doctrina social de la iglesia - Universidad Católica de Valencia

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1
Universidad Católica de Valencia
PCA-27-F-01 Ed.00
FUNDAMENTALS OF ARITHMETICS AND
MEASURE FOR TEACHERS
Faculty of Psychology, Teacher Training and Education
Sciences
Year 2014-15
Universidad Católica de Valencia “San Vicente Mártir”
2
PCA-27-F-01 Ed.00
TEACHING GUIDE TO THE SUBJECT
ECTS
SUBJECT: FUNDAMENTALS OF ARITHMETICS AND
4,5
MEASURE FOR TEACHERS
Module: MATHEMATICS TEACHING AND LEARNING
15
Education type:
YEAR: 1st
DIDACTIC-DISCIPLINARY
Semester: 2nd
OBLIGATORY
Department:
Teachers:
MATHEMATICS, NATURAL
Ana Isabel Cárceles
SCIENCES AND SOCIAL
SCIENCES APPLIED TO
Aida García
EDUCATION
Sonia Martín
E-mail:
Elena Moreno
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
María José Soto
Dionisio F. Yáñez
MODULE ORGANIZATION
____________________________________________________________________________
# 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.
MATHEMATICS TEACHING AND LEARNING
Subjects and Courses
Subject
MATHEMATICS
AND ITS
DIDACTICS
ECTS
Courses
Fundamentals of Arithmetics and
Measure for teachers
15
Fundamentals of Geometry and Data
treatment for teachers
Didactics of Mathematics
ECTS
Course/
semester
4,5
4,5
1/2
3/1
6
3/2
3
PCA-27-F-01 Ed.00
TEACHING GUIDE FOR FIELD/SUBJECT: FUNDAMENTALS OF
ARITHMETICS AND MEASURE FOR TEACHERS
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 identify the different number sets: natural, integer, rationals, and check its basic
properties and operate with them.
-
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.
4
PCA-27-F-01 Ed.00
Competence
measuring scale
GENERAL COMPETENCES
1
2
G3. To express oneself correctly, orally and in writing, in the official
languages of the autonomous region and control the use of different
ways of expression.
G14. To encourage and value effort, perseverance and personal
discipline in the students.
3
4
X
X
G22. To acquire habits and skills for autonomous and cooperative
learning and promote it in the students.
X
G2. To promote reading and critical textual analysis on the diverse
scientific and cultural spheres contained in the scholar curriculum.
X
SPECIFIC COMPETENCES
1
2
3
4
E1. To acquire basic mathematical competences (numerical, calculus,
geometrical, space representation, estimation and measure, organization and
interpretation of information…)
X
E3. To analyze, reason and impart mathematical proposals.
X
E4. To set out and solve daily life related problems
X
E5. To assess the relation between mathematics and science as one of
the pillars of scientific thinking.
X
LEARNING OUTCOMES
R1. The student relates Mathematics to other areas.
R2. The student sets out and solves daily life related
problems by using calculus strategies, explaining the meaning
of data, the given situation, the process and the obtained
solutions.
R3. The student makes clear and detailed oral descriptions
and presentations, developing specific ideas and finishing with
appropriate conclusions.
R4. The student uses properly the terminology and
symbology of mathematics.
COMPETENCES
G4, G10, G12, G17, G18,
E2, E4, E5, E6
E1, E3, E4, E5
G2, G3, G14, G22
E1, E3
G3,
E1, E3, E6
5
PCA-27-F-01 Ed.00
R5. The student knows and explains basic Set Theory.
G2, G12
E1, E3
R6. The student knows and explains the concept of number,
its uses and representations.
R5. The student uses properly the measurement units in
Metric and sexagesimal system corresponding to the basic
magnitudes, as well as its equivalence and operations.
G2
E1, E3
G2, G4, G12
E1, E3, E4, E5, E6
R8. The student has a good command of basic arithmetic
operations, properties and algorithms in the classical sets:
natural, integer, rational and real numbers.
G2
E1, E3, E4, E5
R9. The student uses proper information from different
sources.
G2, G14, G22,
E3, E5
R10. The student uses properly the algebraic language.
He/she is able to solve first and second degree equations and
systems.
G2
E1, E3, E4, E5
ON-CAMPUS EDUCATIONAL ACTIVITIES
ACTIVITY
ON-CAMPUS CLASS
PRACTICAL CLASSES
Teaching-Learning
Methodology
Teacher presentation of
contents, analysis of
competences, explanation and
in-class display of skills, abilities
and knowledge.
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.
GROUP WORK
PRESENTATION
Relationship With
Learning Outcomes
for the subject
ECTS
(express
ECTS
distribution)
R1, R2, R3, R4, R5,
R6, R7, R8, R9, R10,
R12, R13
50%
0,9
R1, R2, R3, R4, R5,
