Information Package / Course Catalogue
| Elementary Mathematics Education | |||||
| Bachelor | Length of the Programme: 4 | Number of Credits: 240 | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF: Level 6 |
Ders Genel Tanıtım Bilgileri
| School/Faculty/Institute | Faculty of Education | ||||
| Course Code | MATH 136 | ||||
| Course Title in English | Philosophy of Mathematics | ||||
| Course Title in Turkish | Matematik Felsefesi | ||||
| Language of Instruction | EN | ||||
| Type of Course | Lecture | ||||
| Level of Course | Seçiniz | ||||
| Semester | Fall | ||||
| Contact Hours per Week |
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| Estimated Student Workload | 118 hours per semester | ||||
| Number of Credits | 2 ECTS | ||||
| Grading Mode | Standard Letter Grade | ||||
| Pre-requisites | None | ||||
| Expected Prior Knowledge | None | ||||
| Co-requisites | None | ||||
| Registration Restrictions | Only Undergraduate Students | ||||
| Overall Educational Objective | To learn about historical development of mathematical philosophies | ||||
| Course Description | This course provides students to state several key philosophical questions that prompted a search for a "foundation" for mathematics and mathematics education in the 19th and 20th centuries. Second, students learn to explain how changes in mathematical practice changed philosophical theorizing. | ||||
| Course Description in Turkish | Bu dersin amacı, 19. ve 20. yüzyıllarda matematik ve matematik eğitimi için bir "temel" arayışına yol açan birkaç temel felsefi soruyu öğrencilerin ifade etmesini ve bu konuda temel bilgilere sahip olmasını sağlamaktır. İkincisi, öğrencilerin matematiksel uygulamadaki değişikliklerin felsefi kuramlaşmayı nasıl değiştirdiğini açıklayabilmeyi öğrenmesidir. |
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) understand how changes in mathematical practice change philosophical theorizing and vice versa; 2) analyze different mathematical proofs; 3) assess validity of mathematical arguments; 4) reflect on historical development of mathematical philosophy. |
| Program Learning Outcomes/Course Learning Outcomes | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 1) Apply effective and student-centered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills. | ||||
| 2) Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics. | ||||
| 3) Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics. | ||||
| 4) Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs. | ||||
| 5) Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning. | ||||
| 6) Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness. | ||||
| 7) Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multi-disciplinary as well as take individual responsibility when they work alone. | ||||
| 8) Have awareness of need for life-long learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways. | ||||
| 9) Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources. | ||||
| 10) Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio. | ||||
| 11) Have awareness of and sensitivity to different cultures, values and students’ democratic rights. | ||||
| 12) Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws. | ||||
| 13) Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities. | ||||
| 14) Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. |
Relation to Program Outcomes and Competences
| N None | S Supportive | H Highly Related |
| Program Outcomes and Competences | Level | Assessed by | |
| 1) | Apply effective and student-centered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills. | H | Presentation,Project |
| 2) | Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics. | N | |
| 3) | Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics. | H | HW,Presentation,Project |
| 4) | Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs. | N | |
| 5) | Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning. | N | |
| 6) | Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness. | N | |
| 7) | Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multi-disciplinary as well as take individual responsibility when they work alone. | S | Presentation |
| 8) | Have awareness of need for life-long learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways. | S | Presentation,Project |
| 9) | Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources. | S | HW,Presentation,Project |
| 10) | Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio. | S | Presentation |
| 11) | Have awareness of and sensitivity to different cultures, values and students’ democratic rights. | N | |
| 12) | Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws. | S | Presentation,Project |
| 13) | Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities. | N | |
| 14) | Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. | S | HW,Presentation,Project |
| Prepared by and Date | RUKİYE DİDEM TAYLAN , |
| Course Coordinator | BENGİ BİRGİLİ |
| Semester | Fall |
| Name of Instructor | Öğr. Gör. TUĞRUL ÖZKARACALAR |
Course Contents
| Week | Subject |
| 1) | Introduction to the class: Philosophy of Mathematics |
| 2) | Importance of Philosophy in Mathematics Education |
| 3) | Investigating Proofs of Major Mathematical Theorems |
| 4) | Generality and Euclidean Geometry |
| 5) | Aristotelian Logic |
| 6) | Theory of Abstract Ideas and Demonstration |
| 7) | Construction of Arguments |
| 8) | Presentation Week |
| 9) | Presentation Week |
| 10) | Knowing in Mathematics |
| 11) | Rules of Inference vs. Axioms (Leibniz) |
| 12) | A Priori vs Analyticity (Kant’s Philosophy of Mathematics) |
| 13) | Overview of Historical Development of Mathematics and Philosophy |
| 14) | Presentation of Final Project |
| 15) | Final Examination Period (Project) |
| 16) | Final Examination Period (Project) |
| Required/Recommended Readings | List of readings and indication whether they are required or recommended. Euclid's Elements J. Locke. An essay concerning human understanding. English. Ed. by P. H. Nidditch. Oxford: Clarendon Press, 1975. S. Shapiro. Thinking about mathematics: The philosophy of mathematics. Oxford University I. Kant. Prolegomena to any future metaphysics: with selections from the Critique of pure reason. Ed. by G. Hatfield. Cambridge: Cambridge University Press, 2004. | ||||||||||||||||||
| Teaching Methods | Flipped Learning Method Active Learning Student Presentations Lecture | ||||||||||||||||||
| Homework and Projects | Students will do several homework on given assigned readings. They will also develop a final project on using mathematical philosophies and to design mathematical activity. | ||||||||||||||||||
| Laboratory Work | None | ||||||||||||||||||
| Computer Use | None | ||||||||||||||||||
| Other Activities | None | ||||||||||||||||||
| Assessment Methods |
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| Course Administration |
tayland@mef.edu.tr |
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ECTS Student Workload Estimation
| Activity | No/Weeks | Hours | Calculation | ||||
| No/Weeks per Semester | Preparing for the Activity | Spent in the Activity Itself | Completing the Activity Requirements | ||||
| Course Hours | 14 | 1 | 1 | 28 | |||
| Presentations / Seminar | 5 | 4 | 2 | 30 | |||
| Project | 5 | 4 | 2 | 30 | |||
| Homework Assignments | 5 | 4 | 2 | 30 | |||
| Total Workload | 118 | ||||||
| Total Workload/25 | 4.7 | ||||||
| ECTS | 2 | ||||||