CC221003 Introduction to Geometry

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Education

Lecture Code CC221003 Subject Classification Specialized Education

Subject Name 幾何学概論

Subject Name
（Katakana）キカガクガイロン

Subject Name in
English Introduction to Geometry

Instructor TERAGAITO MASAKAZU

Instructor
(Katakana) テラガイト　マサカズ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  1Term

Days, Periods, and Classrooms (1T) Fri1-4：EDU L104

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture-oriented

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Required for students of Faculty of Education Cluster 2, Program in Mathematics Education

Keywords Euclidean geometry, non-Euclidean geometry

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Secondary School Mathematics Education
（Knowledge and Understanding）
・To understand basic knowledge of teaching contents of mathematic education.
（Abilities and Skills）
・To acquire and utilize the ability to think mathematically about teaching contents of mathematic education such as algebra, geometry, statistics and computer.

Class Objectives
/Class Outline The objectives of this course are:
- to understand geometric contents of junior high school and high school education,
- to learn Euclid's Elements,
- to understand axiomatic approach, and
- to learn non-Euclidean geometry

Class Schedule Lesson1: Axiomatic Approach: Abstract Geometry and Incidence Geometry
Lesson2: Metric Geometry
Lesson3: Betweeness
Lesson4: Line, Segment and Half Line
Lesson5: Angles and Quadrilaterals
Lesson6: Plane Separation Axiom
Lesson7: Pasch Geometry
Lesson8: Interior and Crossbar Theorem
Lesson9: Angles and Protractor Geometry
Lesson10: Congruence of Angles
Lesson11: Neutral Geometry and Congruence
Lesson12: Exterior Angle Theorem
Lesson13: Right triangles
Lesson14: Parallelism
Lesson15: Equivalent propositions to Euclid's Parallel Postulate

There will be a final exam in Lesson 16.
There will be unscheduled a report assignment.

Text/Reference
Books,etc. Use the textbook written in Japanese.

PC or AV used in
Class,etc. 　

(More Details) None

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Preparation for a lesson is not required. You  should review what you learned in class after every lesson.

Lessons1-15: we will construct geometry with axiomatic approach which is a main topic of this course. Only the basic knowledge of set theory and the characteristics of real numbers are premised and axioms are added gradually and then geometry is evolved. The name will be changed as geometry evolves. You should be aware that in which stage, discussions is carried out.

Requirements ・Students should be familiar with the basics of classes ( high school mathematics level) ,
・If you like sitting at the back of the classroom, you should not take this course. You as a student wishing to become a teacher should not make a teacher uncomfortable.
・ Student’s active contribution in class is appreciated. You will be highly evaluated by asking good questions.
・ The website of this course will be established on BB9. You should actively utilize the site.

Grading Method Students will be evaluated based on final exam.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message I hope you enjoy how things are called by different names at different circumstances in the axiomatic approach just like how fish is called by different names at different stages of the growth and like POKÉMON.
If you hear Euclidean geometry or plane geometry, you may think you know them well. But do you really understand them well? What is ‘a point’? What is ‘a line’?  What is ‘a plane? Euclid struggled with the definitions of those.
For example, think about how difficult to construct real numbers with Dedekind cut.
What is ‘an  angle’? What is ‘ a triangle’? What is ‘the congruence of triangles’?
Are the conditions for congruency of triangles that you learned in junior high school correct? What is 'parallel lines’?
The axiomatic approach will answer those simple questions completely. Of course this is not something you teach children, but is something teacher must know on the side.

Other The grade of this course will be referred to if ‘Study of Instructional Materials in Geometry’ in Grade 3 sets a limit to the number of students.

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Education
Lecture Code	CC221003	Subject Classification	Specialized Education
Subject Name	幾何学概論
Subject Name （Katakana）	キカガクガイロン
Subject Name in English	Introduction to Geometry
Instructor	TERAGAITO MASAKAZU
Instructor (Katakana)	テラガイト　マサカズ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Fri1-4：EDU L104
Lesson Style	Lecture	Lesson Style (More Details)
Lecture-oriented
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Required for students of Faculty of Education Cluster 2, Program in Mathematics Education
Keywords	Euclidean geometry, non-Euclidean geometry
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Secondary School Mathematics Education （Knowledge and Understanding）・To understand basic knowledge of teaching contents of mathematic education. （Abilities and Skills）・To acquire and utilize the ability to think mathematically about teaching contents of mathematic education such as algebra, geometry, statistics and computer.
Class Objectives /Class Outline	The objectives of this course are: - to understand geometric contents of junior high school and high school education, - to learn Euclid's Elements, - to understand axiomatic approach, and - to learn non-Euclidean geometry
Class Schedule	Lesson1: Axiomatic Approach: Abstract Geometry and Incidence Geometry Lesson2: Metric Geometry Lesson3: Betweeness Lesson4: Line, Segment and Half Line Lesson5: Angles and Quadrilaterals Lesson6: Plane Separation Axiom Lesson7: Pasch Geometry Lesson8: Interior and Crossbar Theorem Lesson9: Angles and Protractor Geometry Lesson10: Congruence of Angles Lesson11: Neutral Geometry and Congruence Lesson12: Exterior Angle Theorem Lesson13: Right triangles Lesson14: Parallelism Lesson15: Equivalent propositions to Euclid's Parallel Postulate There will be a final exam in Lesson 16. There will be unscheduled a report assignment.
Text/Reference Books,etc.	Use the textbook written in Japanese.
PC or AV used in Class,etc.
(More Details)	None
Learning techniques to be incorporated
Suggestions on Preparation and Review	Preparation for a lesson is not required. You should review what you learned in class after every lesson. Lessons1-15: we will construct geometry with axiomatic approach which is a main topic of this course. Only the basic knowledge of set theory and the characteristics of real numbers are premised and axioms are added gradually and then geometry is evolved. The name will be changed as geometry evolves. You should be aware that in which stage, discussions is carried out.
Requirements	・Students should be familiar with the basics of classes ( high school mathematics level) , ・If you like sitting at the back of the classroom, you should not take this course. You as a student wishing to become a teacher should not make a teacher uncomfortable. ・ Student’s active contribution in class is appreciated. You will be highly evaluated by asking good questions. ・ The website of this course will be established on BB9. You should actively utilize the site.
Grading Method	Students will be evaluated based on final exam.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	I hope you enjoy how things are called by different names at different circumstances in the axiomatic approach just like how fish is called by different names at different stages of the growth and like POKÉMON. If you hear Euclidean geometry or plane geometry, you may think you know them well. But do you really understand them well? What is ‘a point’? What is ‘a line’? What is ‘a plane? Euclid struggled with the definitions of those. For example, think about how difficult to construct real numbers with Dedekind cut. What is ‘an angle’? What is ‘ a triangle’? What is ‘the congruence of triangles’? Are the conditions for congruency of triangles that you learned in junior high school correct? What is 'parallel lines’? The axiomatic approach will answer those simple questions completely. Of course this is not something you teach children, but is something teacher must know on the side.
Other	The grade of this course will be referred to if ‘Study of Instructional Materials in Geometry’ in Grade 3 sets a limit to the number of students.
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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