Course Language:
Almanca
Course Objectives:
The aim of this course is to investigate mathematical and logical structure of mathematical puzzles, games and brain teasers and solve them.
Course Content:
Problem solving steps
Types of proofs
Investigation of mathematical and logical structure of mathematical puzzles and games
Solution of mathematical puzzles and games
Design of simple mathematical puzzles or games
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) Gives examples for problem solving steps. | 3, 4 | 1, 3, 7 | A |
| 2) Gives examples for types of proofs. | 3, 4 | 1, 3, 7 | A |
| 3) Applies problem solving steps to solve mathematical puzzles and games. | 3, 4 | 7 | A |
| 4) Uses fundamentals of logic and types of proofs to solve mathematical puzzles and games. | 3, 4 | 7 | A |
| 5) Design mathematical puzzles or games aligned with the topics covered in secondary school curriculum. | 7, 8 | 5, 7 | F |
| 6) Design mathematical puzzles or games that motivates students’ to engage in. | 7, 8 | 5, 7 | F |
Course Flow
| Week | Topics | Study Materials |
| 1 | Problem Solving Steps and Problem Solving Strategies | |
| 2 | Proof and Type of Proofs | |
| 3 | Proofs in Secondary School Mathematics Curriculum | Secondary School Mathematics Curriculum |
| 4 | Proofs in Secondary School Geometry Curriculum | Secondary School Geometry Curriculum |
| 5 | Mathematical Puzzles (Numbers) | |
| 6 | Midterm 1 | |
| 7 | Mathematical Puzzles (Algebra I) | |
| 8 | Mathematical Puzzles (Algebra II) | |
| 9 | Mathematical Puzzles (Combinatorics) | |
| 10 | Mathematical Puzzles (Probability) | |
| 11 | Game Theory | |
| 12 | Midterm 2 | |
| 13 | Brain Teasers (Numbers) | |
| 14 | Brain Teasers (Paradoxes) |
Recommended Sources
| Compulsory | Instructor’s notes |
| Recommended |
1) Winkler, P. (2004). Mathematical puzzles: A connoisseur’s collection. Canada: A K Peters.
2) Ensley, D. E., & Crawley, J. W. (2006). Discrete mathematics: Mathematical reasoning and proof with puzzles, patterns, and games. NJ: John Wiley and Sons. 3) Halıcı, E. (2012). Zeka oyunları 1 & 2. TÜBİTAK Yayınları 4) Halıcı, E. (2012). Akıl oyunları 1, 2, 3, & 4. Doğan Kitap. |
Material Sharing
| COURSE MATERIALS | |
| Documents | Handouts for in-class activities |
| Assignments | |
| Exams |
Midterm 1:
Consist of problems and proofs aligned with secondary school mathematics and geometry curricula. Midterm 2: Design of a mathematical puzzle for high school students Final: Design of a mathematical game for high school students |
Assessment
| IN-TERM STUDIES | Quantity | Percentage |
| Midterm | 2 | 30 |
| Quiz | ||
| Final | 1 | 40 |
| Assignment | ||
| Total | 100 | |
| Contribution of Final Exam to Overall Grade | 40 | |
| Contribution of In-term Studies to Overall Grade | 60 | |
| Total | 100 |
| COURSE CATEGORY | Expertise / Field Courses |
Course’s Contribution to Program
| No | Program Outcomes | Level of contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Has in-depth knowledge about secondary school mathematics and geometry contents | X | ||||
| 2 | Knows historical, cultural and scientific developments of the mathematical and geometrical concepts covered in secondary school mathematics and geometry curriculum | X | ||||
| 3 | Applies fundamental mathematical and geometric concepts into other disciplines and real life situations | X | ||||
| 4 | Applies mathematical processes such as problem solving and proving into given cases correctly | X | ||||
| 5 | Plans mathematics and geometry teaching process in line with the secondary school curriculum’s vision, philosophy and goals | X | ||||
| 6 | Uses teaching strategies and techniques that are appropriate for students’ age, grade level, individual differences and readiness level | X | ||||
| 7 | Establishes learning environments that encourages students to learn mathematics and geometry | X | ||||
| 8 | Uses and develop appropriate resources and materials to teach mathematics and geometry | X | ||||
| 9 | Monitors students’ learning process, development and achievement and assesses them by using appropriate assessment tools. | X | ||||
| 10 | Improves professional knowledge by following recent issues in mathematics education | X | ||||
| 11 | Contributes to the development of mathematics education by doing scientific research | X | ||||
| 12 | Knows the philosophy, principles, rules and regulations of Turkish Education System | X | ||||
ECTS
| 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 | 3 | 45 |
| Midterm | 2 | 15 | 30 |
| Quiz | |||
| Assignment | |||
| Final Exam | 1 | 20 | 20 |
| Total Workload | 140 | ||
| Total Workload / 25 (hours) | 5.6 | ||
| ECTS | 6 |