CC220402 Methodology of Mathematics Education

Hiroshima University Syllabus

Japanese

Academic Year 2026Year School/Graduate School School of Education

Lecture Code CC220402 Subject Classification Specialized Education

Subject Name 数学教育方法論

Subject Name
（Katakana）スウガクキョウイクホウホウロン

Subject Name in
English Methodology of Mathematics Education

Instructor OKAZAKI MASAKAZU

Instructor
(Katakana) オカザキ　マサカズ

Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  4Term

Days, Periods, and Classrooms (4T) Weds5-8：EDU L205

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Lecture and Discussions

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 1 : Undergraduate Introductory

Course Area（Area） 24 : Social Sciences

Course Area（Discipline） 08 : Curriculum and Instruction Sciences

Eligible Students Students of Cluster 2 (Program in Mathematic Education) and Others

Keywords Aims and objectives of mathematics education, Methods for the teaching and learning of mathematics, Mathematical attainments of students, Planning lesson for secondary school mathematics

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) This course is the undergraduate introductory for the students of Cluster 2 (Program in Mathematics Education).
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students)

Class Objectives
/Class Outline In this course, students will analyze and study the principles and methods of mathematics education from the viewpoint of integration of theories and practices, through which they will deepen understanding of the principles and methods of mathematics education and learn to utilize them for improving teachers’ practices. Also, the students will learn to see mathematics recognition from a standpoint of learners and to effectively conduct mathematics education with enhanced lesson observation and practice skills.

Class Schedule Lesson1: Course Overview and Objectives
  Students will be provided with an overview of this course to clarify the objective.
Lesson2: Aims and Objectives of Mathematics Education
  Students understand the aims and objectives of secondary school mathematics education in Japan.
Lesson3: The Current State of Japanese Students as Seen in International and Domestic Academic Achievement Surveys
　Students will clarify the challenges of mathematics learning and instruction as seen in academic achievement surveys and other sources.
Lesson4: Instruction in the Areas of Numbers, Expressions, and Algebra (1)
　We consider mathematics teaching in situations where numbers are extended and the meaning of operations associated with them is expanded, focusing on positive and negative numbers, integers, square roots, real numbers, and sets.
Lesson5: Mathematics Teaching in the Areas of Numbers, Expressions, and Algebra (2)
　We consider the significance and difficulty of learning algebraic expressions and methods for teaching proof using algebraic expressions.
[Report 1] Analyze the problems in the National Academic Achievement and Learning Status Survey from the following perspectives: 1) Identify the philosophy and objectives of mathematics education implied in the problems through problem analysis. 2) For problems with low achievement, consider the causes from the perspectives of student learning, teacher guidance, and instructional content, and propose specific instructional methods.
Lesson 6: Teaching of Shape and Geometry (1)
　Students will understand the study of construction and movement from the perspective of the transition process from arithmetic to mathematics. They will also learn through experience how to teach spatial geometry.
Lesson7:  Teaching of Shape and Geometry (2)
　Students will identify the significance and difficulty of geometric proofs and consider how to teach them. They will understand ways of thinking that are unique to the geometry and geometry areas and cultivate an attitude of exploring geometry.
Lesson8: Teaching of Function (1)
　Students will understand the significance of functional perspectives and ways of thinking in mathematics teaching. They will explore the teaching of function representations based on connections to everyday sensibilities.
Lesson9: Teaching of Function
　Students will identify the unique challenges in teaching proportions, linear functions, quadratic functions, trigonometric functions, and exponential and logarithmic functions, and cultivate an attitude of working to improve teaching.
Lesson10: Teaching of statistics and probability (1)
　Students will understand an overview of statistical perspectives, ways of thinking, and activities, and deepen their understanding of statistical problem-solving through hands-on activities. Examine aspects of statistical thinking supported by probability theory.
Lesson11: Teaching of statistics and probability (2)
　Students will understand the characteristics and difficulties of how to view and think about probability. Through experiential activities, consider the meaning of probabilistic phenomena.
Lesson12: The significance and methods of assessment/evaluation in junior high and high school mathematics
　Students will understand the significance and methods of assessment/evaluation in junior high and high school mathematics.
Lesson13: Methods for Creating Mathematical Lessons in Junior High and High School Mathematics
　Students will understand how to create lessons and write lesson plans in junior high and high school mathematics. They actually write a lesson plan.
Lesson14: Implementation of a Mock Lesson for Junior High and High School Mathematics
　A mock lesson will be conducted. Based on what has been learned so far, the mock lesson will be examined, and the results of the discussion will be summarized.
[Assignment Report 2] 1) Refining the lesson plan created for the mock lesson, 2) Conducting or observing the mock lesson and reporting the results of discussions, 3) Considering teaching methods and issues in mathematics based on the mock lesson and discussions.
Lesson15: Summary of the Purpose, Content, Methods, and Assessment of Teaching in Mathematics, and Future Challenges
　Students will reflect on what they have learned through the lectures and mock lessons, and summarize the nature of mathematics education and teaching methods. They will also identify their own research topic and use it to help them grow as mathematics teachers.

