At the end of this course, the students; 1) Approves the accuracy and validity of the inferences. 2) Provides logical generalizations and inferences. 3) Explains and implicates mathematical patterns and relations when analyzing a mathematical situation. 4) Estimates the result of operations and measures using strategies such as rounding, grouping appropriate numbers, using first or last digits, or using the strategies they developed. 5) Estimates the measures using a particular reference point.
MODE OF DELIVERY
Face to face
PRE-REQUISITES OF THE COURSE
No
RECOMMENDED OPTIONAL PROGRAMME COMPONENT
None.
COURSE DEFINITION
Coordinate patches, surfaces in E3. Functions differentiable on surfaces, tangent vectors, differential forms. Surface transformations, integration on surfaces, Topological properties of surfaces. Manifolds. Shape operators, normal curvature, Gauss curvature. Special curves on surfaces. First and second fundamental forms.
COURSE CONTENTS
WEEK
TOPICS
1st Week
Making inferences, defending their accuracy and validity.
2nd Week
Making inferences, defending their accuracy and validity.
3rd Week
Mathematical inference and proof methods.
4th Week
Mathematical inference and proof methods.
5th Week
Analyzing a mathematical situation or problem using mathematical patterns and relationships.
6th Week
Analyzing a mathematical situation or problem using mathematical patterns and relationships.
7th Week
Utilizing logical reasoning strategies such as rounding, grouping appropriate numbers, or using leading or trailing digits to support mathematical reasoning.
8th Week
Mid-term
9th Week
Making predictions about the outcome of operations and measurements using logical reasoning strategies.
10th Week
Making predictions about the outcome of operations and measurements using logical reasoning strategies.
11th Week
Making predictions about the outcome of operations and measurements using logical reasoning strategies, considering a specific reference point.
12th Week
Analyzing, proving, and verifying mathematical solutions using reasoning strategies in different learning areas.
13th Week
Analyzing, proving, and verifying mathematical solutions using reasoning strategies in different learning areas.
14th Week
Analyzing, proving, and verifying mathematical solutions using reasoning strategies in different learning areas.
RECOMENDED OR REQUIRED READING
Askey, R. (1999). Knowing and teaching elementary mathematics. American Educator, 23, 6-13. Eccles, P. J. (1997). An Introduction to Mathematical Reasoning: numbers, sets and functions. Cambridge University Press. English, L. D. (Ed.). (2004). Mathematical and analogical reasoning of young learners. Routledge. Garg, R. (2017). Mathematics and Logical Reasoning. Nunes, T., Bryant, P., Evans, D., Bell, D., Gardner, S., Gardner, A., & Carraher, J. (2007). The contribution of logical reasoning to the learning of mathematics in primary school. British Journal of Developmental Psychology, 25(1), 147-166. Uğurel, I., & Bukova, E. G. (2010). Matematiksel öğrenme etkinlikleri üzerine bir tartışma ve kavramsal bir çerçeve önerisi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 39(39). Umay, A. (2002). Öteki matematik. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23(23).
PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
Lecture,Discussion,Project,Experiment,Other
ASSESSMENT METHODS AND CRITERIA
Quantity
Percentage(%)
Mid-term
1
30
Assignment
1
30
Total(%)
60
Contribution of In-term Studies to Overall Grade(%)
60
Contribution of Final Examination to Overall Grade(%)
40
Total(%)
100
ECTS WORKLOAD
Activities
Number
Hours
Workload
Midterm exam
1
2
2
Preparation for Quiz
Individual or group work
1
13
13
Preparation for Final exam
1
45
45
Course hours
Preparation for Midterm exam
1
28
28
Laboratory (including preparation)
Final exam
1
2
2
Homework
Term Project Research
Experiment design
1
30
30
Total Workload
120
Total Workload / 30
4
ECTS Credits of the Course
4
LANGUAGE OF INSTRUCTION
Turkish
WORK PLACEMENT(S)
No
KEY LEARNING OUTCOMES (KLO) / MATRIX OF LEARNING OUTCOMES (LO)