R6, R7, R8, R9, R10,
R12, R13
26,7%
0,48
R1, R2, R3, R4, R5,
R6, R7, R8, R9, R11,
R12, R13
6,7%
0,12
6
PCA-27-F-01 Ed.00
TUTORING
ASSESSMENT
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.
Group of oral and/or written tests
used during initial, formative or
additive assessment.
R1, R2, R3, R4, R5,
R6, R7, R8, R9, R11,
R12, R13
11,1%
0,2
R1, R2, R3, R4, R5,
R6, R7, R8, R9, R11,
R12, R13
5,5%
0,1
Total
1,8
INDEPENDENT WORK ACTIVITIES
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,
R6, R7, R8, R9, R11,
R12, R13
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, R4, R5,
R6, R7, R8, R9, R11,
R12, R13
75%
2,025
Teaching-Learning
Methodology
ACTIVITY
Total
2,7
SYSTEM FOR ASSESSING THE ACQUISITION OF THE COMPETENCES
AND ASSESSMENT SYSTEM
Assessment Tool
A Type
LEARNING OUTCOMES
ASSESSED
Allocated
Percentage
7
PCA-27-F-01 Ed.00
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.
2. Oral presentation of groupal and
individual work. If this section is not
passed, it will be made up through an oral
exam in the second examination session.
50%
R1, R2, R4, R5, R6, R7, R8, R9,
R11, R12, R13
35%
R1, R2, R3, R4, R5, R6, R7, R8, R9,
R10, R11
3. Individual assesment of attendance and
active participation in theoretical-practical and
tutoring sessions. To pass this section the
student must attend at least the 80% of the
sessions.
R3
10-12%
3-5%*
*Is mandatory for the overcoming of the subject to pass each section 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)
Assessment Tool
B Type
LEARNING OUTCOMES
ASSESSED
Allocated
Percentage
70%
R1, R2, R4, R5, R6, R7, R8, R9,
R11, R12, R13
20-22%
R1, R2, R3, R4, R5, R6, R7, R8, R9,
R10, R11
3. Individual assessment of attendance and
active participation in tutoring sessions (at
least once a month).
R3
5%
3-5%**
* Only the students who present in the beginning of the semester an appropriate justification for
not attending the lessons will be admitted to this type of assessment.
**Is mandatory for the overcoming of the subject to pass each section above.
***Is mandatory for the overcoming of the subject that the student does not make more than 3
Assessment Tool
C Type: 3rd examination session
LEARNING OUTCOMES
ASSESSED
Allocated
Percentage
8
PCA-27-F-01 Ed.00
70%
R1, R2, R4, R5, R6, R7, R8, R9,
R11, R12, R13
20-22%
R1, R2, R3, R4, R5, R6, R7, R8, R9,
R10, R11
3. Individual assessment of attendance and
active participation in tutoring sessions (at
least once a month).
R3
5%
3-5%*
*Is mandatory for the overcoming of the subject to pass each section above.
**Is mandatory for the overcoming of the subject that the student does not make more than 3
DESCRIPTION OF CONTENTS
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: Arithmetics and Measure.
COMPETENCES
R1 to R13
The contents to be developed throughout the subject are:
- Arithmetics: numeral systems, natural numbers,
operations on the natural numbers, divisibility, integer
numbers, rational numbers.
- Measure: proporcionality, magnitudes and units of
measurement, equivalences.
REFERENCES
Alsina i Pastells, A. (2004). Desarrollo de competencias matemáticas con recursos lúdicosmanipulativos. 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.
9
PCA-27-F-01 Ed.00
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.
Gateño, C. (1961). Introducción al método Cuisenaire Gateño de los números en color para la
enseñanza de la aritmética. Libro del maestro. Cuisenaire de España
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.
Kamii, C. (2003). El niño reinventa la aritmética. Implicaciones de la teoría de Piaget.
Machado.
A.
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. (1993). Matemáticas y su didáctica. Tema-DM.
TEMPORAL ORGANIZATION OF LEARNING:
BLOCK CONTENT / TEACHING UNIT
# OF MEETINGS
0
Introduction
1
1
Elementary set theory.
4
10
PCA-27-F-01 Ed.00
2
3
4
5
6
Set construction of natural numbers.
Definition of opertions.
Number systems.
Equations.
Relationships of divisibility on natural numbers. Fundamental
theorem.
Multiples and factors.
Primes and composite numbers.
Highest common factor and lowest common
Integer numbers.
Definition and operations.
Hierarchy of operations.
Rational numbers.
Definition and operations.
Decimal expressions.
Introduction to magnitudes and to measurement
Proportionality and percentages.
International System of Measurement.
4
4
4
4
3

doctrina social de la iglesia - Universidad Católica de Valencia

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