Task Reports. Final Examination.

Text/Reference
Books,etc. Handouts will be provided.
Text Books:
中学校学習指導要領（平成29年３月告示文部科学省）
中学校学習指導要領解説数学編（平成29年７月文部科学省）
高等学校学習指導要領（平成30年３月告示文部科学省）
高等学校学習指導要領解説数学編（平成30年７月文部科学省）
高等学校学習指導要領解説理数（平成30年７月文部科学省）
Junior high school textbooks: Grade 1, 2, & 3
High school textbooks: Math I, Math A, Math II, Math B, Math III, & Math C.
文部科学省『中学校学習指導要領解説数学編(MEXT Commentary to the Curriculum Guidelines for Junior High Schools, Mathematics) 』，教育出版，September 2008
文部科学省『高等学校学習指導要領解説数学編理数編(MEXT Commentary to the Curriculum Guidelines for High Schools, Mathematics and Science)』，実教出版，December 2009.
小山正孝編著『教師教育講座第14巻　中等数学教育』，協同出版．
礒田正美・影山和也編著『新・教職課程演習第19巻　中等数学科教育』，協同出版．
数学教育研究会編『新訂数学教育の理論と実際』，聖文新社．
Reference Books:
国立教育政策研究所『全国学力・学習状況調査報告書』，国立教育政策研究所．
日本数学教育学会編『学校数学の授業構成を問い直す』，産業図書．
中原忠男編『算数・数学科重要用語300の基礎知識』，明治図書．

PC or AV used in
Class,etc. Text, Handouts, Microsoft Teams, moodle

(More Details) Textbook, Handouts, Audio materials
PC

Learning techniques to be incorporated Discussions, Quizzes/ Quiz format, Post-class Report

Suggestions on
Preparation and
Review The more you prepare and review, the more independent research reports you need to submit.
Lesson plans, lesson observation records, and commitment to trial lessons are important.

Requirements This course is for the students of Cluster 2 (Program in Mathematic Education) and Others who wish to become a mathematics teacher.

Grading Method Students will be evaluated based on report assignments (20%) and final examination (80%).
Students’ Knowledge & Understanding will be evaluated mainly based on final examination.
Students’ Intellectual Capabilities & Skills will be evaluated mainly based on report assignments and work to be submitted.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

