COURSE UNIT TITLE

: MATHEMATICAL REASONING AND PROOF TEACHING

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
FMM 6066 MATHEMATICAL REASONING AND PROOF TEACHING ELECTIVE 3 0 0 10

Offered By

Mathematics Teacher Education

Level of Course Unit

Third Cycle Programmes (Doctorate Degree)

Course Coordinator

PROFESSOR DOCTOR IŞIKHAN UĞUREL

Offered to

Mathematics Teacher Education

Course Objective

To comprehend to what extend proof and proving is important and a large field of study in mathematics education. To provide participants a personal view and insight based on a spesific theoretical ground related to prof, proving and teaching to proof.

Learning Outcomes of the Course Unit

1   To comprehend the meanings that proof possess in terms of mathematics, history of mathematics and philosophy of mathematics and to be able to perceive this variety of semantic.
2   To comprehend the meanings that attributed to prof and proving in mathematics education. To be able improve interpretations and ideas about the subject from different research perspectives under the basic terminology.
3   To comprehend the place and the importance of proof and proving within the scope of curriculums and instructional standarts (national and international).
4   To have knowledge about the problems/difficulties that students at different levels (e. g. 6-8, 9-12, undergraduate, graduate students) experienced towards prof and proving and to be able to imporve idea to remove them.
5   To comprehend and exemplify traditional and alternative proving merhods/approaches/tools and to be able to evaluate them.
6   To generate a view to the teaching of proof within the scope of mathematics education understanding and to be able to develop instructional practices under this point of view.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Some basic concepts and their relations - Proposition, axiom, postulate, theorem, proof, generalization, abstraction, sampling, digestion, verification, axiomatic system, etc.
2 What is proof What is not - Historical and philosophical point of view of proof, and proving.
3 - The place and the importance of proof and proving in mathematics and mathematics education. - Overview to proof and proving within the perspective of mathematics curriculums and international standarts
4 - How is a proof read How is it generated Practice-I
5 - How is a proof read How is it generated Practice-II
6 Proving methods and Practice-I
7 Proving methods and Practice-II
8 Midterm project
9 Difficulties, problems and their reasons that experienced in proving.
10 Proving approaches, categories and proof schemes.
11 Proving approaches, categories and proof schemes.
12 Alternative approaches to proof and proving. Proof without words
13 Two column proof
14 Using comprehension tests in proving process.
15 Presentations of the participants that based on their research on the subject matter.

Recomended or Required Reading

Textbooks(s)/References/Materials:
Advanced Mathematical Thinking, (Ed.) David Tall, Kluwer Academic Publishers.
--Teaching and Learning Proof Across The Grades A K16 Perspectives, (Eds.) Despine A. Stylianou, Maria L. Blanton, Eric J. Knuth, Routledge.
--Explanation and Proof in Mathematics, Philosophical and Educational Perspectives (Eds.) Gila Hanna, H. Niels Jahnke, Helmut Pulte, Springer.
--Matematikçi Gibi Düşünmek, Kevin Houston, (Çev.) Mehmet Terziler, Tahsin Öner, Palme Yayıncılık.
--Proof and Knowledge in Mathematics, (Ed.) Michale Detlefsen, Routledge.
--Proceedings of the ICMI Study 19 Conference (2009): Proof and Proving in Mathematics Education Vol 1-2.

Planned Learning Activities and Teaching Methods

Lecture, Question-Answer, Learning by the way of Problem solving, Learning by the way of Research-Examination, Small group work.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 PRJ PROJECT
2 ASG ASSIGNMENT
3 PRS PRESENTATION
4 FCG FINAL COURSE GRADE PRJ * 0.40 + ASG * 0.40 + PRS * 0.20


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

Turkish

Course Policies and Rules

70% attendance is required.
Individual and group work is done.

Contact Details for the Lecturer(s)

Contact Details for the Instructor:
Office Tel: 0 232 420 4882-12429
E-mail: isikhan.ugurel@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Theoretical 14 3 42
Application 0 0 0
Pre Class Self Study 14 3 42
Midterm Preparation 10 1 10
Final Preparation 10 1 10
Quiz Preparation 5 4 20
Paper Preparation 5 4 20
Research Presentation 5 3 15
Others (Please indicate) 70 1 70
Final Exam 3 1 3
Midterm Exam 2 1 2
Quizzes 5 1 5
TOTAL WORKLOAD (hours) 239

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14
LO.15433
LO.25433
LO.35344
LO.4554324
LO.55543544
LO.65543544

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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