Universitat Internacional de Catalunya

Teaching and Learning Mathematics 1

Teaching and Learning Mathematics 1
3
10603
2
First semester
OB
Main language of instruction: Catalan

Other languages of instruction: English, Spanish
If the student is enrolled for the English track then classes for that subject will be taught in the same language.

Teaching staff


Before the class.

Introduction

In the event that the health authorities announce a new period of confinement due to the evolution of the health crisis caused by COVID-19, the teaching staff will promptly communicate how this may effect the teaching methodologies and activities as well as the assessment.


We cannot understand the world that surrounds us without good mathematical skills.

The main purpose of this module is to ensure that we know and appreciate this science as a tool necessary for daily life, and for the transformation of society.

In essence, to study mathematics is to learn to reason and become accustomed to being conscious of this reasoning.

A good mathematical background is essential for adapting to life in today’s world. The concepts of number, ratio and proportion, and the language and symbols of mathematics, are part of the standard intellectual knowledge of any modern man or woman.

Pre-course requirements

None

Objectives

General

1. Enjoyment of mathematics.

2. Knowledge of the primary level mathematics curriculum.

3. Learn the content of procedures, facts, concepts and conceptual systems and attitudes, values and standards.

4. Work on mathematical skills.

5. Through articles in academic journals, reflect on how mathematics is taught today.

Specific.

1. Learn various games, so that pupils will have fun doing mathematics.

2. Work on primary level mathematics skills and objectives.

3. Prepare teaching units: organisation of content, educational objectives and learning and assessment activities.

4. Create ongoing assessment exercises and global learning processes in accordance with the general stage and subject objectives and final objectives.

5. Seek and make proposals for active teaching of mathematics.

6. Identify the difficulties of teaching mathematics and find possible solutions.

7. Hear different experiences of teaching mathematics.

8. Seek and read short biographies of great mathematicians.

 

Competencies

CEM - 38 Acquire basic mathematics skills (numerical, calculation, geometric, spatial representation, estimation, measures, organisation and interpretation of information, etc.)

CEM - 39 Know the school mathematics curriculum.

CEM - 40 Analyse, reason and communicate mathematical approaches.

CEM - 41 State and solve problems related to daily life.

CEM - 42 Assess the relationship between mathematics and the sciences as one of the pillars of scientific thought.

CEM - 43 Develop and evaluate curriculum content through appropriate teaching resources and promote the corresponding skills to pupils.

COMPETENCESMETHODOLOGYTRAINING ACTIVITY
CEM-38 problem-based learning
cooperative learning
learning contract
case study method
expository method / master class
problem-solving method
practical classes
theory classes
group study and work
individual / independent study and work.
seminar-workshops
CEM-39 problem-based learning
cooperative learning
learning contract
expository method / master class
problem-solving method
practical classes
theory classes
group study and work
individual / independent study and work.
seminar-workshops
CEM-40 problem-based learning
cooperative learning
project-based learning
learning contract
case study method
practical classes
group study and work
individual / independent study and work.
tutorials
CEM-41 problem-based learning
cooperative learning
project-based learning
learning contract
case study method
problem-solving method
practical classes
group study and work
individual / independent study and work.
internships
seminar-workshops
CEM-42 problem-based learning
cooperative learning
project-based learning
case study method
expository method / master class
practical classes
theory classes
group study and work
individual / independent study and work.
internships
CEM-43 cooperative learning
project-based learning
learning contract
expository method / master class
problem-solving method
practical classes
theory classes
group study and work
individual / independent study and work.
internships
tutorials

Learning outcomes

1. Have sufficient knowledge of mathematics to be able to perform teaching duties confidently.
2. Become familiar with the mathematics curriculum.
3. Learn the basic elements of the history of mathematics in order to recognise its key role in the educational framework.
4. Analyse and communicate mathematics approaches.
5. State problems associated with modern life, and resolve them innovatively.
6. Develop and assess curriculum content through relevant teaching resources, in order to promote pupils’ skills.
7. Ability to manage a mathematics class with the interactive elements involved, providing motivation and handling pupil diversity appropriately.
8. Use research, proposal and problem-solving strategies in the school environment.
9. Design mathematics teaching sequences.
10. Identify and work with professionals to resolve the difficulties involved in teaching mathematics and focus on quality.
11. Regard the relationship between mathematics and sciences as one of the fundamental pillars of scientific thought.
12. Creative interdisciplinary activities combining mathematics with other areas of the curriculum.
13. Incorporate information and communication technologies into teaching and learning activities.
14. Be able to communicate and express oneself appropriately in the language of instruction, both orally and in writing.
15. Learn how to interpret and incorporate knowledge from documents in English on this subject.

