Course Detail
Course Detail
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| PROBLEM SOLVINGIN MATHEMATICS | İM4112043 | Fall Semester | 2+0 | 2 | 3 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Esra YEMENLİ |
| Name of Lecturer(s) | Assist.Prof. Esra YEMENLİ |
| Assistant(s) | |
| Aim | The aim of this course is to inform pre-service teachers about problem types and problem solving processes. Other objectives are as follows: To enable prospective teachers to experience problem solving strategies by working on examples. To enable prospective teachers to gain experience in problem posing. To inform prospective teachers about current developments in problem solving. |
| Course Content | This course contains; What is problem and problem solving?,Problem types and problem solving strategies,Recent developments in problem solving.,Mathematical problem solving strategies and the importance of multiple representations in problem solving.,Organization data strategy,Estimation and control strategy,Solve a simpler problem strategy,Animation / Analogy strategy,Working backwards and Pattern finding strategies,Logical Reasoning and Drawing strategies,Developing a different perspective strategy,Definition, process, characteristics and importance of problem posing,,Problem posing strategies, different problem posing studies.,Problem posing in secondary school mathematics curriculum and textbooks; evaluation of problem posing.. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| Poses a problem appropriate to the given context. | 10, 12, 16, 19 | E |
| Prepare sample problems for problem solving strategies. | 10, 12, 16, 19 | E |
| Explain the difference between problem and exercise. | 10, 16, 9 | |
| Evaluates students' problem solving process. | 10, 16, 9 | A |
| Defines the problem. | 10, 12, 16, 19, 5, 9 | |
| Knows the stages of problem solution. | 10, 12, 16, 19 | A |
| Recognizes the complexity levels and types of problems. | 10, 16, 19, 5 | |
| Uses problem solving strategies. | 10, 12, 16 | A, E |
| Teaching Methods: | 10: Discussion Method, 12: Problem Solving Method, 16: Question - Answer Technique, 19: Brainstorming Technique, 5: Cooperative Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | What is problem and problem solving? | Posamentier & Krulik (2016). pp.1-6 |
| 2 | Problem types and problem solving strategies | Posamentier & Krulik (2016). pp.5-6 |
| 3 | Recent developments in problem solving. | Literature review on problem solving |
| 4 | Mathematical problem solving strategies and the importance of multiple representations in problem solving. | Literature review on multiple representation |
| 5 | Organization data strategy | Posamentier & Krulik (2016). pp.7-10 |
| 6 | Estimation and control strategy | Posamentier & Krulik (2016). s.27-30 |
| 7 | Solve a simpler problem strategy | Posamentier & Krulik (2016). pp.42-44 |
| 8 | Animation / Analogy strategy | Posamentier & Krulik (2016). pp.55-60 |
| 9 | Working backwards and Pattern finding strategies | Posamentier & Krulik (2016). pp.68-84 |
| 10 | Logical Reasoning and Drawing strategies | Posamentier & Krulik (2016). pp.100-116 |
| 11 | Developing a different perspective strategy | Posamentier & Krulik (2016). pp.130-132 |
| 12 | Definition, process, characteristics and importance of problem posing, | Literature review on problem posing |
| 13 | Problem posing strategies, different problem posing studies. | Prepare problem posing examples |
| 14 | Problem posing in secondary school mathematics curriculum and textbooks; evaluation of problem posing. | Examining the curriculum and textbooks |
| Resources |
| Alfred S. Posamentier & Stephen Krulik (2016). Matematikte Problem Çözme. (Çeviri: Levent Akgün, Tuğrul Kar, M. Fatih Öçal) Pegem Akademi. Alfred S. Posamentier & Stephen Krulik (2020). Etkili ve Yaratıcı Çözümler İçin Problem Çözme Stratejileri 6-12. Sınıflar (Çeviri Levent Akgün,2. Baskı) Pegem Akademi. Çeker, F. & Ev Çimen, E. (2017). Ortaokul matematik öğretmenlerinin problem çözme stratejilerine ilişkin görüşleri. Eskişehir Osmangazi Üniversitesi Türk Dünyası Uygulama ve Araştırma Merkezi (ESTÜDAM) Eğitim Dergisi, 2 (1), 44-60. |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | It compares the fundamental theoretical frameworks in the field of elementary mathematics education (constructivism, cognitive development theories, models of mathematical thinking) along with their strengths and weaknesses. | X | |||||
| 2 | It compares the national mathematics curriculum (MEB) with international frameworks (NCTM, PISA, TIMSS) in terms of learning objectives and content areas. | ||||||
| 3 | Explains the principles of assessment and evaluation, research methods, and ethical guidelines relevant to their profession, as well as their practical applications. | ||||||
