CC220304 Introduction to Mathematics Education II

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Education

Lecture Code CC220304 Subject Classification Specialized Education

Subject Name 数学教育学概論II

Subject Name
（Katakana）スウガクキョウイクガクガイロンII

Subject Name in
English Introduction to Mathematics Education II

Instructor KOYAMA MASATAKA

Instructor
(Katakana) コヤマ　マサタカ

Campus Higashi-Hiroshima Semester/Term 2nd-Year, Second Semester, 3Term

Days, Periods, and Classrooms (3T) Weds5-8：EDU L205

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture and Seminar

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

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 24 : Social Sciences

Course Area（Discipline） 08 : Curriculum and Instruction Sciences

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

Keywords Methodology of mathematics education, teaching　theory of mathematics, methodology of instructions of mathematics, evaluation theory of mathematics, instruction and learning theory of mathematics

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 methods of mathematic education.
（Abilities and Skills）
・To be able to collect documents and materials on a principle and method of mathematic education, and to be able to read and analyze them.

Class Objectives
/Class Outline Students will understand the methodology of mathematics education and cultivate basic capabilities needed to be a mathematics teacher, by discussing the methodology of teaching such as instructions & learning theories, problem solving, and conceptual configurations of mathematics and by analyzing mathematics lessons.

Class Schedule Lesson1: Course Overview and Objectives
Students will be provided with an explanation of the course overview to clarify the objectives of this course.
Lesson2: How instruction in mathematics education should be
Students will be provided with an opportunity to experience teaching in a math class and think about how instruction in mathematics education should be, using specific examples of mathematics teaching contents.
Lesson3: Teaching Theory of Mathematics (1) Structure
Students will think about what mathematics class is from the viewpoints of four composing elements: objectives, students, teachers, and teaching contents to clarify the lesson structure and viewpoints in observation.
Lesson4: Teaching Theory of Mathematics (2): Instruction and Learning Theories
This lesson will examine From Special to General and From Specific to Abstract as general instruction and learning principles in mathematics class, taking teaching contents of junior high and high schools as examples.
Lesson5: Teaching Theory of Mathematics (3) Learning Theories
Students will understand each of these phases: knowledge, skills, problem solving, and problem setting, and the related learning theories through specific mathematics problems.
Lesson6: Evaluation, Explanation, and Discussion on Report Assignment 1
Through discussions on students’ ideas of how mathematics teaching (lessons) should be, students can share their ideas and think about issues more deeply.
Lesson7: Methodology of Mathematics Education (1) Teaching of Mathematical Problem Solving and Problem Solving
This lesson will explain the stages and strategies of problem solving as a teaching methods of mathematical problem solving. Specific examples will be shown to help students understand.
Lesson8: Methodology of Mathematics Education (2) Teaching of Mathematical Problem Solving and Problem Setting
This lesson will explain problem setting and strategies of problem setting as a teaching method of mathematical problem solving. Specific examples will be shown help students understand.
Lesson9: Methodology of Mathematics Education (3) Teaching of Mathematical Concept Formation
This lesson will explain heuristic and constructive learning as a teaching method of mathematical concept formation. Specific examples will be shown help students understand.
Lesson10: Actual Mathematics Lessons (1) Analysis of Mathematics Lesson 1
Students will watch a DVD of recorded mathematic lesson 1 and analyze the lesson to understand how mathematics teaching (lessons) should be and how to realize it.
Lesson11: Actual Mathematics Lessons (2) Analysis of Mathematics Lesson 2
Students will watch a DVD of recorded mathematic lesson 2 and analyze the lesson to understand how mathematics teaching (lesson) should be and how to realize it.
Lesson12: Actual Mathematics Lessons (3) Structure of Mathematics Lesson
Students will become able to design a structure of a mathematics lesson by having a discussion over how mathematics teaching (lesson) should be and how to realize it.
Lesson13: Theory of Evaluation in Mathematics Education (1) Unification of Teaching and Evaluation
This lesson will explain evaluation in mathematics education, and students will think about unification of teaching and evaluation.
Lesson14: Theory of Evaluation in Mathematics Education (2) Evaluation Standards, Criteria, and Methods
Students will think about evaluation in mathematics lessons.
Lesson15: Evaluation, Explanation, and Discussion on Report Assignment 2
Through discussions on students’ ideas of how mathematics teaching (lessons) should be, students can share their ideas and think about issues more deeply.

Test and Report assignments

Text/Reference
Books,etc. Materials：Handouts will be provided when needed.
Textbooks：
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）
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)』
文部省『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)』．
数学教育学研究会編『新訂数学教育の理論と実際』，聖文新社．
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．
Reference Books：
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. 　

(More Details) DVD will be used (2 DVD；50 min.)
PC

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review After Lesson1:
Review the outline of the lesson and identify your objectives. Find a textbook and/or books for reference.
After Lesson2-5:
Review what you learned in the lesson and clarify your questions.
Based on that, read a textbook and reference books and think about what you find.
【Report Assignment 1】
Investigate the results of mathematics achievement surveys of Japan and overseas, identify and sort out issues of mathematics education methods, concerning students’ mathematical recognition, and find measures to overcome those issues.
After Lesson6:
Examine the evaluation of your report assignment and discussions that we had in class to identify your challenge.
After Lesson7-11
Review what you learned in the lesson and clarify your questions. Based on that, read the textbook and/or books for reference and think about what you find.
【Report Assignment２】
Select one specific teaching content of junior high school mathematics and high school mathematics (one each) from literatures about mathematics learning theories and/or mathematics understanding model, and/or junior high school and high school textbooks, and think about how to teach the contents.
After Lesson12:
Identify your challenge based on the evaluation of your report assignment returned and discussions as a reference.
After Lesson13-15:
Review what you learned in the lesson and clarify your questions.
Review the previous lessons and report assignments to be prepared for a final exam.
After Lesson16
Examine the result of your final exam and reflect on your learning process and outcome to identify your challenge for the future and find a way to overcome the challenge.

Requirements Teaching methods of school subject (mathematics)
It is desirable that students have taken the Introduction to Mathematics Education I.

Grading Method Students will be evaluated based on test (80%) and report assignments (20%).

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	2024Year	School/Graduate School	School of Education
Lecture Code	CC220304	Subject Classification	Specialized Education
Subject Name	数学教育学概論II
Subject Name （Katakana）	スウガクキョウイクガクガイロンII
Subject Name in English	Introduction to Mathematics Education II
Instructor	KOYAMA MASATAKA
Instructor (Katakana)	コヤマ　マサタカ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Weds5-8：EDU L205
Lesson Style	Lecture	Lesson Style (More Details)
Lecture and Seminar
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	24 : Social Sciences
Course Area（Discipline）	08 : Curriculum and Instruction Sciences
Eligible Students	Required for students of Cluster 2, Program in Mathematics Education
Keywords	Methodology of mathematics education, teaching　theory of mathematics, methodology of instructions of mathematics, evaluation theory of mathematics, instruction and learning theory of mathematics
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 methods of mathematic education. （Abilities and Skills）・To be able to collect documents and materials on a principle and method of mathematic education, and to be able to read and analyze them.
Class Objectives /Class Outline	Students will understand the methodology of mathematics education and cultivate basic capabilities needed to be a mathematics teacher, by discussing the methodology of teaching such as instructions & learning theories, problem solving, and conceptual configurations of mathematics and by analyzing mathematics lessons.
Class Schedule	Lesson1: Course Overview and Objectives Students will be provided with an explanation of the course overview to clarify the objectives of this course. Lesson2: How instruction in mathematics education should be Students will be provided with an opportunity to experience teaching in a math class and think about how instruction in mathematics education should be, using specific examples of mathematics teaching contents. Lesson3: Teaching Theory of Mathematics (1) Structure Students will think about what mathematics class is from the viewpoints of four composing elements: objectives, students, teachers, and teaching contents to clarify the lesson structure and viewpoints in observation. Lesson4: Teaching Theory of Mathematics (2): Instruction and Learning Theories This lesson will examine From Special to General and From Specific to Abstract as general instruction and learning principles in mathematics class, taking teaching contents of junior high and high schools as examples. Lesson5: Teaching Theory of Mathematics (3) Learning Theories Students will understand each of these phases: knowledge, skills, problem solving, and problem setting, and the related learning theories through specific mathematics problems. Lesson6: Evaluation, Explanation, and Discussion on Report Assignment 1 Through discussions on students’ ideas of how mathematics teaching (lessons) should be, students can share their ideas and think about issues more deeply. Lesson7: Methodology of Mathematics Education (1) Teaching of Mathematical Problem Solving and Problem Solving This lesson will explain the stages and strategies of problem solving as a teaching methods of mathematical problem solving. Specific examples will be shown to help students understand. Lesson8: Methodology of Mathematics Education (2) Teaching of Mathematical Problem Solving and Problem Setting This lesson will explain problem setting and strategies of problem setting as a teaching method of mathematical problem solving. Specific examples will be shown help students understand. Lesson9: Methodology of Mathematics Education (3) Teaching of Mathematical Concept Formation This lesson will explain heuristic and constructive learning as a teaching method of mathematical concept formation. Specific examples will be shown help students understand. Lesson10: Actual Mathematics Lessons (1) Analysis of Mathematics Lesson 1 Students will watch a DVD of recorded mathematic lesson 1 and analyze the lesson to understand how mathematics teaching (lessons) should be and how to realize it. Lesson11: Actual Mathematics Lessons (2) Analysis of Mathematics Lesson 2 Students will watch a DVD of recorded mathematic lesson 2 and analyze the lesson to understand how mathematics teaching (lesson) should be and how to realize it. Lesson12: Actual Mathematics Lessons (3) Structure of Mathematics Lesson Students will become able to design a structure of a mathematics lesson by having a discussion over how mathematics teaching (lesson) should be and how to realize it. Lesson13: Theory of Evaluation in Mathematics Education (1) Unification of Teaching and Evaluation This lesson will explain evaluation in mathematics education, and students will think about unification of teaching and evaluation. Lesson14: Theory of Evaluation in Mathematics Education (2) Evaluation Standards, Criteria, and Methods Students will think about evaluation in mathematics lessons. Lesson15: Evaluation, Explanation, and Discussion on Report Assignment 2 Through discussions on students’ ideas of how mathematics teaching (lessons) should be, students can share their ideas and think about issues more deeply. Test and Report assignments
Text/Reference Books,etc.	Materials：Handouts will be provided when needed. Textbooks：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）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)』文部省『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)』．数学教育学研究会編『新訂数学教育の理論と実際』，聖文新社．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． Reference Books：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.
(More Details)	DVD will be used (2 DVD；50 min.) PC
Learning techniques to be incorporated
Suggestions on Preparation and Review	After Lesson1: Review the outline of the lesson and identify your objectives. Find a textbook and/or books for reference. After Lesson2-5: Review what you learned in the lesson and clarify your questions. Based on that, read a textbook and reference books and think about what you find. 【Report Assignment 1】 Investigate the results of mathematics achievement surveys of Japan and overseas, identify and sort out issues of mathematics education methods, concerning students’ mathematical recognition, and find measures to overcome those issues. After Lesson6: Examine the evaluation of your report assignment and discussions that we had in class to identify your challenge. After Lesson7-11 Review what you learned in the lesson and clarify your questions. Based on that, read the textbook and/or books for reference and think about what you find. 【Report Assignment２】 Select one specific teaching content of junior high school mathematics and high school mathematics (one each) from literatures about mathematics learning theories and/or mathematics understanding model, and/or junior high school and high school textbooks, and think about how to teach the contents. After Lesson12: Identify your challenge based on the evaluation of your report assignment returned and discussions as a reference. After Lesson13-15: Review what you learned in the lesson and clarify your questions. Review the previous lessons and report assignments to be prepared for a final exam. After Lesson16 Examine the result of your final exam and reflect on your learning process and outcome to identify your challenge for the future and find a way to overcome the challenge.
Requirements	Teaching methods of school subject (mathematics) It is desirable that students have taken the Introduction to Mathematics Education I.
Grading Method	Students will be evaluated based on test (80%) and report assignments (20%).
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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