Syllabus

1. Child psychological development.

2 The origin of mathematics.

3. Primary level mathematics curriculum.

4. Solving different types of problems.

5. Use of mathematical language.

6 Strategies for teaching mathematics.

7. Mathematical instruments.

8. Diversity awareness.

9. Difficulties in learning mathematics.

10. Assessment methods.

11. Unique activities.

 

 

Teaching and learning activities

In person



SKILLS METHODOLOGY TRAINING ACTIVITIES

CEM-38

problem-based learning
cooperative learning
apprenticeship contract
case studies
presentation/lecture
solving exercises and problems

practical classes
theoretical classes
group study and work
individual/independent study and work
seminars/workshops

 

CEM-39

problem-based learning
cooperative learning
apprenticeship contract
presentation/lecture
solving exercises and problems

practical classes
theoretical classes
group study and work
individual/independent study and work
seminars/workshops

 

CEM-40

problem-based learning
cooperative learning
project-focused learning
apprenticeship contract
case study

practical classes
group study and work
individual/independent study and work
tutorials

 

CEM-41

problem-based learning
cooperative learning
project-focused learning
apprenticeship contract
case study
solving exercises and problems

practical classes
group study and work
individual/independent study and work
external placement
seminars/workshops

 

CEM-42

problem-based learning
cooperative learning
project-focused learning
case study
presentation/lecture

practical classes
theoretical classes
group study and work
individual/independent study and work
external placement

 

CEM-43

cooperative learning
project-focused learning
apprenticeship contract
presentation/lecture
solving exercises and problems

practical classes
theoretical classes
group study and work
individual/independent study and work
external placement
tutorials

 

COMPETENCESMETHODOLOGYTRAINING ACTIVITY
CEM-38 problem-based learning
cooperative learning
learning contract
case study method
expository method / master class
problem-solving method
practical classes
theory classes
group study and work
individual / independent study and work.
seminar-workshops
CEM-39 problem-based learning
cooperative learning
learning contract
expository method / master class
problem-solving method
practical classes
theory classes
group study and work
individual / independent study and work.
seminar-workshops
CEM-40 problem-based learning
cooperative learning
project-based learning
learning contract
case study method
practical classes
group study and work
individual / independent study and work.
tutorials
CEM-41 problem-based learning
cooperative learning
project-based learning
learning contract
case study method
problem-solving method
practical classes
group study and work
individual / independent study and work.
internships
seminar-workshops
CEM-42 problem-based learning
cooperative learning
project-based learning
case study method
expository method / master class
practical classes
theory classes
group study and work
individual / independent study and work.
internships
CEM-43 cooperative learning
project-based learning
learning contract
expository method / master class
problem-solving method
practical classes
theory classes
group study and work
individual / independent study and work.
internships
tutorials

Evaluation systems and criteria

In person



Skills acquisition assessment and grading system

1. Make contributions to discussions and debates in the classroom.

2. Written presentation of the psychopedagogical conditions of primary pupils with respect to mathematics.

3. Individual oral presentation of a fun mathematics activity.

4. Oral presentation, in the form of short story, of the life of a mathematician.

5. In small groups, create a short general plan about a traditional Catalan celebration.

6. In small groups, create an audiovisual medium to make the introduction to a teaching unit more interesting.

7. Quality of presentation of individual and group work.

8. Overall written assessment of the different subjects on the curriculum.

Continuous assessment throughout the semester.

Activities in the classroom account for 50% of the final grade.

The other 50% is obtained from the final evaluation of the semester .

