COURSE UNIT TITLE

: FIELD ELC. 4 (PROOF AND PROVING IN MATHEMATICS EDUCATION)

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
LMÖ 2016 FIELD ELC. 4 (PROOF AND PROVING IN MATHEMATICS EDUCATION) ELECTIVE 2 0 0 4

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR IŞIKHAN UĞUREL

Offered to

Mathematics Teacher Education

Course Objective

The aim of this course to make them comprehend how important and wide field of study is proof and proof in mathematics education literature. To enable the participants to develop personal views and understandings based on a certain theoretical ground on proof, proving and teaching proof.

Learning Outcomes of the Course Unit

1   Understanding the meanings of proof in terms of mathematics, history of mathematics and philosophy of mathematics and being able to perceive this semantic variety.
2   Comprehending the meanings attributed to proof and proving in the field of mathematics education. Develop comments and ideas on the subject from different research perspectives under basic terminology.
3   Comprehending the place and importance of proof and proving within the framework of curricula and (national and international) instructional standards.
4   Obtain information about the difficulties experienced by students at different levels (eg 5th-8th, 9th-12th grades, undergraduate and graduate students) in proof and proving, and developing ideas for solving them.
5   Comprehend, exemplify and evaluate traditional and alternative methods/approaches/tools of proof.
6   Creating a view towards teaching proof within the scope of today's understanding of mathematics education and developing instructional applications under this 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 relationships between them - Proposition, axiom, postulate, theorem, proof, generalization, abstraction, sampling, refutation, verification, axiomatic system, etc.
2 What is Proof What is not - View of proof and proving from a historical and philosophical point of view.
3 - The place and importance of proof in mathematics and mathematics education. - An overview of proof and proving from the perspective of mathematics curriculum and international standards.
4 How to read a proof How is it created Applications.
5 How to read a proof How is it created Applications.
6 Proof methods and applications.
7 Proof methods and applications.
8 General review, course evaluation, midterm exam
9 Difficulties in proof, proving and reasons.
10 Proving approaches, categories, schemes (Proof Schemes).
11 Proving approaches, categories, schemes (Proof Schemes).
12 Alternative approaches to proof and proving - Visual proof
13 Two column proof
14 Utilizing comprehension tests in the proofing process. (Proof comprehension tests)
15 Final Exam

Recomended or Required Reading

--Matematiksel ispat ve öğretimi. Okul yıllarında ispat öğretimini destekleyen çok yönlü bir bakış. (Ed. Işıkhan Uğurel), Ankara: Anı Yayınları, 2. Baskı. (2021).
--Proofs without words. Exercises in visual thinking. R. Nelsen, MAA Publishing, (1993).
--Matematikçi gibi düşünmek. K. Houston, Palme Yayıncılık, (2009).
--Matematiksel düşünme. C. Yıldırım, Remzi Kitapevi, (2019).
--Kanıt nasıl yapılır D. J. Velleman, Palme Yayıncılık, (2008).

Planned Learning Activities and Teaching Methods

Lecture, discussion, question-answer, observation, group work, prepare and present teaching practices and learning activities.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 VZ Midterm
2 FN Semester final exam
3 BNS BNS Student examVZ * 0.40 + Student examFN * 0.60
4 BUT Make-up note
5 BBN End of make-up grade Student examVZ * 0.40 + Student examBUT * 0.60


Further Notes About Assessment Methods

Homework and presentations, discussion, reflection of students, research proposal

Assessment Criteria

Assessment of students is measured by midterm and final exams in line with the learning outcomes.

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

isikhan.ugurel@deu.edu.tr

Office Hours

It will be announced at the beginning of the semester.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 2 26
Preparations before/after weekly lectures 13 2 26
Preparation for midterm exam 1 15 15
Preparation for final exam 1 20 20
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 91

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1234523213121112112
LO.2343423212121122111
LO.3222515222121112111
LO.4333213553132213211
LO.5232313334242224112
LO.6244313554242125312

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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