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Information
| Code | MATZ402 |
| Name | Philosophy of Mathematics |
| Term | 2024-2025 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. PERİHAN ARTUT |
| Course Instructor |
1 2 |
Course Goal / Objective
To have teacher candidates knowledge of ontology and epistemology of mathematics, be aware of the philosophical problems of the nature of mathematics, studies of the mathematical philosophical pioneers and increase their awareness of the basic theories in mathematical philosophy
Course Content
Ontology and epistemology of mathematics; numbers, sets, functions, etc. mathematical concepts and propositions and meanings of mathematical expressions; the philosophical problems of mathematics through its the foundations, methods and the nature, objectivity in mathematics and applicability to the real world; Studies of mathematical philosophical pioneers such as Frege, Russel, Hilbert, Brouwer and Gödel; level and dimension concept, basic theories in mathematics philosophy Logicism, Formalism and intuitionism, semi-experimentalists and Lakatos; relation of mathematical philosophy with mathematics education; social groups in the philosophy of mathematics education.
Course Precondition
None
Resources
Matematik Tarihi ve Felsefesi (Pegem Akademi Yayıncılık) Matematik Felsefesi (Stephen F. Barker /İmge Kitapevi) Matematik Felsefesi (Bekir Gür) Matematik Üzerine Diyaloglar (Alfred Renyi/Dost Yayınevi) Bilim felsefesi, Cemal Yıldırım, Remzi Kitabevi. -Matematik felsefesi, Baki, A. (2008). Kuramdan Uygulamaya Matematik Öğretimi. Harf yayınları. Yıldırım, C. Matematiksel Düşünme, Remzi Kitabevi.
Notes
https://library.cu.edu.tr/cu/e-kaynaklar/veritabanlari
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explains the ontology and epistemology of mathematics |
| LO02 | Evaluates some mathematical objects, such as numbers, sets, functions, in terms of their meanings. |
| LO03 | Analyses philosophical problems related to the nature of mathematics. |
| LO04 | Compares the basic theories of the philosophy of mathematics in terms of the development of mathematics. |
| LO05 | Interprets the works of the pioneers of philosophy of mathematics. |
| LO06 | Recognizes the relationship between philosophy of mathematics and mathematics education. |
| LO07 | Explains the work of the pioneers of the philosophy of mathematics |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has enough knowledge about mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has pedagogical knowledge about teaching profession and field. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Implements classroom management approaches to be used in educational environments effectively. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Uses Turkish properly and effectively according to the rules. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Selects and designs appropriate materials, in mathematics teaching. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Monitors students' progress using different assessment and evaluation methods and techniques. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Takes responsibility as an individual and as a team member to solve problems related to the field. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people. | 5 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses information and communication technologies and other related materials for an effective mathematics teaching. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Has enough foreign language knowledge to follow foreign resources related to the field. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Has the knowledge of the purpose, structure and functioning of the Turkish education system. | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes a teacher who adheres to Atatürk's principles and revolutions. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | The birth and historical development of the philosophy of mathematics | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 2 | The birth of logical and abstract thinking, its philosophical aspects. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 3 | The beauty of mathematics, philosophical thoughts about the nature of mathematics. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 4 | Philosophical views of Aristotle, Socrates, Euclidean, Phythogoras and Descartes. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 5 | The relationship between the philosophy of mathematics and mathematics education. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 6 | Social groups in the philosophy of mathematics education. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 7 | Objectivity in mathematics and its applicability to the real world. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 8 | Mid-Term Exam | prepare to exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The relationship of the philosophy of mathematics with other sciences. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 10 | Philosophical views on the foundations of mathematics. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 11 | Logicism, ontology. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 12 | Formalism, metaphysics, quasi-experimentalists. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 13 | Intuitionism, structuralism. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 14 | Studies of the pioneers of the philosophy of mathematics such as Frege, Russell, Hilbert, Brouwer, Lakotos, Kant and Gödel. | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Bireysel Çalışma |
| 15 | General evulation | Examination of relevant resources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 16 | Term Exams | prepare to exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | prepare to exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||