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

Ders Genel Tanıtım Bilgileri

School/Faculty/Institute

Faculty of Education

Course Code

MATH 134

Course Title in English

Advanced Calculus

Course Title in Turkish

Advanced Calculus

Language of Instruction

Type of Course

Flipped Classroom

Level of Course

Select

Semester

Spring

Contact Hours per Week

Lecture: 4

Recitation:

Lab:

Other:

Estimated Student Workload

172 hours per semester

Number of Credits

7 ECTS

Grading Mode

Standard Letter Grade

Pre-requisites

MATH 133 - Calculus

Expected Prior Knowledge

Differentiation and integration of real valued function of a single variable.

Co-requisites

None

Registration Restrictions

Only Undergraduate Students

Overall Educational Objective

To learn the differentiation of multivariable functions and multiple integration.

Course Description

Polar coordinates, analytical geometry, infinite sequences and series, Taylor’s series, vectors, multivariable functions, partial derivatives and their applications, the gradient and directional derivative, extrema of functions of two variables, multiple integrals and their applications.

Course Description in Turkish

Kutupsal koordinatlar, analitik geometri, sonsuz dizi ve seriler, Taylor serisi, vektörler, çok değişkenli fonksiyonlarda kısmi türev ve uygulamaları, gradyan ve doğrultusal türev, iki değişkenli fonksiyonların ekstremum noktaları, çok katlı integraller ve uygulamaları.

Course Learning Outcomes and Competences

Upon successful completion of the course, the learner is expected to be able to:
1) expand a function in a Taylor series about a point;
2) use polar coordinates and classify conic sections;
3) identify and use vector operations;
4) calculate and differentiate multivariable functions;
5) identify local minima, local maxima and saddle points of a function of two variables
6) evaluate double and triple integrals.

Program Learning Outcomes/Course Learning Outcomes	1	2	3	4	5	6
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.

Relation to Program Outcomes and Competences

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	Participation
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,Participation
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	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	Project
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	Exam
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.	N
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	Spring
Name of Instructor	Asst. Prof. Dr. İLKER ARSLAN

Course Contents

Week	Subject
1)	Infinite sequences and series
2)	Infinite sequences and series
3)	Infinite sequences and series
4)	Polar coordinates and analytical geometry
5)	Polar coordinates and analytical geometry
6)	Vectors, Vector algebra
7)	Geometric applications: Equations of planes and lines in space
8)	Multivariable functions, partial derivatives
9)	Partial derivatives and their applications
10)	Partial derivatives and their applications
11)	The Gradient and Directional Derivative
12)	Extrema of a function of two variables
13)	Multiple integrals and their applications
14)	Multiple integrals and their applications
15)	Final Examination/Project/Presentation Period
15)	Final Examination/Project/Presentation Period
16)	Final Examination/Project/Presentation Period

Required/Recommended Readings

Thomas' Calculus, 13th Ed., G. Thomas, M. Weir, J. Hass, F. Giordano, Pearson/ Addison Wesley, 2010.

Teaching Methods

Lectures/contact hours using “flipped classroom” as an active learning technique

Homework and Projects

Laboratory Work

Computer Use

Other Activities

Assessment Methods

Assessment Tools	Count	Weight
Application	1	% 15
Quiz(zes)	2	% 10
Homework Assignments	13	% 5
Project	14	% 5
Midterm(s)	1	% 25
Final Examination	2	% 40
TOTAL		% 100

Course Administration

cafuat.delale@mef.edu.tr

ECTS Student Workload Estimation

Activity	No/Weeks	Hours			Calculation
	No/Weeks per Semester	Preparing for the Activity	Spent in the Activity Itself	Completing the Activity Requirements
Course Hours	14	2	4	2	112
Quiz(zes)	2	6	1		14
Midterm(s)	1	12	2		14
Final Examination	1	30	2		32
Total Workload					172
Total Workload/25					6.9
ECTS					7