History and Philosophy of Mathematics

Course Code:

EDEM 491

Course Type:

Elective

P:

3

Credits:

3

ECTS:

5

Course Language:

İngilizce

Course Objectives:

The aim of this course is both to discuss history of mathematics in terms of contributions of early civilizations to the development of mathematics and also to investigate fundamentals of philosophy of mathematics and its impacts on mathematics education.

Course Content:

Importance of history of mathematics in mathematics education; Ancient Egyptians’ mathematics; Ancient Greek’s mathematics, Far East’s mathematics; mathematicians in Islamic world; emergence of modern mathematics; historical development of mathematical concepts. Ontology and epistemology of mathematics; meanings of mathematical concepts such as, numbers, sets, functions, etc. and meanings of propositions and mathematical expressions; philosophical problems related to foundations, nature and methods of mathematics, objectivity in mathematics and applicability to the real world; relation of mathematical philosophy with mathematics education.

Course Methodology:

1. Lecture 2. Case study 3. Discussion 4. Demonstration 5. Group work 6. Microteaching 7. Problem solving

Course Evaluation Methods:

A. Supply type B. Multiple-choice test C. Incomplete D. True-False E. Oral exam F. Portfolio G. Performance type H. Report

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Outcomes	Teaching Methods	Assessment Methods
1) Explains contributions of early Egyptian civilization to development of mathematics.	1, 2, 3, 4	1, 3, 7	A, E
2) Explains contributions of early Greek civilization to development of mathematics.	1, 2, 3, 4	1, 3, 7	A, E
3) Explains contributions of early Far East civilizations to development of mathematics.	1, 2, 3, 4	1, 3, 7	A, E
4) Explains contributions of Islamic world to development of mathematics.	1, 2, 3, 4	1, 3, 7	A, E
5) Explains contributions of modern civilizations to development of mathematics.	1, 2, 3, 4	1, 3, 7	A, E
6) Explains the historical development of mathematical concepts.	1, 2	1, 3, 7	A, E, G
7) Explains ontology and epistemology of mathematics.	1, 2	1, 3, 7	A, E
8) Knows meanings of mathematical terms and symbols and can write mathematical propositions.	1, 2, 4	1, 3, 7	A, E, G
9) Gives examples about philosophical problems related to the nature of mathematics.	1, 2, 3, 4	1, 3, 7	A, E, G
10) Explains the relationship between mathematics and philosophy.	1, 2	1, 3, 7	A, E, G

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Importance of history of mathematics in teaching
2	Early Egyptian mathematics
3	Early Greek mathematics
4	Mathematicians of Islamic world
5	Evolution of modern mathematics
6	Historical development of mathematical concepts
7	Midterm
8	Ontology and epistemology of mathematics
9	Mathematics and logic
10	Objectivity in mathematics
11	Mathematics and philosophical problems
12	Mathematics and philosophical problems
13	Teaching mathematical philosophy
14	Teaching mathematical philosophy

Recommended Sources

RESOURCES

Compulsory

Baumgart, J. K. (Ed). (2006). Historical topics for the mathematics classroom. Reston, VA: National Council of Teachers of Mathematics.

Eves, H. (1990). An introduction to the history of mathematics. New York: Brooks Cole.

Eves, H. (1990). Foundations and fundamental concepts of mathematics. New York: Dover

Baki, A. (2014). Matematik tarihi ve felsefesi. Ankara: Pegem Akademi.

Recommended

TÜBİTAK Popüler Bilim Yayınları

Material Sharing

COURSE MATERIALS
Documents	Handouts of in-class activities
Assignments	1) Investigation of one of the concepts taught under Numbers or Algebra domain in middle school curriculum 2) Investigation of one of the concepts taught under Geometry domain in middle school curriculum 3) Discussion of 3 philosophical problems related to nature of mathematics
Exams	Midterm and final exams

Assessment

ASSESSMENT
IN-TERM STUDIES	Quantity	Percentage
Midterm	1	30
Final	1	40
Assignment	3	30
Total		100
Contribution of Final Exam to Overall Grade		40
Contribution of In-term Studies to Overall Grade		60
Total		100

Course’s Contribution to Program

COURSE CONTRIBUTION TO PROGRAM OUTCOMES
No	*Program Outcomes*	*Level of contribution*
No	*Program Outcomes*	1	2	3	4	5
1	Knows historical, cultural and scientific developments of the mathematical and geometrical concepts covered in elementary school mathematics curriculum.					X
2	Applies fundamental mathematical and geometric concepts into other disciplines and real life situations.					X
3	Applies mathematical processes (e.g. problem solving, proving theorems, etc.) into given cases accurately.					X
4	Plans for teaching mathematics in line with the elementary school mathematics curriculum’s vision, philosophy and goals.					X
5	Uses teaching strategies and techniques that are appropriate for students’ age, grade level, individual differences and readiness level.			X
6	Determines and applies appropriate strategies and materials to foster and evaluate students’ mathematical thinking skills.			X
7	Uses and develops appropriate resources and materials to teach mathematics.			X
8	Monitors students’ learning process, development and achievement and assesses them by using appropriate assessment tools.				X
9	Improves professional knowledge by following recent issues in mathematics education			X
10	Contributes to the development of mathematics education by doing scientific research	X

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
*Activities*	*Quantity*	Duration (Hour)	*Total Workload (Hour)*
Course hours (including the exam week: 15 x total course)	15	3	45
Hours for off-the-classroom study (pre-study, practice)	15	2	30
Midterm	1	10	10
Assignment	5	5	25
Final	1	15	15
Total Workload			115
Total Workload / 25 (hours)			4.6
ECTS			5

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