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	2026Year	School/Graduate School	School of Education
Lecture Code	CC220402	Subject Classification	Specialized Education
Subject Name	数学教育方法論
Subject Name （Katakana）	スウガクキョウイクホウホウロン
Subject Name in English	Methodology of Mathematics Education
Instructor	OKAZAKI MASAKAZU
Instructor (Katakana)	オカザキ　マサカズ
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Weds5-8：EDU L205
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face
Lecture and Discussions
Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	1 : Undergraduate Introductory
Course Area（Area）	24 : Social Sciences
Course Area（Discipline）	08 : Curriculum and Instruction Sciences
Eligible Students	Students of Cluster 2 (Program in Mathematic Education) and Others
Keywords	Aims and objectives of mathematics education, Methods for the teaching and learning of mathematics, Mathematical attainments of students, Planning lesson for secondary school mathematics
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	This course is the undergraduate introductory for the students of Cluster 2 (Program in Mathematics Education).
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)
Class Objectives /Class Outline	In this course, students will analyze and study the principles and methods of mathematics education from the viewpoint of integration of theories and practices, through which they will deepen understanding of the principles and methods of mathematics education and learn to utilize them for improving teachers’ practices. Also, the students will learn to see mathematics recognition from a standpoint of learners and to effectively conduct mathematics education with enhanced lesson observation and practice skills.
Class Schedule	Lesson1: Course Overview and Objectives Students will be provided with an overview of this course to clarify the objective. Lesson2: Aims and Objectives of Mathematics Education Students understand the aims and objectives of secondary school mathematics education in Japan. Lesson3: The Current State of Japanese Students as Seen in International and Domestic Academic Achievement Surveys 　Students will clarify the challenges of mathematics learning and instruction as seen in academic achievement surveys and other sources. Lesson4: Instruction in the Areas of Numbers, Expressions, and Algebra (1) 　We consider mathematics teaching in situations where numbers are extended and the meaning of operations associated with them is expanded, focusing on positive and negative numbers, integers, square roots, real numbers, and sets. Lesson5: Mathematics Teaching in the Areas of Numbers, Expressions, and Algebra (2) 　We consider the significance and difficulty of learning algebraic expressions and methods for teaching proof using algebraic expressions. [Report 1] Analyze the problems in the National Academic Achievement and Learning Status Survey from the following perspectives: 1) Identify the philosophy and objectives of mathematics education implied in the problems through problem analysis. 2) For problems with low achievement, consider the causes from the perspectives of student learning, teacher guidance, and instructional content, and propose specific instructional methods. Lesson 6: Teaching of Shape and Geometry (1) 　Students will understand the study of construction and movement from the perspective of the transition process from arithmetic to mathematics. They will also learn through experience how to teach spatial geometry. Lesson7: Teaching of Shape and Geometry (2) 　Students will identify the significance and difficulty of geometric proofs and consider how to teach them. They will understand ways of thinking that are unique to the geometry and geometry areas and cultivate an attitude of exploring geometry. Lesson8: Teaching of Function (1) 　Students will understand the significance of functional perspectives and ways of thinking in mathematics teaching. They will explore the teaching of function representations based on connections to everyday sensibilities. Lesson9: Teaching of Function 　Students will identify the unique challenges in teaching proportions, linear functions, quadratic functions, trigonometric functions, and exponential and logarithmic functions, and cultivate an attitude of working to improve teaching. Lesson10: Teaching of statistics and probability (1) 　Students will understand an overview of statistical perspectives, ways of thinking, and activities, and deepen their understanding of statistical problem-solving through hands-on activities. Examine aspects of statistical thinking supported by probability theory. Lesson11: Teaching of statistics and probability (2) 　Students will understand the characteristics and difficulties of how to view and think about probability. Through experiential activities, consider the meaning of probabilistic phenomena. Lesson12: The significance and methods of assessment/evaluation in junior high and high school mathematics 　Students will understand the significance and methods of assessment/evaluation in junior high and high school mathematics. Lesson13: Methods for Creating Mathematical Lessons in Junior High and High School Mathematics 　Students will understand how to create lessons and write lesson plans in junior high and high school mathematics. They actually write a lesson plan. Lesson14: Implementation of a Mock Lesson for Junior High and High School Mathematics 　A mock lesson will be conducted. Based on what has been learned so far, the mock lesson will be examined, and the results of the discussion will be summarized. [Assignment Report 2] 1) Refining the lesson plan created for the mock lesson, 2) Conducting or observing the mock lesson and reporting the results of discussions, 3) Considering teaching methods and issues in mathematics based on the mock lesson and discussions. Lesson15: Summary of the Purpose, Content, Methods, and Assessment of Teaching in Mathematics, and Future Challenges 　Students will reflect on what they have learned through the lectures and mock lessons, and summarize the nature of mathematics education and teaching methods. They will also identify their own research topic and use it to help them grow as mathematics teachers. Task Reports. Final Examination.
Text/Reference Books,etc.	Handouts will be provided. Text Books: 中学校学習指導要領（平成29年３月告示文部科学省）中学校学習指導要領解説数学編（平成29年７月文部科学省）高等学校学習指導要領（平成30年３月告示文部科学省）高等学校学習指導要領解説数学編（平成30年７月文部科学省）高等学校学習指導要領解説理数（平成30年７月文部科学省） Junior high school textbooks: Grade 1, 2, & 3 High school textbooks: Math I, Math A, Math II, Math B, Math III, & Math C. 文部科学省『中学校学習指導要領解説数学編(MEXT Commentary to the Curriculum Guidelines for Junior High Schools, Mathematics) 』，教育出版，September 2008 文部科学省『高等学校学習指導要領解説数学編理数編(MEXT Commentary to the Curriculum Guidelines for High Schools, Mathematics and Science)』，実教出版，December 2009. 小山正孝編著『教師教育講座第14巻　中等数学教育』，協同出版．礒田正美・影山和也編著『新・教職課程演習第19巻　中等数学科教育』，協同出版．数学教育研究会編『新訂数学教育の理論と実際』，聖文新社． Reference Books: 国立教育政策研究所『全国学力・学習状況調査報告書』，国立教育政策研究所．日本数学教育学会編『学校数学の授業構成を問い直す』，産業図書．中原忠男編『算数・数学科重要用語300の基礎知識』，明治図書．
PC or AV used in Class,etc.	Text, Handouts, Microsoft Teams, moodle
(More Details)	Textbook, Handouts, Audio materials PC
Learning techniques to be incorporated	Discussions, Quizzes/ Quiz format, Post-class Report
Suggestions on Preparation and Review	The more you prepare and review, the more independent research reports you need to submit. Lesson plans, lesson observation records, and commitment to trial lessons are important.
Requirements	This course is for the students of Cluster 2 (Program in Mathematic Education) and Others who wish to become a mathematics teacher.
Grading Method	Students will be evaluated based on report assignments (20%) and final examination (80%). Students’ Knowledge & Understanding will be evaluated mainly based on final examination. Students’ Intellectual Capabilities & Skills will be evaluated mainly based on report assignments and work to be submitted.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
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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