FUNDAMENTALS OF GEOMETRY AND DATA TREATMENT FOR …

Universidad Católica de Valencia

PCA-27-F-01 Ed.00

Universidad Católica de Valencia “San Vicente Mártir”

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FUNDAMENTALS OF GEOMETRY AND DATA TREATMENT FOR TEACHERS

Faculty of Teacher Training and Education Sciences


Year 2021-22


PCA-27-F-01 Ed.00

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TEACHING GUIDE TO THE SUBJECT

ECTS

SUBJECT: FUNDAMENTALS OF GEOMETRY AND DATA TREATMENT FOR TEACHERS 4,5

Module: MATHEMATICS TEACHING AND LEARNING 15 Education type: DIDACTIC-DISCIPLINARY OBLIGATORY

YEAR: 3rd Semester: 1st

Teachers: Ana Isabel Cárceles Carlos Ferreira Sonia Martín Elena Moreno María José Soto

Department: MATHEMATICS, NATURAL SCIENCES AND SOCIAL SCIENCES APPLIED TO EDUCATION E-mail: [email protected] [email protected] [email protected] [email protected] [email protected]

MODULE ORGANIZATION ____________________________________________________________________________

MATHEMATICS TEACHING AND LEARNING # ECTS 15

Duration and time location within the curriculum: It is developed in the first year (second semester) and the third year (both semesters). It consists of a module in which the student acquires the basic concepts of mathematics and its didactics that will act as basis for his/her work as a teacher in the elementary school.

Subjects and Courses

Subject ECTS Courses ECTS Course/ semester

MATHEMATICS AND ITS DIDACTICS

15

Fundamentals of Arithmetics and Measure for teachers

Fundamentals of Geometry and Data treatment for teachers

4,5 4,5

1/2 3/1

Didactics of Mathematics 6 3/2


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TEACHING GUIDE FOR FIELD/SUBJECT: FUNDAMENTALS OF GEOMETRY AND DATA TREATMENT Previous requirements: not established

GENERAL GOALS

- To obtain knowledge (conceptual, procedural and attitudinal) of geometrical and

statistical nature that allows the student to intervene properly in the teaching of

mathematics in elementary school.

- To research on different ways of presenting the school mathematics such that

encourage in the students positive attitudes towards this subject.

- To provide tools, specific techniques and general guidelines for problem solving.

- To know two and three-dimensional shapes, to define their parts and deduce their basic properties, as well as calculate their areas and volumes.

- To collect, organize and describe data using statistic language.

- To use new technologies in basic geometric and statistic treatment.

- To recognize random phenomena and calculate the probability for a given event.

- To apply mathematical knowledge in order to solve specific problems.

- To understand and follow the reasonings found in straightforward mathematical

proofs.

- To anticipate different ways to confront a problem, troubles that can appear, the varied solutions that it admits and different languages that can be used in each

case.

- To recognize the value of mathematics as a useful science, achievable and

applicable to daily life.

- To find, in mathematical learning, the possibility of developing abilities of a general

nature such as logical reasoning, analysis, critical thinking skills, intuition,

creativity or self-esteem. - To have interest on clarity and precision in the course of works and pleasure in

order in presentation.


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GENERAL COMPETENCES Competence measuring scale

1 2 3 4

G3. To promote reading and critical textual analysis on the diverse scientific and cultural spheres contained in the scholar curriculum. X

G5. To encourage and value effort, perseverance and personal discipline in the students.

X

G10. To acquire habits and skills for autonomous and cooperative learning and promote it in the students.

X

G11. To know and apply communication technologies in classroom. To discern selectively audiovisual information which contributes to civic knowledge and cultural riches.

X

SPECIFIC COMPETENCES

1 2 3 4

E36. To acquire basic mathematical competences (numerical, calculus, geometrical, space representation, estimation and measure, organization and interpretation of information…)

X

E38. To analyze, reason and impart mathematical proposals. X

E39. To set out and solve daily life related problems X

E40. To assess the relation between mathematics and science as one of the pillars of scientific thinking. X


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LEARNING OUTCOMES COMPETENCES

R1. Students set out and solve daily life related problems of geometrical or data treatment nature. E36, E38, E39, E40

R2. Students apply and demonstrate basic properties of geometric figures.

G3 E36, E38, E39, E40

R3. Students use statistical techniques for data treatment. G3 E36, E38, E39, E40

R4. Students participate actively in the tasks proposed in class G3 E36, E38, E39, E40

R5. Students show a high level of correction in grammar and spelling. E38

ON-CAMPUS EDUCATIONAL ACTIVITIES

ACTIVITY Teaching-Learning Methodology

Relationship With Learning Outcomes

for the subject

ECTS

(express ECTS

distribution)

ON-CAMPUS CLASS Teacher presentation of contents, analysis of competences, explanation and in-class display of skills, abilities and knowledge.

