1. FIRST CYCLE - BACHELOR'S DEGREE
  2. FACULTY OF EDUCATION
  3. DEPARTMENT OF MATHEMATICS AND SCIENCE TEACHING DEPARTMENT
  4. 133 ELEMENTARY MATHEMATICS EDUCATION
Course Information Course Learning Outcomes Course's Contribution To Program ECTS Workload Course Details
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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
IMO 4005LOGICAL REASONING2 + 01st Semester4

COURSE DESCRIPTION
Course Level Bachelor's Degree
Course Type Compulsory
Course Objective Make prospective teachers have knowledge about making deductions, defending the validity of propositions, making generalizations, configuring strategies using logical patterns and make them use logical reasoning processess effectively and aright.
Course Content Defending the accuracy and validity of deductions, offering legitimate generalizations and deductions; using and explaining mathematical patterns and relations while analysing a mathematical situation; making estimations about the results of operations and measurements by using strategies like rounding off, grouping proper numbers, using first and last digits or by using their own strategies; making estimations regarding a reference point related to measurement.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.

COURSE LEARNING OUTCOMES
1• Knows about deduction and reasoning processes.
2• Makes generalizations through different thinking processes.
3• Analyses a mathematical situation by using and explaining patterns and relationships
4• Makes estimations about the results of operations and measurements by rounding offs
5• Makes estimations about the results of operations and measurements by grouping proper numbers
6• Makes estimations about the results of operations and measurements by using the first and last digits
7• Makes estimations about the results of operations and measurements by using his/her own strategies
8• Makes estimations regarding a reference point related to measurement
9• Offers a micro teaching instructional design about logical reasoning processess in middle school mathematics.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08PO 09PO 10PO 11PO 12PO 13PO 14
LO 00133343235322111
LO 00233343234443111
LO 00333342224443221
LO 00444342225422211
LO 00544332225422211
LO 00644332225422211
LO 00744332225522211
LO 00844332225522211
LO 00945555455555545
Sub Total3334293323202343382523191313
Contribution44343235433211

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)21428
Hours for off-the-classroom study (Pre-study, practice)14342
Assignments144
Mid-terms11212
Final examination11818
Total Work Load

ECTS Credit of the Course





104

4
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2026-2027 Fall1EMİNE GAYE ERMEÇ ÇONTAY
Details 2026-2027 Fall2EMİNE GAYE ERMEÇ ÇONTAY


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester Mode of Delivery
IMO 4005 LOGICAL REASONING 2 + 0 1 Turkish 2026-2027 Fall Face to Face
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Asts. Prof. Dr. EMİNE GAYE ERMEÇ ÇONTAY germec@pau.edu.tr EGT A0232-02 %70
Goals Make prospective teachers have knowledge about making deductions, defending the validity of propositions, making generalizations, configuring strategies using logical patterns and make them use logical reasoning processess effectively and aright.
Content Defending the accuracy and validity of deductions, offering legitimate generalizations and deductions; using and explaining mathematical patterns and relations while analysing a mathematical situation; making estimations about the results of operations and measurements by using strategies like rounding off, grouping proper numbers, using first and last digits or by using their own strategies; making estimations regarding a reference point related to measurement.
Topics
WeeksTopics
1 Introduction of course content and course expectations, Nature of mathematics; what is mathematics? Mathematics and science Is mathematics a discovery? Is it an invention? https://www.youtube.com/watch?v=gPAPqoz2MAU&t=3s
2 The nature of mathematics, the subject of mathematics Two stages in thinking: examples from everyday life, science and mathematics Mathematics and science Making inferences, defending their truth and validity
3 The inductive-deductive distinction, empirical verification and mathematical proof Two stages in thinking: examples from everyday life, science and mathematics Empirical verification and mathematical proof What does it mean to do mathematics and the appropriate classroom environment for doing mathematics
4 Euclid's Elements Euclid's content Book One Book 1 Definitions, axioms and common concepts Propositions: the first 3 propositions and their proofs
5 Types of reasoning and the reasoning/proof relationship, NCTM (2000) Standard for Reasoning and Proof
6 Axiomatic system - proof process proof methods
7 Axiomatic method and argumentation; the relationship between argumentation and proof
8 Midterm Exam
9 Spatial Reasoning and its implications for education
10 Reasoning and patterns and their implications for education
11 Proportional Reasoning and its implications for education
12 Supporting Reasoning Through Activities
13 Learning environments/group work presentations to develop reasoning
14 Learning environments/group work presentations to develop reasoning
Materials
FileFile NameFile LanguageOriginal File NameAdded Date
Download File egc -2024-2025 güz MANTIKSAL AKIL YÜRÜTME (1).docxTürkçeegc -2024-2025 güz MANTIKSAL AKIL YÜRÜTME (1).docx9.10.2026 16:25:42
Resources
ResourcesResources Language
Aeseven, A. Matematik öğretim yöntemleri. Matematik Öğretimi ve Matematiksel modelllemeTürkçe
Aggarwal, R.S. A modern approach to logical reasoning (2 colour edition)Türkçe
Baykul, Y. Ortaokulda matematik öğretimiTürkçe
Baki, A. Kuramdan uygulamaya matematik EğitimiTürkçe
Bronkhorst, H., Roorda, G. , Suhre, c., Goedhart, M. (2020). Logical reasoning in formal and everyday reasoning tasks., International Journal of Science and Mathematics Education, 18, 1673-1694.Türkçe
Düzüak, A. V (. ). Bilimsel muhakeme becerileri ile düşünme sanatı, Ankara: Anı YayıncılıkTürkçe
İmamoğlugil, H. Klasik mantıkta akıl yürütme, Araştırma YayınlarıTürkçe
Uğurel, I, (2020)(ED) . Matematiksel ispat ve öğretimi. Ankara: Anı Yayıncılık.Türkçe
Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., Carraher, J. (2007). The contribution of logical reasoning to the learning of mathematics in primary school, 25, 147-166.Türkçe
Van de Walle, J.A., Karp, K.S., & Bay Williams, J.M. (2012). İlkokul ve Ortaokul Matematiği Gelişimsel Yaklaşımla Öğretim (7. Baskıdan) (Çev. Ed. S. Durmuş). Ankara: Nobel Akademik YayıncılıkTürkçe
Yıldırım, C. (2011). Matematiksel düşünme. İstanbul: Remzi Kitabevi. Türkçe
Course Assessment
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes