Nature of the course: Theoretical Course no: Math. Ed. 525
Teaching hours: 48 Credit hours: 3
Level: M.Ed. Semester: II
Course Introduction
This course has been designed and prepared to trace the trends of various aspects of teaching/learning (T/L) mathematics education. It deals with the recent trends of T/L mathematics practices at different levels, from school to university. It focuses on the reforms of major areas of school mathematics along with their T/L issues and problems. It also assesses the rationale of T/L applied mathematics and illustrates some mathematical modeling. Besides this, it provides an updated overview of the themes, issues, and recommendations made by different international conferences on mathematics education. The social, cultural, and inclusive educational issues and problems are also critically assessed. Further, this course presents the trends of research in mathematics education.
General Objectives
The general objectives of this course are as follows:
To enable the students to sketch the global trends in mathematics education from school to university levels, especially with respect to the development of curriculum, content; teaching/learning methods and materials, evaluation system and research.
To enable them to sketch the developmental trends, reform and teaching/learning issues and problems in three basic areas of school mathematics.
To have the students elucidate the trends how the concept of applied mathematics changes with time (This objective needs rewriting).
To enable the students to trace out the different trends that are observed in the historical development of different Commissions, Unions, Conferences, and Olympiads, along with different activities of Nepalese mathematical organizations.
To acquaint the students with the critical appraisal to address different issues (social and cultural roles, popularization, gender differences, ethnomathematics, and inclusion) in mathematics education.
To provide them with historical and modern trends of knowledge observed in the area of research in mathematics education.
Contents and specific objectives
Specific objectives
Contents
Unit I: Mathematics Education at School and Tertiary Levels (12 hrs)
Discuss briefly the roles of philosophy and learning theory to trace the trends in ME.
Sketch global trends of ME at different levels with respect to curriculum, content, methods and materials, evaluation system, research, and sociological components.
Introduction
TME at the basic level
TME at the secondary level
TME at the tertiary level
Unit II: Trends in the Three Basic Areas of School Mathematics (9 hrs)
Sketch trends of the three basic areas of school mathematics.
Review the trends of school geometry, arithmetic and algebra (with reference to curriculum, content, methods, materials and evaluation system).
Give comprehensive views on the issues and problems of teaching/learning school mathematics.
Introduction
Reforms in Geometry
Reforms in Arithmetic
Reform in Algebra
Issues and problems in the T/L the three basic areas of mathematics for the 21st century
Unit III: Educational Implications of Applied Mathematics (6 hrs)
Explain the trends showing how the concept of applied mathematics changes with time.
Clarify the reason for teaching the application of mathematics at different levels of schooling.
State the issues and problems of applied mathematics in mathematics education.
Analyze the impact of applied mathematics on mathematics education.
Use practical knowledge and skills in the area of mathematical modeling.
Introduction
Rationale to teach application of mathematics
Trends in teaching applied mathematics
Issues and problems of T/L applied mathematics
The impact of T/L applied mathematics
Some examples of mathematical modeling
Unit IV: Mathematics Education Conferences (6 hrs)
Sketch the different trends of Union, Commission, Study groups, Conferences, and Olympiads.
Describe the aims, activities and responsibilities of IMU and ICMI.
Describe the achievements of different international congresses (ICMEs).
Explain different formalities (selection of Jury, conditions of participation, and topics asked) in IMO.
Describe the aims and activities of professional organizations of mathematics in Nepal.
International Commission on Mathematical Instruction (ICMI)
International Congress on Mathematical Education (ICME)
Organization of ICME in different countries
International Mathematical Olympiad (IMO)
Nepalese mathematical organizations (NMO)
Unit V: Issues in Mathematics Education (9 hrs)
Give critical comments on the social issues and problem in T/L mathematics.
Appraise the role of culture in T/L mathematics.
Discuss on the assessment system of mathematics education.
Give critical appraisal to address different issues (popularization, gender differences, ethnomathematics, and inclusion) in mathematics education.
Give critical comments on tensions occurring while dealing with mathematics education for the stakeholders of the 21st century.
Social issues and problems in T/L mathematics education
Cultural role in T/L mathematics education
Issues and problems in students' evaluation system
Challenges of T/L mathematics in the 21st century
Popularization of mathematics education
Gender difference in mathematics education
Ethnomathematics
Individual difference of students
Special needs of students
Instructional Techniques
General Instructional Technique
Lecture, mini-lecture, brainstorming, group works, presentation and discussion methods
Specific Instructional Techniques
Unit
Specific Instructional Techniques
Unit I
Reading, discussing, reflecting and presenting different aspects of mathematics education at different levels from school to tertiary levels.
Unit II
Internet Browse and presentation in basic areas of school mathematics in classrooms.
Unit III
Peer-study, discussion, comparison and presentation in applied part of mathematics.
Unit IV
Net Browse, reading of the text, searching journals and reporting about the resolutions of different conferences.
Unit V
Critical discourse on different issues and problems, presentation and reflective writings.
Unit VI
Mini-lecture followed by students' group-presentations in different philosophical views of research and research-areas.
Evaluation
Internal Evaluation
Internal evaluation will be conducted by the subject teacher based on the following activities.
Activities
Marks
Attendance
5 marks
Participation in learning activities
5 marks
First assignment/assessment
10 marks
Second assignment/midterm exam
10 marks
Third assignment/assessment
10 marks
Total
40 marks
External Examination (Final examination)
The Examination Division, Office of the Dean, Faculty of Education will conduct the final examination at the end of the semester. The number of questions, types of questions and marks allocated to each type of question will be as follows.
