Faculty of Education · Secondary School Mathematics Education · Undergraduate
Course Objective
To develop the awareness of prospective mathematics teachers about the nature of mathematics, to ensure that they are equipped with the place of mathematics in science, mathematical thinking methods, crises experienced in the history of mathematics and philosophical views on the foundations of mathematics.
Course Content
In this course, the definition of mathematics, its place in science, mathematical thinking methods, distinctions between inductive and deductive thinking, various meanings of mathematical concepts and propositions, applicability of mathematics in the real world, mathematical crises, and philosophical views on the foundations of mathematics will be discussed.
Required Resources
Matematiksel düşünme, Cemal Yıldırım, Remzi Kitabevi.
Bilim felsefesi, Cemal Yıldırım, Remzi Kitabevi. -Matematik felsefesi,
Stephen F. Barker, İmge Kitabevi
Matematik Felsefesi, Bekir Sami GÜR, Kadim Yayınları
Recommended Resources
Shapiro, S. (2002). Thinking about mathematics. The philosophy of mathematics.
Barrow, J. D., Güpgüpoğlu, İ., & Karman, İ. (2001). Gökteki Pi. Beyaz Yayınları.
Hardy, G. H. (2004). Bir matematikçinin savunması. Eronus books.
Ifrah, G., & Dinçer, K. (1999). Rakamların evrensel tarihi. Tübitak.
Chaitin, G. J. (1999). Matematiğin temelleri üzerine uyuşmazlık yüzyılı. Matematik Felsefesi, 335-374.
Rules
Students must have %70 attendance whole the term to be able to entered the final exam.Student must have minimum 50 point to pass the final exam.
Course Learning Outcomes
- Students will understand the ontology and epistemology of mathematics.
- Students will examine the work of the pioneers of mathematical philosophy such as Frege, Russel, Hilbert, Brouwer and Gödel.
- Students willl learn the basics of mathematics, methods and philosophical problems related to the nature of mathematics.
- Students will learn the basic theories of mathematical philosophy, logicism, formalism and intuitionism.
- Students will establish the relationship between mathematics philosophy and mathematics education.
Core Area Distribution
Teaching Methods
Assessment & Evaluation
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 14 | 2 | 28 |
| Out of Class Study Period | 19 | 2 | 38 |
| Midterm | 0 | 2 | 0 |
| Quiz | 0 | 0 | 0 |
| Assignment | 3 | 5 | 15 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 2 | 2 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Introduction, Information about the purpose, scope and process of the course Mathematical Philosophy in Curricula | Introduction of the course |
| 2 | Discussion on the question of what is mathematics. | Resource Book |
| 3 | Ontology of mathematics, Epistemology of mathematics | Resource Book |
| 4 | Numbers, sets, functions etc. the meaning of mathematical concepts and the meaning of mathematical expressions | Resource Book |
| 5 | Fundamentals of mathematics | Resource Book |
| 6 | Methods of mathematics | Resource Book |
| 7 | Philosophical problems about the nature of mathematics | Resource Book |
| 8 | Midterm | Midterm |
| 9 | Objectivity in mathematics and applicability to the real world | Resource Book |
| 10 | The works of pioneers such as the philosophy of mathematics such as Frege, Russell, Hilbert Brouwer and Gödel | Resource Book |
| 11 | Flatness and dimension concept | Resource Book |
| 12 | Basic theories of mathematics philosophy (Logisicm), formalism and intuitionism | Resource Book |
| 13 | Semi-experimentalists and Lakatos | Resource Book |
| 14 | The relationship between mathematics philosophy and mathematics education | Resource Book |
| 15 | Social groups in the philosophy of mathematics education | Course Evaluation |
| 16 | Final | Final |