R1, R2, R3, R4, R5 50% 0,9

PRACTICAL CLASSES

Group work sessions supervised by the professor. Case studies, diagnostic tests, problems, field work, computer room, visits, data search, libraries, on-line, Internet, etc. Meaningful construction of knowledge through interaction and student activity.

R1, R2, R3, R4, R5 26,7% 0,48

GROUP WORK PRESENTATION

Use of interdisciplinary knowledge R1, R2, R3, R4, R5 6,7%

0,12


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TUTORING

Personalized and small group attention. Period of instruction and/or orientation carried out by a tutor for the purpose of reviewing and discussing the materials and topics presented in lectures, seminars, readings, writing papers, etc.

R1, R2, R3, R5 11,1% 0,2

ASSESSMENT Group of oral and/or written tests used during initial, formative or additive assessment.

R1, R2, R3, R4, R5 5,5% 0,1

Total 1,8

INDEPENDENT WORK ACTIVITIES

ACTIVITY Teaching-Learning Methodology

Learning Outcomes Relationship

Course ECTS

GROUP WORK

Groupal preparation of readings, problem solving, seminars, papers, reports, ect. to be presented or submitted in theoretical lectures, practical and/or small-group tutoring.

R1, R2, R3, R4, R5 25% 0,675

INDEPENDENT WORK

Student study: Individual preparation of readings, essays, problem solving, seminars, papers, reports, etc. to be presented or submitted in theoretical lectures, practical and/or small-group tutoring sessions.

R1, R2, R3, R5 75% 2,025

Total 2,7


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SYSTEM FOR ASSESSING THE ACQUISITION OF THE COMPETENCES AND ASSESSMENT SYSTEM

Assessment Tool A Type

LEARNING OUTCOMES ASSESSED

Allocated Percentage

1. Written examination:Final theoretical-practical test (open

questions, objective questions, etc.)**

Worksheet elaboration** If this section is not passed, it will be

made up through an oral exam in the second examination session.

R1, R2, R5

50%

35%

2. Oral presentation of groupal andindividual work. If this section is not passed, it will be made up through an oral exam in the second examination session.

R1, R2, R3, R4, R5 10-12%

3. Individual assessment ofattendance and active participation in theoretical-practical and tutoring sessions. To pass this section the student must attend at least the 80% of the sessions.

R1, R2, R3, R4, R5 3-5%*

*Is mandatory for the overcoming of the subject to pass section 1 and 2 above.***Is mandatory for the overcoming of the subject that the student does not make more than 3 spelling mistakes in each written proof (such as works or written exam)

DESCRIPTION OF CONTENTS COMPETENCIAS

Mathematics constitutes one of the basic areas in elementary education. Hence the importance for future teachers to master mathematical notions which are taught in this stage and transmit them in a proper way, according to the children cognitive level. To this end, two basic content units will be developed attending to what is established in the curriculum: geometry and data treatment.

The contents to be developed throughout the subject are: - Geometry: two-dimensional geometry, areas and lengths

of figures, movements in the plane, three-dimensional geometry, areas and volumes in the space.

- Data treatment: basis of descriptive statistics, introduction to probability calculus.

R1, R2, R3, R4, R5


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REFERENCES

Alsina i Pastells, A. (2004). Desarrollo de competencias matemáticas con recursos lúdicos-manipulativos. Para niños y niñas de 6 a 12 años. Narcea.

Callejo, MªL. (1994). Un club matemático para la diversidad. Narcea

Cascallana, M. T. (1988). Iniciación a la matemática. Materiales y recursos didácticos. Ed. Aula XXI / Santillana.

Castro, E. (2001). Didáctica de la matemática en la Educación Primaria. Madrid: Síntesis.

Chamorro, M. C. (2003). Didáctica de las Matemáticas para Primaria. Prentice Hall.

Chauvel, D., Michel, V. (1989). Juegos de reglas para desarrollar la inteligencia. Nancea.

Colección (1991). Matemáticas: Cultura y aprendizaje. Madrid: Síntesis.

Corbalán, F. (1996). Números, cultura y juegos. Tu mundo y las matemáticas. Videocinco, Madrid.

De Guzmán, M. (2004). Para pensar mejor. Ediciones Pirámide (Grupo Anaya S.A.).

Ferrero, L. (1991). El juego y la matemática. La Muralla. Madrid.

Godino, J. D. (2004) Matemáticas para maestros, Depto. Didáctica de las Matemáticas, Univ. Granada.

Gómez Chacón, I.Mª. (1992). Los juegos de estrategia en el currículo de Matemáticas. Narcea.