Question Type
Marks
Objective questions (multiple choice 10 x 1)
10 marks
Short answer questions (6 questions x 5 points) with two OR questions
30 marks
Long answer questions (2 questions x 10 points) with one OR question
Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.
Attempt all questions
Group "B"6 X 5 marks =30
Short answer questions
Discuss on the trends in mathematics education in terms of methods and materials at primary level.
Describe the major reforms in the instruction of school geometry with special reference to aim, content and method.
Compare and contrast between pure and applied mathematics with suitable examples.
Sketch the trends how and why ICMI was established by mathematicians.
Present strong evidences in regard to role of mathematical Olympiads for the popularization of mathematics.
Explain the trends in mathematics education research.
Group "C"2 X 10 marks = 20
Long answer questions
What trends do you sketch in mathematics education at university level?
Discuss about the three traditions of research in mathematics education with suitable examples.
Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.
Attempt all questions
Group "B"6 X 5 marks =30
Short answer questions
Sketch the trends in contents of mathematics education at college level.
Give the brief sketch of the development of Arithmetic from palpable phase of Arithmetization phase.
OR
State the major reforms in the instruction of school Algebra with reference to its teaching methods and materials.
Write four different definitions of applied mathematics and compare them with suitable diagram.
Write a summary table showing the data, the place and major issues raised in the last two ICMES.
What is popularization of mathematics? Write the importance of popularization of math-education with suitable examples.
OR
Discuss the role of culture in teaching/learning mathematics education.
Sketch the trends in mathematics education from 1950 Ad to date.
Group "C"2 X 10 marks = 20
Long answer questions
State the importance of "Adult and Continuous Education System" in the context of Nepal. Also, discuss its problems and challenges.
OR
How is the trends of goals and content of mathematics education at pre-primary and primary levels? Explain this trend with suitable examples.
Discuss Empiricist, Intuitionist and constructivist views in research of mathematics education with suitable examples.
Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.
Attempt all questions
Group "B"6 X 5 marks =30
Short answer questions
How do we trace the philosophical changes in mathematics education? Explain in brief.
Explain the development of arithmetic with reference to national curriculum of mathematics at school level.
Establish the relationship logically between applied mathematics and mathematical modeling with example.
Argue for the 'issues on assessment system' at school level mathematics with example.
How do ICMI contribute to the ICME? Explain with reference to ICMI activities.
OR
Explain the importance of IMO along with its criteria for participation.
Why action research is important in mathematics education? Explain action research cycle with example in brief.
OR
Explain the areas of research in mathematics education.
Group "C"2 X 10 marks = 20
Long answer questions
Sketch the trends of basic level of mathematics education with respect to content, method and assessment system with example according to nation level curriculum.
How do different issues—gender difference, individual difference, and students with special needs—hinder classroom teaching? Elaborate with your idea to make classroom inclusive.
OR
Critically examine the issues and problems of teaching-learning school mathematics for 21st-century era with examples.
Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.
Attempt all questions
Group "B"6 X 5 marks =30
Short answer questions
Describe the trends in four areas of courses of Mathematics Education provided at College level.
State the trends of major reforms observed in teaching/learning 'School Algebra' with reference to its 'Evaluation system'.
How is the recent trends of 'Applied Mathematics'? Compare pure and Applied Mathematics with suitable examples.
Name the different Nepalese Mathematical Organizations and write down each one's mathematical activities.
State the major problems appeared against Popularization of Mathematics Education in Nepal.
OR
What does it mean to say 'Gender difference in Mathematics Education'? State the agendas proposed by UNESCO for gender equality in Mathematics Education.
What are the major areas of research in Mathematics Education? Describe them briefly.
OR
Why do academic experts prefer Action Research to improve classroom teaching/learning situation? Illustrate its different stages.
Group "C"2 X 10 marks = 20
Long answer questions
How do children learn pre-concepts or beginning concepts of mathematics? Describe the trends of different roles of Mathematics teachers at Basic level education.
OR
What are the different teaching methods of Mathematics Education being used at University level? Describe them in Nepalese context.
What are the issues and problems in teaching/learning (T/L) Geometry for 21st century? Describe them with reference to Geometrical curriculum, content, and T/L methods and materials.
Candidates are required to give their answers in their own words as far as practicable.
The figures in the margin indicate full marks.
Attempt all questions
Group "B"6 X 5 marks =30
Short answer questions
Discuss about the trend in mathematics education in Bachelor's level with respect to research and sociological components.
OR
State and briefly explain Ethno-mathematics with example.
Discuss briefly the reforms in school algebra.
What is applied mathematics? Analyze the trends in teaching of applied mathematics in secondary level.
Describe the aims and activities of ICMI.
OR
State the aims and objectives of IMU.
Give critical appraisal on the issue "Popularization of mathematics education"
What is action research for teachers, and what are the challenges that teachers face when doing action research?
Group "C"2 X 10 marks = 20
Long answer questions
Sketch the global trends that observed in mathematics education at basic level with respect to teaching/learning methods, materials and evaluation system.
OR
State Intuitionist's view in the research. Compare the Empiricist's and Constructionist's views in the research of mathematics education.
What are the issues and problems in teaching geometry for 21st century?
Why is Ethno-mathematics an issue in mathematics education?
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