Elementary Mathematics Education | |||||
Bachelor | Length of the Programme: 4 | Number of Credits: 240 | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF: Level 6 |
School/Faculty/Institute | Faculty of Education | ||||
Course Code | MATH 133 | ||||
Course Title in English | Calculus | ||||
Course Title in Turkish | Calculus | ||||
Language of Instruction | EN | ||||
Type of Course | Flipped Classroom | ||||
Level of Course | Introductory | ||||
Semester | Fall | ||||
Contact Hours per Week |
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Estimated Student Workload | 56 hours per semester | ||||
Number of Credits | 7 ECTS | ||||
Grading Mode | Standard Letter Grade | ||||
Pre-requisites | None | ||||
Co-requisites | None | ||||
Expected Prior Knowledge | None | ||||
Registration Restrictions | Only Undergraduate Students | ||||
Overall Educational Objective | To acquire a basic knowledge and understanding of important concepts of differentiation and integration of a single variable. | ||||
Course Description | This course provides a comprehensive introduction to some fundamental aspects of function of a single variable, trigonometric functions, limit, continuity of a function, differentiation of a single variable function, extremum of a function, mean value theorem, L’Hospital’s rule, antiderivative and the indefinite integral, definite integrals, fundamental theorem of calculus, applications of the definite integral, the exponential and logarithmic function, the inverse trigonometric functions, hyperbolic functions and their inverses, integration techniques. |
Course Learning Outcomes and CompetencesUpon successful completion of the course, the learner is expected to be able to:1) calculate limit at a point and limit at infinity of single variable functions 2) solve applied optimization extrema problems and sketch graphs of functions 3) evaluate definite and indefinite integrals using integration techniques 4) apply definite integrals for calculating arc-lengths, volumes, area of surface of revolution, center of mass and moments of inertia 5) calculate, differentiate and integrate exponential functions, logarithmic functions, trigonometric and inverse trigonometric functions and hyperbolic and inverse hyperbolic functions |
Program Learning Outcomes/Course Learning Outcomes | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
1) Apply effective and student-centered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills. | |||||
2) Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics. | |||||
3) Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics. | |||||
4) Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs. | |||||
5) Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning. | |||||
6) Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness. | |||||
7) Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multi-disciplinary as well as take individual responsibility when they work alone. | |||||
8) Have awareness of need for life-long learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways. | |||||
9) Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources. | |||||
10) Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio. | |||||
11) Have awareness of and sensitivity to different cultures, values and students’ democratic rights. | |||||
12) Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws. | |||||
13) Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities. | |||||
14) Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. |
N None | S Supportive | H Highly Related |
Program Outcomes and Competences | Level | Assessed by | |
1) | Apply effective and student-centered specific teaching methods and strategies in order to improve students’ mathematical thinking and problem solving skills. | S | Exam |
2) | Design lesson plans based on how students learn mathematics and students’ difficulties in learning mathematics. | N | |
3) | Demonstrate knowledge in various areas of mathematics (such as analysis, algebra, linear algebra, geometry, topology, mathematical modeling, statistics and probability, differential equations) and nature of science and mathematics. | H | Exam |
4) | Display knowledge and skills in developing programs, teaching technologies and materials in order to teach mathematics in effective and meaningful ways based on student needs. | S | Exam,Participation |
5) | Evaluate and assess students’ individual developmental paths, difficulties in understanding mathematics in multiple ways and use assessment results in improving teaching and learning. | N | |
6) | Have an awareness of students’ social, cultural, economic and cognitive differences and plan the lessons and activities based on this awareness. | S | Participation |
7) | Collaborate and respectively communicate with colleagues and student parents such that students learn mathematics in best ways and at the same time feel happy and safe. Work effectively within teams of their own discipline and multi-disciplinary as well as take individual responsibility when they work alone. | H | Exam,Participation |
8) | Have awareness of need for life-long learning. Access information and following developments in education, science and technology. Display skills of solving problems related to their field, renew and improve themselves and critically analyze and question their own work. Use information technologies in effective ways. | S | Participation |
9) | Use scientific investigation effectively to solve problems in mathematics teaching and learning based on scientific methods. Critically investigate, analyze and make a synthesis of data, and develop solutions to problems based on data and scientific sources. | S | Exam |
10) | Exhibit skills of communicating effectively in oral and written Turkish and command of English at least at B2 general level of European Language Portfolio. | S | Exam,Participation |
11) | Have awareness of and sensitivity to different cultures, values and students’ democratic rights. | N | |
12) | Display ethical and professional responsibilities. Have awareness of national and universal sensitivities that are expressed in National Education Fundamentals Laws. | N | |
13) | Demonstrate consciousness and sensitivity towards preserving nature and environment in the process of developing lesson activities. | N | |
14) | Display knowledge in national culture and history as well as international cultures and recognize their richness. Have awareness of and participate to developments in society, culture, arts and technology. | N |
Prepared by and Date | CANFUAD DELALE , |
Course Coordinator | BENGİ BİRGİLİ |
Semester | Fall |
Name of Instructor | Asst. Prof. Dr. NAMIK KILIÇ |
Week | Subject |
1) | Function of a single variable, trigonometric functions |
2) | Limit and continuity |
3) | The derivative of a function |
4) | Applications of the derivative |
5) | Curve sketching and L’Hospital’s rule |
6) | Antiderivative, the indefinite and definite integral |
7) | The fundamental theorem of calculus |
8) | Applications of definite integrals |
9) | Applications of definite integrals |
10) | Inverse of a function. Transcendental functions: Logarithmic and exponential functions |
11) | Transcendental functions: Inverse trigonometric functions |
12) | Transcendental functions: Hyperbolic and inverse hyperbolic functions |
13) | Integration techniques: Integration by parts, integration by partial fractions |
14) | Integration techniques: Trigonometric integrals, trigonometric substitutions |
15) | Final Examination Period |
16) | Final Examination Period |
Required/Recommended Readings | Thomas' Calculus, 13th Ed., G. Thomas, M. Weir, J. Hass, F. Giordano, Pearson/ Addison Wesley, 2015 | ||||||||||||||||||
Teaching Methods | Lectures/contact hours using “flipped classroom” as an active learning technique | ||||||||||||||||||
Homework and Projects | Review questions as homework | ||||||||||||||||||
Laboratory Work | |||||||||||||||||||
Computer Use | |||||||||||||||||||
Other Activities | |||||||||||||||||||
Assessment Methods |
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Course Administration |
arslanilk@mef.edu.tr (0212) 3953653 Office hours: Cinar : Monday 13:00- 15:00. Yildirim: Tuesdays 15:00-17:00 |
Activity | No/Weeks | Calculation | |||
No/Weeks per Semester | |||||
Course Hours | 28 | 112 | |||
Total Workload | 112 | ||||
Total Workload/25 | 4.5 | ||||
ECTS | 7 |