| 4 | Applies appropriate pedagogical interventions in connection with the training received regarding the instructional situations and challenges encountered in the field of elementary mathematics education. | X | |||||
| 5 | By analyzing students' misconceptions and learning difficulties in mathematics, they design appropriate teaching strategies and materials to address them. | X | |||||
| 6 | Solves professional problems related to mathematics education independently using scientific methods. | X | |||||
| 7 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 8 | By formulating a research question on a professional topic, they plan the appropriate research method. | X | |||||
| 9 | Distinguishes between situations that fall within the scope of their professional duties and responsibilities and those that do not. | ||||||
| 10 | Monitors the instructional activities and implementation process aimed at the development of the students under their supervision. | X | |||||
| 11 | Guides the professional development process by integrating this information in line with national and international developments and research findings in mathematics education. | ||||||
| 12 | By interpreting the results of their own teaching practices, they develop recommendations for professional development. | X | |||||
| 13 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 14 | Ensures compliance with research ethics, professional ethics for teachers, and national education regulations in their professional practice. | ||||||
| 15 | In the math classroom, we plan for an equitable and inclusive learning environment, activities that support each student’s mathematical potential, and the necessary safety measures regarding workplace safety. | ||||||
| 16 | In mathematics instruction, they use dynamic software (GeoGebra, Desmos, etc.), learning management systems, and other information and communication technologies at a level equivalent to at least the ECDL Advanced Level. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |
| ECTS / Workload Table | ||||||
| Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
| Course Hours | 14 | 2 | 28 | |||
| Guided Problem Solving | 13 | 2 | 26 | |||
| Resolution of Homework Problems and Submission as a Report | 10 | 2 | 20 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 1 | 5 | 5 | |||
| General Exam | 1 | 10 | 10 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 89 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(89/30) | 3 | |||||
| ECTS of the course: 30 hours of work is counted as 1 ECTS credit. | ||||||
Detail Informations of the Course
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| PROBLEM SOLVINGIN MATHEMATICS | İM4112043 | Fall Semester | 2+0 | 2 | 3 |
| Course Program |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | Turkish |
| Course Level | First Cycle (Bachelor's Degree) |
| Course Type | Required |
| Course Coordinator | Assist.Prof. Esra YEMENLİ |
| Name of Lecturer(s) | Assist.Prof. Esra YEMENLİ |
| Assistant(s) | |
| Aim | The aim of this course is to inform pre-service teachers about problem types and problem solving processes. Other objectives are as follows: To enable prospective teachers to experience problem solving strategies by working on examples. To enable prospective teachers to gain experience in problem posing. To inform prospective teachers about current developments in problem solving. |
| Course Content | This course contains; What is problem and problem solving?,Problem types and problem solving strategies,Recent developments in problem solving.,Mathematical problem solving strategies and the importance of multiple representations in problem solving.,Organization data strategy,Estimation and control strategy,Solve a simpler problem strategy,Animation / Analogy strategy,Working backwards and Pattern finding strategies,Logical Reasoning and Drawing strategies,Developing a different perspective strategy,Definition, process, characteristics and importance of problem posing,,Problem posing strategies, different problem posing studies.,Problem posing in secondary school mathematics curriculum and textbooks; evaluation of problem posing.. |
| Course Learning Outcomes | Teaching Methods | Assessment Methods |
| Poses a problem appropriate to the given context. | 10, 12, 16, 19 | E |
| Prepare sample problems for problem solving strategies. | 10, 12, 16, 19 | E |
| Explain the difference between problem and exercise. | 10, 16, 9 | |
| Evaluates students' problem solving process. | 10, 16, 9 | A |
| Defines the problem. | 10, 12, 16, 19, 5, 9 | |
| Knows the stages of problem solution. | 10, 12, 16, 19 | A |
| Recognizes the complexity levels and types of problems. | 10, 16, 19, 5 | |
| Uses problem solving strategies. | 10, 12, 16 | A, E |