Gutiérrez, A. (1991). Matemáticas: Cultura y aprendizaje. Madrid: Síntesis.

Hidalgo Alonso, S. (1997). Las matemáticas en el título de maestro. Consideraciones teóricas, didácticas y prácticas. L. Diagonal.

Martínez, J. Bujanda, M.P., Velloso, J.M. (1984). Matemáticas 1, Ediciones SM.

Miranda Casas, A. (1988). Dificultades del aprendizaje de las matemáticas. Un enfoque evolutivo. Aljibe.

Nortes Checa, A. (1993). Matemáticas y su didáctica. Tema-DM.

Nortes Checa, A. (2013). Actividades prácticas de Matemáticas y su didáctica 1. EDITORIAL CCS.

Nortes Checa, A. (2014). Actividades prácticas de Matemáticas y su didáctica 2. EDITORIAL CCS.


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TEMPORAL ORGANIZATION OF LEARNING:

BLOCK CONTENT / TEACHING UNIT # OF MEETINGS

0 Introduction 1

1

Two-dimensional geometry - Basic concepts. Classification of two-dimensional

shapes. - Congruence. Metric relations in a triangle.- Movements in a plane.- Length and area.-

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2

Three-dimensional geometry - Polyhedra. Basic concepts. Classification.- Solids of revolution.- Plane developement- Surface of solids. Volume.

4

3 Statistics

- Basic concepts-- Statistic measures.- Graphical representation.-

4

4 Probability

- Basic concepts.- Laplace law.

2

Nortes Checa, A., Nortes Martínez-Artero, R.(2012). La resolución de problemas de Geometría. EDITORIAL CCS.


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Addendum to the Course Guide of the Subject

Teaching Training in Primary Education

Due to the exceptional situation caused by the health crisis of the COVID-19 and

taking into account the security measures related to the development of the

educational activity in the Higher Education Institution teaching area, the

following changes have been made in the guide of the subject to ensure that

Students achieve their learning outcomes of the Subject:

Situation 1: Teaching without limited capacity (when the number of

enrolled students is lower than the allowed capacity in classroom, according to

the security measures taken).

In this case, no changes are made in the guide of the subject.

Situation 2: Teaching with limited capacity (when the number of enrolled

students is higher than the allowed capacity in classroom, according to the

security measures taken).

In this case, the following changes are made:

Educational Activities of Onsite Work:

All the foreseen activities to be developed in the classroom as indicated in this

field of the guide of the subject will be made through a simultaneous teaching

method combining onsite teaching in the classroom and synchronous online

teaching. Students will be able to attend classes onsite or to attend them online



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through the telematic tools provided by the university (videoconferences). In any

case, students who attend classes onsite and who attend them by

videoconference will rotate periodically.

In the particular case of this subject, these videoconferences will be made

through:

X Microsoft Teams

Kaltura X Plataforma UCV Net

Situation 3: Confinement due to a new State of Alarm.

In this case, the following changes are made:

1. Educational Activities of Onsite Work:

All the foreseen onsite activities described in this section of the Course Guide,

as well as the group and personalized tutoring, will be done with the telematic

tools provided by the University, through:

X Microsoft Teams

Kaltura X Plataforma UCV Net

Explanation about the practical sessions:

1. They will be carried out individually or in groups through Teams or the UCVNet

Platform.


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2. Telematic attendance at practical sessions is compulsory. In case of not being

able to attend the online sessions for a justified reason, it will be compulsory

to present that justification and hold tutorials with the teacher to follow up on

the practical sessions.

2. System for Assessing the Acquisition of the competences and Assessment

System

ONSITE WORK

Regarding the Assessment Tools, the Assessment Tools will not be modified. If

onsite assessment is not possible, it will be done online through the UCVnet

Campus.

ONLINE WORK

Regarding the Assessment Tools, the following changes will be made to adapt

the subject’s assessment to the online teaching.

Course guide Adaptation

Assessment tool Allocated

Percentage

Description of

the suggested

changes

Platform to be used

Exam 50% 35-40% UCVNet /Teams Worksheet

ellaboration 35% 45% UCVNet /Teams

Oral

presentation 12-15% 15-20% UCVNet /Teams

Participation 3-5% 0%



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The other Assessment Tools will not be modified with regards to what is

indicated in the Course Guide.

Observations to the assessment system:

1.The exam wil consist of two parts: first, a close-ended questions test that Will

be worth 50-60% of the overall exam result and secondly a section comprising

problems resolution that will be worth 40-50% of the overall exam result.

2. It is still essential to pass all the sections to pass the course.

3. The criteria regarding grammatical expression and spelling are maintained.

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FUNDAMENTALS OF GEOMETRY AND DATA TREATMENT FOR …