MATHEMATICAL LOGIC
LOGICA MATEMATICA
Set theory and research logic
Insiemistica e logica della ricerca
A.Y. | Credits |
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2020/2021 | 8 |
Lecturer | Office hours for students | |
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Giovanna Marani | Tuesday ( hours 16-17) and Wednesday ( hours 16 -17) palazzo Albani C1 Email: giovanna.marani@uniurb.it |
Assigned to the Degree Course
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Learning Objectives
The course aims at providing the basic principles and logical structures underlying investigation as a process of action in research. In this context, there will be particularly the usage of theoretical knowledge coming from Dewey’s logic for methodological competences learning related to action research project elaboration. Action-research as a permanent reflective practice model represents a formative element leading to practice the teaching as profession.
Moreover, the course aims at outlining the educational and operational paths on to the objectives of logic and mathematics prospected by the national guidelines for the nursery and primary school curriculum.
In particular the course is aimed at knowledge and understanding of:
- The basic elements of action-research
- The Distinctive peculiarities and limits of the context operational research
- The main features of Dewey’s research
- The Value of reflection in action-research
- The Set concept and its employment in logical and mathematical fields in nursery and primary school
Program
1. Action research epistemology
1. Dewey’s logic as investigation theory
2. Investigation structure as a dynamic and experimental procedure
3. Dewey’s logic as epistemological and methodological framework of action research
4. The inductive and deductive processes in the investigation
5. Research as interaction between recognition and transformation
6. The relation between theory and practice in research
7. Reflectivity as a fundamental practice in the path of action-research
2 Some elements of logic
1. The logic of statements
2. The connectives
3. The logic of predicates
4. The simple set theory
5. Reports
Learning Achievements (Dublin Descriptors)
In relation to the teaching , students must demonstrate :
1. KNOWLWDGE AND UNDERSTANDING .
In particular:
- Knowledge of main lines of the epistemological debate in the context operative research area with particular reference to its constitutive components;
- Knowledge of Dewey’ s research;
- Mastery of basic knowledge of the set theory with particular regard to the aspects which are most related to their use in the didactic-disciplinary approach.
2. APPLYING KNOWLEDGE AND UNDERSTANDING
- Knowledge and understanding of the theoretical and methodological basic principles of action-research according to Dewney’s perspective;
- Knowledge of the epistemological and procedural framework of action- research ;
- Ability to recognize peculiarities and issues of action-research in the field of pedagogy 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 analyse and critically assess, in its fundamental methodological features, the action research as research practice usable in education;
- Ability to use knowledge and concepts to think and autonomously suggest possible didactic and operative paths - research to solve logical and mathematical issues
- Ability to use the set theory knowledge to solve logical and mathematical issues.
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
Some educational support lessons held by the teacher and/or a subject expert and concerning the practical use of the introduced theoretical concepts are planned.
Teaching, Attendance, Course Books and Assessment
- Teaching
Frontal lessons (lectures), practical exercises and some laboratory activities.
- Course books
- Marani G., La ricerca-azione. Una prospettiva deweyana, Franco Angeli, Milano 2013. (pagine 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)
- Lanciotti C., Marazzani I., Logica, Carocci, Roma, 2004. ( pagine 112)
Other material will be indicated during the lessons and / or made available in digital form.
In-depth texts
Giovannoni L.,Lingua e Logica, Franco Angeli, Milano,1986
Varga T.,Fondamenti di logica per insegnanti,Bollati Boringhieri,Torino,1973
- Assessment
The objectives set are verified through a written test which includes three open questions and one set exercise. The time available to answer the questions is 1 hour.
The evaluation criteria are:
- relevance of the answers to the questions related to the contents of the program;
- level of articulation and argumentation of the answer;
- adequacy of the language used;
- logical resolution capabilities.
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.
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