

RA6.7. Apply individualised and group teaching methodologies, managing both the search for full personal development and the integration of students in a multicultural society.

RA6.8. Design, develop and evaluate didactic units related to mathematics in Primary Education, seeking quality training in basic competences.

RA6.9. Analyse and solve problems related to everyday life, following a process that involves understanding, design, application and review of them.

 

Contents:

  1. Fundamentals concepts of Geometry: Study of 2-dimensions figures. Areas. Didactic materials and resources. Errors and difficulties. Activities in Primary classroom.
  2. Isometric transformations in the plane:  Friezes and mosaics. Didactic materials and resources. Errors and difficulties. Activities in Primary classroom.
  3. 3-dimensions Geometry: Elementary concepts. Polyhedrons. Solid of revolution. Volumes. Teaching materials and resources . Didactic materials and resources. Errors and difficulties. Activities in Primary classroom.

Methodology and work plan:

During the expository classes (CEX), the mathematical concepts of the Primary Education curriculum will be explained. The methodology will be supported by visual presentations and will use computer programs such as GeoGebra to illustrate some of the properties of the concepts explained, as well as the relationship between some of them. It is mainly related to learning outcomes RA6.1, RA6.2, RA6.3, RA6.8 and RA6.9.

Classroom practice (PA) will be mainly articulated with students organised in small groups. They will consist of presentations by students, knowledge and manipulation of different teaching materials (structured or not), problem-solving activities, simulations of teaching situations, construction of learning environments and exploration of different resources for the classroom, including m-learning. It relates mainly to learning outcomes RA6.1, RA6.2, RA6.3, RA6.4, RA6.5, RA6.6, RA6.7, RA6.8 and RA6.9.

The main objective of the group tutorials (TG) will be to attend to the difficulties that students may have in the study of the subject. Alternatively, and as long as the availability of the facilities allow it, activities related to the use of the GeoGebra software will be proposed. It is mainly related to learning outcomes RA6.1, RA6.2, RA6.3, RA6.4, RA6.5, RA6.6, RA6.7, RA6.8 and RA6.9.

Group work aims to enable students to obtain the solution space of a problem, which will allow them to anticipate possible learning difficulties and to propose strategies or tools to help overcome them. It is mainly related to learning outcomes RA6.1, RA6.2, RA6.3, RA6.4, RA6.5, RA6.6, RA6.7, RA6.8 and RA6.9.

The distribution of training activities is shown in the table below:

Lessons

Total

hours

CEX

PA

TG

Evaluation

Total

Group Work

Autonomous Work

Total

Weeks

Lesson 1

78

22.5

13.5

   

36

15

27

42

1 to 9

Lesson 2

25

5

3

   

8

8

9

17

10 to 11

Lesson 3

29

7,5

4,5

1

 

13

4

12

16

12 to 14

Exam

18

     

3

3

3

12

15

 

Total

150

35

21

1

3

60

30

60

90

 

 

                   

 

Exceptionally, if health conditions so require, non-classroom teaching activities may be included. In this case, students will be informed of the changes made.

Assessment of students learning:

a) To evaluate the subjet the following ítems will be used. It is shown the weigth of each ítem in the final note of the subject.

Items to evaluate

Weigth (%)

1. Written exam

60

2. Group work

          20

3. Participation  and questionnaire(s)

          20

 

 

 
 

 

All items to evaluate the subject are related to results of learning.

b) The written exam is divided in two parts: theoretic and practice. To pass the subject it is necessary to obtain at least the 50% of the total mark of the written exam. Moreover, to pass the subject the final note calculated envolving all the ítems to evaluate with the corresponding weigth shown in a) must be betwen 5 and 10 points.

c) In the case that condition in b) is not satisfied, the final note will be the one calculated envolving all the ítems to evaluate if the computation is less than 5, otherwise it will be 4.9.

d) As regards written expression, the existence of orthographic or syntactic mistakes may lead to a lowering of the mark in the corresponding instrument for the students concerned.

e) In the extraordinary call in January 2023, the marks for instruments 2 and 3 obtained in the academic year 2021-2022 will be used for the weighted average, with the weightings indicated in section a). In the extraordinary exam session in June/July 2023, the marks for instruments 2 and 3 will be those obtained in the ordinary exam session of the academic year 2022-2023 with the weightings indicated in section a).

f) In the case of students who have been granted differentiated assessment, the assessment instruments, with the weight that each of them will represent in the final grade, will be: Written exam (60%), Individual work(s) and questionnaire(s) (30%) and Participation through the Virtual Campus Forum (10%).

g) Exceptionally, if health conditions so require, non-attendance assessment methods may be included. In this case, students shall be informed of the changes made.

 

Resources, bibliography and documentation:

 

Basic bibliography:

GeoGebra. (2019). Accessible in https://www.geogebra.org/

Godino, J. D. (2004). Didáctica de las matemáticas para maestros. Granada, España: Universidad de Granada. Accessible in http://www.ugr.es/local/jgodino/

Godino, J. D. (2004). Matemáticas para maestros. Granada, España: Universidad de Granada. Accessible in http://www.ugr.es/local/jgodino/

 

Other references:

Albarracín, L., Badillo, E., Giménez, J., Vanegas Y. y Vilella, X. (2018) Aprender a enseñar matemáticas en la educación primaria. Madrid, España: Síntesis.

Alsina, À. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12 años). Barcelona, España: Editorial Graó.

Carrillo, J. et al. (2016). Didáctica de las Matemáticas para maestros de Educación Primaria. Colección: Didáctica y Desarrollo. Madrid, España: Ediciones Paraninfo, SA.

Chamorro, M. C. (2005). Didáctica de las matemáticas para Primaria. Madrid, España: Pearson.

Editorial Síntesis. (2019). Matemáticas: Cultura y Aprendizaje. Madrid, España: Editorial Síntesis.

García, J. (2019). Resolución de problemas. MetaMoDeLos TIC. Accessible in http://ntic.educacion.es/w3/eos/MaterialesEducativos/mem2009/problematic/menuppal.html

González, R. (2019). Recursos Loreto. Accesible en http://www.ceiploreto.es/

Marea Verde. (2019). Apuntes Marea Verde. Matemáticas. Accessible in http://www.apuntesmareaverde.org.es/

Nortes, A. (2013). Actividades prácticas de matemática y su didáctica 1. Madrid, España: CCS.

Parker T., y Baldridge H. (2006). Elementary Geometry for Teachers. United States: Sefton-Ash Publishing.

Piaget, J.,  Inhelder B. and Szwminska A. (1960) The child's conception of geometry. Routhledge.

Proyecto Descartes. (2019). Accessible in http://recursostic.educacion.es/descartes/web/

Proyecto Gauss. (2019). Accessible in http://recursostic.educacion.es/gauss/web/materiales_didacticos/materiales_didacticos.htm

Proyecto Nrich. University of Cambriadge (from 1997). Accessible in http://nrich.maths.org/frontpage 

Revistas SUMA, Revista sobre la enseñanza y el aprendizaje de las matemáticas, FESPM, Madrid. Accessible in www.revistasuma.es