COURSE SYLLABUS

METHODS OF ARGUMENTATION AND PROOF

1	Course Title:	METHODS OF ARGUMENTATION AND PROOF
2	Course Code:	MAT3105
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	3
6	Semester:	5
7	ECTS Credits Allocated:	4
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Doç. Dr. MENEKŞE SEDEN TAPAN BROUTIN
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	Y.Doç.Dr. Menekşe Seden TAPAN BROUTIN tapan@uludag.edu.tr 0 224 2942162 Uludağ Üniversitesi Eğitim Fakültesi, A Blok, İlköğretim Bölümü, 16059 Nilüfer, Bursa
18	Website:
19	Objective of the Course:	Conceptualizing mathematical proof methods and basic proof theories in didactics of mathematics, and making analyzes based on these theories.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Axiomatic structure of mathematics will be internalized.;
2	Basic proof methods are analyzed and used;
3	Differences between mathematical reasoning, explanation, argumentation and proof methods can be explained with a educational viewpoint.;
4	The place and importance of proof in mathematical science can be explained.;
5	Basic proof teaching theorems are learnt and articles related with these theorems are analyzed.;

22	Course Content:

Week	Theoretical	Practical
1	Axiomatic structure in Maths, proving and methods of proving
2	Direct proof, proof with deduction and its examples
3	Proof-by-contradiction and contradiction principle. Examples.
4	Proves with examples and reverse examples and their exercises.
5	Place of proof in mathematical study and theorems of basic proof teaching
6	Mathematical reasoning, explanation, argumentation and proof
7	Development of mathematical consideration of children and Van Heil Model
8	Scientific article research based on the theory of Van Heile
9	Proof structures of Duval and proof gradations of Balacheff
10	Scientific article research based on the theory of Balacheff
11	The proof theory of Harel and Sowder and concept of proof scheme
12	Scientific article research based on the theory of Harel and Sowder
13	Proof concepts of Hanna, Tall. Mariotti, Batista
14	Synthesis of all theories of proof

23	Textbooks, References and/or Other Materials:	Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, Special issue on "Proof in Dynamic Geometry Environments", 44 (1-2), 5-23. Hanna, G. & De Villiers, M. (2012). Proof and Proving in Mathematics Education, The 19th ICMI Study, New ICMI Studies Series (v. 15). Springer, New York. Harel, G. & Sowder, L. (1998). Students' proof schemes. Research on Collegiate Mathematics Education, Vol. III. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), AMS, 234-283. Harel, G. & Sowder, L (2007). Toward a comprehensive perspective on proof, In F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning, National Council of Teachers of Mathematics Duval, R. & Egret M. A. (1989). Organisation déductive du discours, Annales de Didactique et de Sciences Cognitives 2, pp. 25-40, Strasbourg : IREM de Strasbourg. Clements, D. H. & Battista, M. T. (1992)."Geometry and Spatial Reasoning." In Handbook of Research on Mathematics Teaching and Learning, edited by Douglas A. Grouws, 420-64. New York: Macmillan and Reston. Battista, M. T. & Clements, D. H. (1995). Geometry and proof. Mathematics Teacher, 88(1), 48–54. Balacheff, N. (1999). Apprendre la preuve. In: Sallantin J., Szczeciniarz J. J. (eds.) Le concept de preuve à la lumière de l'intelligence artificielle (pp.197–236). Paris: PUF. (Balacheff on 1987). Stylianides, A. J. (2007). Proof and Proving in School Mathematics, Journal for Research in Mathematics Education, 38(3), pp. 289-321.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	2	28
Practicals/Labs	0	0	0
Self Study and Preparation	0	0	0
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	12	12
Others	0	0	0
Final Exams	1	20	20
Total WorkLoad			60
Total workload/ 30 hr			2
ECTS Credit of the Course			2

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

	PQ1	PQ2	PQ3	PQ4	PQ5	PQ6	PQ7	PQ8	PQ10	PQ11	PQ12	PQ16
LO1	5	2	3	1	5	1	5	1	0	0	1	0
LO2	5	4	3	2	5	2	5	1	0	0	2	0
LO3	5	5	3	4	5	2	5	1	2	4	5	1
LO4	5	5	4	4	5	4	5	2	2	3	4	0
LO5	5	2	5	3	5	5	5	3	4	2	3	0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High