Università degli Studi di Urbino Carlo Bo / Portale Web di Ateneo


MATHEMATICAL LOGIC
LOGICA MATEMATICA

A.Y. Credits
2024/2025 8
Lecturer Email Office hours for students
Giovanna Marani Tuesday and Wednesday after the lesson if possible by appointment palazzo Albani Email: giovanna.marani@uniurb.it

Assigned to the Degree Course

Primary teacher education (LM-85bis)
Curriculum: PERCORSO COMUNE
Date Time Classroom / Location
Date Time Classroom / Location

Learning Objectives

The course aims to provide the basic principles and logical structures underlying the investigation as a process of action in research. In this context, there will be in particular the use of theoretical knowledge deriving from Dewey's logic for the learning of methodological skills related to the elaboration of research-action projects. Action research as a model of permanent reflective practice represents a formative element that leads to the exercise of teaching as a profession. The course also aims to outline the training and operational paths with respect to the objectives of logic and mathematics envisaged by the national guidelines for the nursery and primary school curriculum. In particular, the course is aimed at the knowledge and understanding of:

- The basic elements of action research

- The peculiarities and distinctive limits of contextual operational research - The main features of Dewey's research

- The value of reflection in action research

- The concept of Set and its use in logic and mathematics in kindergarten and primary school

- Some forms of scientific reasoning - Some of the most common reasoning errors

Program

1. Action research epistemology: 1. Dewey's logic as a theory of inquiry 2. The structure of the investigation as a dynamic and experimental procedure 3. Dewey's logic as an epistemological and methodological framework for action research 4. Inductive and deductive processes in the investigation 5. Research as an interaction between recognition and transformation 6. The relationship between theory and practice in research 7. Reflexivity as a fundamental practice in the path of action research

2 Some elements of logic 1. The logic of the statements 2. The connectives 3. The logic of predicates 4. The theory of simple sets 5. Reports

3-The logical reasoning and its fallacies The forms of scientific reasoning The most common reasoning errors

Bridging Courses

Not provided

Learning Achievements (Dublin Descriptors)

In relation to teaching, students must demonstrate

1. KNOWLEDGE AND UNDERSTANDING.

In particular :

- Knowledge of Dewey's research;

- Mastery of the basic knowledge of set theory with particular regard to the aspects most related to their use in the didactic-disciplinary approach.

- Knowledge of the forms of scientific reasoning and related fallacies

2.        . APPLY KNOWLEDGE AND UNDERSTANDING

-            Knowledge and understanding of the basic theoretical and methodological principles of action research according to Dewney's  perspective;

-            Knowledge of the epistemological and procedural framework of action research;

-           Ability to recognize peculiarities and problems of action research in the field of pedagogical research;

-  Ability to examine the use of action research in the field of school education ;

-  Ability to recognize the employment of set theory  in logical and mathematical education paths.

3.         MAKING JUDMENTS

-  Ability to detect action-research as a fundamental research methodology in educational field;

-  Ability to think of possible action-research paths ;

-  Ability to employ the set theory to speculate on methodological and didactic paths.

4.         COMMUNICATION SKILLS

-  Ability to communicate the acquired learnings using the proper language;

-  Ability to discuss and explain the suggested methodological and didactic paths.

5.   LEARNING SKILLS

-           Ability to critically analyze and evaluate, in its fundamental methodological characteristics, action research as a research practice that can be used in education;

-         Ability to use knowledge and concepts to independently think and suggest possible educational and operational paths - research to solve logical and mathematical problems

-        Ability to use the knowledge of set theory to solve logical and mathematical problems.

Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Supporting Activities

Group exercises, laboratory activities and lectures are planned


Teaching, Attendance, Course Books and Assessment

Teaching

The course includes: lectures, individual and group practical exercises, laboratory activities, construction of some teaching units

Innovative teaching methods

Group exercises, laboratory activities and lectures are planned

Attendance

Not provided

Course books
  • Marani G., La ricerca-azione. Una prospettiva deweyana , Franco Angeli, Milano 2013. (pagina 185)
  • Tombolato M.,  Il ruolo della pratica della ricerca nello sviluppo delle competenze di decision making degli insegnanti in D'ugo R., Marani G., Le pratiche collaborative per la sperimentazione e l'innovazione scolastica , FrancoAngeli, Milano 2020. ( pp. 150-182)

Other material will be indicated during the lessons and/or made available in digital form.

In-depth texts

Lanciotti C., Marazzani I., Logica,   Carocci, Roma, 2004. ( pagine 112)

Giovannoni L.,Lingua e Logica, Franco Angeli, Milano,1986

Varga T.,Fondamenti di logica per insegnanti,Bollati Boringhieri,Torino,1973

Assessment

The expected objectives are verified through a written test which includes three open questions - two of which on action research and one on the forms of logical reasoning and its fallacies - and a set theory exercise. The time available to answer the proposed questions is 1 hour.

The evaluation criteria are:

- relevance of the answers to the questions posed in relation to the contents of the programme;
- level of articulation and argumentation of the answer;
- adequacy of the language used;
- logical resolution capabilities
Each of the criteria is assessed on the basis of a four-level scale of values/judgments with equal weight assigned to each criterion.
The final evaluation is expressed in thirtieths.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

Additional Information for Non-Attending Students

Teaching

The course includes: lectures, individual and group practical exercises, laboratory activities, construction of some teaching units

Attendance

Not provided

Course books
  • Marani G., La ricerca-azione. Una prospettiva deweyana , Franco Angeli, Milano 2013. (pagina 185)
  • Tombolato M.,  Il ruolo della pratica della ricerca nello sviluppo delle competenze di decision making degli insegnanti in D'ugo R., Marani G., Le pratiche collaborative per la sperimentazione e l'innovazione scolastica , FrancoAngeli, Milano 2020. ( pp. 150-182.

In order to give the opportunity for non-attending students to compensate with self-study what is done during the lectures, the following materials referring to the same contents of the program are indicated for the purpose of promoting their full understanding: a high school mathematics textbook chapter on sets, the Moodle platform ' blended.uniurb.it  on which exercises are posted.,lectures and all materials used.

Translated with DeepL.com (free version)

Other material will be indicated during the lessons and/or made available in digital form.

In-depth texts

Lanciotti C., Marazzani I., Logica,   Carocci, Roma, 2004. ( pagine 112)

Giovannoni L.,Lingua e Logica, Franco Angeli, Milano,1986

Varga T.,Fondamenti di logica per insegnanti,Bollati Boringhieri,Torino,1973

Assessment

The expected objectives are verified through a written test which includes three open questions - two of which on action research and one on the forms of logical reasoning and its fallacies - and a set theory exercise. The time available to answer the proposed questions is 1 hour.

The evaluation criteria are:

- relevance of the answers to the questions posed in relation to the contents of the programme;
- level of articulation and argumentation of the answer;
- adequacy of the language used;
- logical resolution capabilities
Each of the criteria is assessed on the basis of a four-level scale of values/judgments with equal weight assigned to each criterion.
The final evaluation is expressed in thirtieths.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

« back Last update: 12/07/2024

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