 

Learning outcome

Assessment system

1

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4

5

6

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8

9

10

11

12

1

 

X

X

X

 

X

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2

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X

   

3

X

 

X

X

X

X

X

X

 

X

 

X

4

   

X

   

X

       

X

X

5

X

X

 

X

X

X

X

X

X

   

X

6

 

X

 

X

X

X

X

X

X

X

X

X

7

X

X

X

X

X

X

X

X

X

X

X

X

8

X

X

X

X

X

X

X

X

X

X

X

X

 

  • Class attendance -80%
  • Participation and involvement in the class dynamic
  • Specific work on the different themes covered
  • Creativity and imagination and contribution of personal opinions and criteria
  • Submission and presentation of a teaching unit
  • Completion of written exercises

 

Bibliography and resources

  • Curriculum management of education primary education in Catalonia..
  • Alsina, C. (1993) Del número 0 al 99. Fem comptes amb els contes. Barcelona: Graó.
  • Alsina, C. i altres (1997) Ensenyar matemàtiques. Barcelona: Graó.
  • Alsina, C. i altres (1987) Invitación a la didáctica de la geometria. Madrid: Síntesis
  • Baroody, A.J. (1994) El pensamiento matemático de los niños. Madrid : Aprendizaje Visor .
  • Canals, M.A. (1989) Per una didàctica de la matemàtica a l’escola. Vic: EUMO
  • Canals, M.A. (2010) Problemes i més problemes. Barcelona. A.Rosa Sensat 
  • Chamorro, Mª C (2008) Didáctica de las matemáticas para primária. Pearson. Madrid 
  • Cockcroft (Informe). (1986) Las matemáticas sí cuentan. Madrid: MEC.
  • Codina, R.; Enfedaque,J i altres (1993) Fer matemàtiques. Vic.: Eumo.
  • Giménez, J.; Girondo,L (1990) El càlcul a l’escola. Barcelona: Graó.
  • Gómez, B. (1988) Numeración y cálculo. Madrid: Síntesis.
  • Gutierrez, A. i altres (1991) Didáctica de la matemática. Madrid: Síntesis.
  • Herman, F. (1988) Recursos en el aula de matemáticas. Madrid: Sínteis
  • Mialaret, G. (1987) Las matemáticas, cómo se aprenden, cómo se enseñan. Madrid: Pablo del Rio.
  • Segarra,Ll. Encercla el cercle. Barcelona: Graó. Col, Punt i seguit
  • Shell Centre for Mathematical Education (1984) Problemeas con pautas y números. Universidad País Vasco , Leiva (1993)
  • Udina, I. (1989) Aritmética y calculadoras. Madrid: Síntesis.
  • Vallés, J. (1985) Didàctica de la matemàtica al cicle inicial. Barcelona: Rosa Sensat.
  • Vidal, S. (2009) Estrategias para la enseñanza de las matemáticas en secundaria. Barcelona. Ed. Laertes
  • Vidal, S. (2005) Dia del Número, motivació de la Matemàtica. Barcelona.Publicacions de l'Abadia de Montserrat.
  • Vidal, S i altres (2009) Matemàtiques 6, A Bon Pas. Barcelona. Edebé.
  • Vidal, S. (2009) Estrategias para la enseñanza de las matemáticas en secundaria. Barcelona. Ed. Laertes
  • Vidal, S. (2010). Dibudoku. En S. De la Torre, & M. A. Pujol, Creatividad e innovación. Enseñar e investigar con otra conciencia (págs. 201-210). Madrid: Editorial Universitas, S.A.

  • Vidal, S. (2010). Didàctica de les matemàtiques a secundària. En A. Mora, La situació de les matemàtiques a la secundària catalana. Anàlisis de l'estat de l'ensenyament i l'aprenentatge (págs. 43-58). Barcelona: Furtwagen Editores.

  • Vidal, S. (2010). Talens dag, att skapa lust för matemtiklärande. (G. universitet, Ed.) Nämnaren, Tidskrift för matematikundervisning, 173(1), 43-46

  • .Vidal, S. (2011). La situació de la didàctica de les matemàtiques a la secundària catalana. Analísi de l'estat de l'ensenyament i l'aprenetatge. Temps d'Educació(41), 185-199.

  • Vidal, S. (2013). El dia del número, motivación de la matemática. Saarbrücken: Publicia.

  • Vidal, S., & Balaguer, C. (2013). La comunicación de los problemes de matemáticas en la didàctica de los Grados de Educación en la UIC. (UCM, Ed.) Estudios sobre el Mensaje Periodistico(19), 531-541.

  • Different articles for different magazines.

Teaching and learning material