TÜRKÇE
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Information
| Code | ME813 |
| Name | Algebraic Thinking |
| Term | 2024-2025 Academic Year |
| Term | Fall and Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 8 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | |
| Course Instructor |
1 |
Course Goal / Objective
It is to enable them to have knowledge about algebra and algebraic thinking, which is one of the main and difficult areas of mathematics teaching, and to increase their knowledge and skills in teaching algebraic concepts. In addition, it is to enable them to have an idea about student knowledge on these subjects and to establish the relationship of these subjects with daily life and other lessons.
Course Content
algebraic thinking, the importance of algebraic thinking in mathematics teaching; pre-algebraic period; arithmetic-algebra relationship; generalized arithmetic and functional thinking; basic algebra concepts; different representations in algebra teaching; teaching variables, algebraic expression, equality and equation, linear equations, identities and inequalities (organizing the course content, using appropriate teaching materials and strategies, etc.); student knowledge about these subjects (understanding and interpreting student ideas about concepts, knowing students' difficulties, mistakes, misconceptions and their reasons); The relationship of these subjects with daily life and other lessons.
Course Precondition
NONE
Resources
Sarpkaya Aktaş (2019). Uygulama Örnekleriyle Cebirsel Düşünme ve Öğretimi. Ankara Pegem Akademi. Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The mathematics educator, 8(1), 139-151. Barbosa, A., Vale, I., Jablonski, S., & Ludwig, M. (2022). Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails. Education Sciences, 12(5), 346. Akkan, Y. (2009). Examination of primary school students' transition processes from arithmetic to algebra. (PhD thesis) Karadeniz Technical University, Institute of Science and Technology. Akkan, Y., Baki, A., Çakıroğlu, Ü. (2012). 5-8. Examining the transition processes of primary school students from arithmetic to algebra in the context of problem solving. Hacettepe University Faculty of Education Journal. 43:1-13.
Notes
Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: a Knowledge in Pieces perspective on the development of algebraic thinking. ZDM–Mathematics Education, 1-12. Sukmaningrum, R., & Kurniasari, I. (2022). Profile of student's algebraic thinking in solving mathematics problems reviewing from adversity quotient. Jurnal Pijar Mipa, 17(2), 252-259.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the historical development and levels of algebra, algebraic thinking. |
| LO02 | Explain the difference between arithmetic-algebraic thinking and the importance of algebraic thinking in mathematics teaching. |
| LO03 | Explain the concepts of equality, variable, algebraic modeling, generalization, pattern and functional thinking. |
| LO04 | Knows student misconceptions encountered in algebra teaching and chooses appropriate teaching methods to eliminate misconceptions. |
| LO05 | Designs algebra learning environments in accordance with daily life situations with a problem-solving approach. |
| LO06 | Makes algebra teaching planning suitable for different learning models. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | 1- Based on master's qualifications, he/she develops and deepens current and advanced knowledge in the field with original thought and/or research at the level of expertise and reaches original definitions that will bring innovation to science. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | 2- Establishes relationships between various disciplines and sub-fields that the field is related to, and reaches original results by using their expertise in the analysis, synthesis and evaluation of new and complex ideas. | 5 |
| PLO03 | Beceriler - Bilişsel, Uygulamalı | 1-Approaches new information in the field in a systematic way and conducts advanced research in the field. | 3 |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | 2-Develops a new scientific method that brings innovation to science or applies a known method to a different field; At this point, it designs and carries out an original research. | 5 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | 3-Makes critical analysis, synthesis and evaluation of new and complex ideas. | 3 |
| PLO06 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | 1- Contributes to science with an original, publishable work that brings innovation to science, develops a new scientific method or applies a known method to a field. | 5 |
| PLO07 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | 2-Expands the limits of knowledge in the field by publishing scientific articles related to the field in national and/or international refereed journals. | 2 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | 3- Takes leadership in original and interdisciplinary studies. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | 4-It carries out its work independently or as a team member. | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | 1-Creative and critical thinkers; develops new ideas and methods related to the field by using high-level mental processes such as problem solving and decision making. | 2 |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | 2-Becomes a facilitator/director in education and training activities in his/her field. | 2 |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | 3-Continues the teaching processes on an interactive and ethical basis. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | 4-Develops and implements effective teaching strategies in order to provide students with knowledge and skills related to the field. | 3 |
| PLO14 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | 1- Examines social relations and the norms that guide these relations with a critical perspective, develops them and manages actions to change them when necessary. | |
| PLO15 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | 2- Defends their original views in a community of experts. | |
| PLO16 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | 3-Using a foreign language at least at the C1 General Level of the European Language Portfolio, communicates and discusses advanced written, oral and visual communication. | |
| PLO17 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | 4-Communicates by considering cultural differences in all national and international studies. | |
| PLO18 | Yetkinlikler - Alana Özgü Yetkinlik | 1- It contributes to the process of becoming an information society by introducing technological, social and cultural advances to the society in the academic and professional context. | 2 |
| PLO19 | Yetkinlikler - Alana Özgü Yetkinlik | 2- Establishes functional interaction with relevant persons and institutions by using strategic decision-making processes in solving the problems encountered in the field. | 3 |
| PLO20 | Yetkinlikler - Alana Özgü Yetkinlik | 3- It produces solutions on social, scientific and ethical issues related to its field and supports the development of these values at the national and international level. | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Course introduction and historical development and mathematical value of algebra | Reading related resources | Öğretim Yöntemleri: Tartışma, Soru-Cevap |
| 2 | Algebra and algebraic thinking and its development | Reading related resources | Öğretim Yöntemleri: Tartışma, Anlatım, Soru-Cevap |
| 3 | Variable and equality concepts in primary and secondary school mathematics teaching | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Anlatım, Tartışma |
| 4 | Common misconceptions in algebra and removal methods | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Anlatım, Tartışma |
| 5 | In primary and secondary school mathematics teaching pattern concepts | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Anlatım |
| 6 | article review: KABAEL, T. U. and TANIŞLI, D. (2010). Teaching from pattern to function in algebraic thinking process. Elementary Education Online, 9(1), 213-228. | Reading related resources | Öğretim Yöntemleri: Tartışma, Soru-Cevap |
| 7 | Algebraic thinking levels and secondary school types of students' encounters with algebra | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Anlatım, Tartışma |
| 8 | Midterm Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Transition processes from arithmetic to algebra | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma |
| 10 | Article review: Akkan, Y. (2009). Examination of primary school students' transition processes from arithmetic to algebra. (PhD thesis) Karadeniz Technical University, Institute of Science and Technology. Akkan, Y., Baki, A., Çakıroğlu, Ü. (2012). 5-8. Examining the transition processes of primary school students from arithmetic to algebra in the context of problem solving. Hacettepe University Faculty of Education Journal. 43:1-13. | Reading related resources | Öğretim Yöntemleri: Tartışma, Soru-Cevap |
| 11 | Worksheets in algebra teaching, problem solving approaches | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma |
| 12 | Designing algebra learning environments 1 | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 13 | Designing algebra learning environments 2 | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 14 | Designing algebra learning environments 3 | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 15 | Designing algebra learning environments 4 | Reading related resources | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 16 | Final Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Final Exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 9 | 126 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 2 | 2 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 9 | 9 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 197 | ||
| Total Workload / 25 (h) | 7,88 | ||
| ECTS | 8 ECTS | ||