| Teaching Methods: | 10: Discussion Method, 12: Problem Solving Method, 16: Question - Answer Technique, 19: Brainstorming Technique, 5: Cooperative Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | What is problem and problem solving? | Posamentier & Krulik (2016). pp.1-6 |
| 2 | Problem types and problem solving strategies | Posamentier & Krulik (2016). pp.5-6 |
| 3 | Recent developments in problem solving. | Literature review on problem solving |
| 4 | Mathematical problem solving strategies and the importance of multiple representations in problem solving. | Literature review on multiple representation |
| 5 | Organization data strategy | Posamentier & Krulik (2016). pp.7-10 |
| 6 | Estimation and control strategy | Posamentier & Krulik (2016). s.27-30 |
| 7 | Solve a simpler problem strategy | Posamentier & Krulik (2016). pp.42-44 |
| 8 | Animation / Analogy strategy | Posamentier & Krulik (2016). pp.55-60 |
| 9 | Working backwards and Pattern finding strategies | Posamentier & Krulik (2016). pp.68-84 |
| 10 | Logical Reasoning and Drawing strategies | Posamentier & Krulik (2016). pp.100-116 |
| 11 | Developing a different perspective strategy | Posamentier & Krulik (2016). pp.130-132 |
| 12 | Definition, process, characteristics and importance of problem posing, | Literature review on problem posing |
| 13 | Problem posing strategies, different problem posing studies. | Prepare problem posing examples |
| 14 | Problem posing in secondary school mathematics curriculum and textbooks; evaluation of problem posing. | Examining the curriculum and textbooks |
| Resources |
| Alfred S. Posamentier & Stephen Krulik (2016). Matematikte Problem Çözme. (Çeviri: Levent Akgün, Tuğrul Kar, M. Fatih Öçal) Pegem Akademi. Alfred S. Posamentier & Stephen Krulik (2020). Etkili ve Yaratıcı Çözümler İçin Problem Çözme Stratejileri 6-12. Sınıflar (Çeviri Levent Akgün,2. Baskı) Pegem Akademi. Çeker, F. & Ev Çimen, E. (2017). Ortaokul matematik öğretmenlerinin problem çözme stratejilerine ilişkin görüşleri. Eskişehir Osmangazi Üniversitesi Türk Dünyası Uygulama ve Araştırma Merkezi (ESTÜDAM) Eğitim Dergisi, 2 (1), 44-60. |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | It compares the fundamental theoretical frameworks in the field of elementary mathematics education (constructivism, cognitive development theories, models of mathematical thinking) along with their strengths and weaknesses. | X | |||||
| 2 | It compares the national mathematics curriculum (MEB) with international frameworks (NCTM, PISA, TIMSS) in terms of learning objectives and content areas. | ||||||
| 3 | Explains the principles of assessment and evaluation, research methods, and ethical guidelines relevant to their profession, as well as their practical applications. | ||||||
| 4 | Applies appropriate pedagogical interventions in connection with the training received regarding the instructional situations and challenges encountered in the field of elementary mathematics education. | X | |||||
| 5 | By analyzing students' misconceptions and learning difficulties in mathematics, they design appropriate teaching strategies and materials to address them. | X | |||||
| 6 | Solves professional problems related to mathematics education independently using scientific methods. | X | |||||
| 7 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 8 | By formulating a research question on a professional topic, they plan the appropriate research method. | X | |||||
| 9 | Distinguishes between situations that fall within the scope of their professional duties and responsibilities and those that do not. | ||||||
| 10 | Monitors the instructional activities and implementation process aimed at the development of the students under their supervision. | X | |||||
| 11 | Guides the professional development process by integrating this information in line with national and international developments and research findings in mathematics education. | ||||||
| 12 | By interpreting the results of their own teaching practices, they develop recommendations for professional development. | X | |||||
| 13 | Explains proposed solutions to professional challenges to both expert and non-expert stakeholders, supported by quantitative and qualitative data. | X | |||||
| 14 | Ensures compliance with research ethics, professional ethics for teachers, and national education regulations in their professional practice. | ||||||
| 15 | In the math classroom, we plan for an equitable and inclusive learning environment, activities that support each student’s mathematical potential, and the necessary safety measures regarding workplace safety. | ||||||
| 16 | In mathematics instruction, they use dynamic software (GeoGebra, Desmos, etc.), learning management systems, and other information and communication technologies at a level equivalent to at least the ECDL Advanced Level. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 40 | |
| Rate of Final Exam to Success | 60 | |
| Total | 100 | |