Math Ed525: Trends in Mathematics Education

Math Ed525 Overview

Browse the course units below.

Course

Introduction

Unit 1

ME at School

Unit 2

Three Areas

Unit 3

Applied Mathematics

Unit 4

Conferences

Unit 5

Issues in ME

Instructional Techniques

& Evaluation

Test

MCQ

Old Questions

MCQ

Trends in Mathematics Education

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:

1. 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.
2. To enable them to sketch the developmental trends, reform and teaching/learning issues and problems in three basic areas of school mathematics.
3. To have the students elucidate the trends how the concept of applied mathematics changes with time (This objective needs rewriting).
4. 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.
5. 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.
6. To provide them with historical and modern trends of knowledge observed in the area of research in mathematics education.

Unit I: Mathematics Education at School and Tertiary Levels (12 hrs)

1. Discuss briefly the roles of philosophy and learning theory to trace the trends in ME.
2. Sketch global trends of ME at different levels with respect to curriculum, content, methods and materials, evaluation system, research, and sociological components.

1. Introduction
2. TME at the basic level
3. TME at the secondary level
4. TME at the tertiary level

Unit II: Trends in the Three Basic Areas of School Mathematics (9 hrs)

1. Sketch trends of the three basic areas of school mathematics.
2. Review the trends of school geometry, arithmetic and algebra (with reference to curriculum, content, methods, materials and evaluation system).
3. Give comprehensive views on the issues and problems of teaching/learning school mathematics.

1. Introduction
2. Reforms in Geometry
3. Reforms in Arithmetic
4. Reform in Algebra
5. Issues and problems in the T/L the three basic areas of mathematics for the 21^st century

Unit III: Educational Implications of Applied Mathematics (6 hrs)

1. Explain the trends showing how the concept of applied mathematics changes with time.
2. Clarify the reason for teaching the application of mathematics at different levels of schooling.
3. State the issues and problems of applied mathematics in mathematics education.
4. Analyze the impact of applied mathematics on mathematics education.
5. Use practical knowledge and skills in the area of mathematical modeling.

1. Introduction
2. Rationale to teach application of mathematics
3. Trends in teaching applied mathematics
4. Issues and problems of T/L applied mathematics
5. The impact of T/L applied mathematics
6. Some examples of mathematical modeling

Unit IV: Mathematics Education Conferences (6 hrs)

1. Sketch the different trends of Union, Commission, Study groups, Conferences, and Olympiads.
2. Describe the aims, activities and responsibilities of IMU and ICMI.
3. Describe the achievements of different international congresses (ICMEs).
4. Explain different formalities (selection of Jury, conditions of participation, and topics asked) in IMO.
5. Describe the aims and activities of professional organizations of mathematics in Nepal.

1. International Mathematical Union (IMU)
2. International Commission on Mathematical Instruction (ICMI)
3. International Congress on Mathematical Education (ICME)
4. Organization of ICME in different countries
5. International Mathematical Olympiad (IMO)
6. Nepalese mathematical organizations (NMO)

Unit V: Issues in Mathematics Education (9 hrs)

1. Give critical comments on the social issues and problem in T/L mathematics.
2. Appraise the role of culture in T/L mathematics.
3. Discuss on the assessment system of mathematics education.
4. Give critical appraisal to address different issues (popularization, gender differences, ethnomathematics, and inclusion) in mathematics education.
5. Give critical comments on tensions occurring while dealing with mathematics education for the stakeholders of the 21^st century.

1. Social issues and problems in T/L mathematics education
2. Cultural role in T/L mathematics education
3. Issues and problems in students' evaluation system
4. Challenges of T/L mathematics in the 21^st century
5. Popularization of mathematics education
6. Gender difference in mathematics education
7. Ethnomathematics
8. Individual difference of students
9. Special needs of students

Content Details: Unit 5

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	20 marks
Total	60 marks

Test your understanding

1. Unit 1
2. Unit 2
3. Unit 3
4. Unit 4
5. Unit 5

Old Questions

TRIBHUVAN UNIVERSITY
Faculty of Education
Year

Master / 2ⁿᵈ Semester Time: 3 hrs.
Course Title: Trends in Mathematics EducationFull Marks: 60
Course Code: Math Ed. 525Pass Marks: 30

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

1. Discuss on the trends in mathematics education in terms of methods and materials at primary level.
2. Describe the major reforms in the instruction of school geometry with special reference to aim, content and method.
3. Compare and contrast between pure and applied mathematics with suitable examples.
4. Sketch the trends how and why ICMI was established by mathematicians.
5. Present strong evidences in regard to role of mathematical Olympiads for the popularization of mathematics.
6. Explain the trends in mathematics education research.

Group "C"2 X 10 marks = 20
Long answer questions

7. What trends do you sketch in mathematics education at university level?
8. Discuss about the three traditions of research in mathematics education with suitable examples.

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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 "A"10 X 1 marks =10

1. Which one of the following persons attacks more severely on the application of behaviorism and mastery of learning to math education?
   1. Stanely Erhwanger
   2. Hans Freudenthal
   3. Newton
   4. Bloom
2. Which one of the following is considered as the lowest level of strategy for mathematical computation?
   1. Counting strategy
   2. Additive strategy
   3. Multiplicative strategy
   4. Thinking strategy
3. Which one of the following is not a synthetic geometry?
   1. Euelidean
   2. Projective
   3. Co-ordinate
   4. Topology
4. After development of which geometry Euelidean geometry is easier?
   1. Projective
   2. Transformational
   3. Elliptical
   4. Affine
5. What is philosophy behind using applied mathematics?
   1. Practical aspects are interesting
   2. Practical aspects are easier to understand
   3. Practical course let students get hands - on experience
   4. Students learn through mistake
6. What is the full form of ST in connection to ICME?
   1. Study Team
   2. Survey Team
   3. Study technology
   4. Survey technology
7. Which one of the following theory is supported by adult learning theory?
   1. Ausubel's scheme theory
   2. Piaget's stage theory
   3. Gagne's information theory
   4. Lave's situated learning theory
8. Which one of the following is not the boundary to be dwindled in mathematics education in order to harmonized society?
   1. Between boys and girls
   2. Between social groups
   3. Between slow and gifted students
   4. Between haves and have not
9. When the term popularization of mathematics was used for the first time?
   1. 1983 AD
   2. 1986 AD
   3. 1989 AD
   4. 1990 AD
10. Which of the following is not component of research endeavors?
    1. Enquiry
    2. Evidence
    3. Theory
    4. None

Group "B"6 X 5 marks =30
Short answer questions

1. Sketch the trends in contents of mathematics education at college level.
2. Give the brief sketch of the development of Arithmetic from palpable phase of Arithmetization phase.
   OR
   
3. State the major reforms in the instruction of school Algebra with reference to its teaching methods and materials.
4. Write four different definitions of applied mathematics and compare them with suitable diagram.
5. Write a summary table showing the data, the place and major issues raised in the last two ICMES.
6. 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.
7. Sketch the trends in mathematics education from 1950 Ad to date.

Group "C"2 X 10 marks = 20
Long answer questions

7. 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.
8. Discuss Empiricist, Intuitionist and constructivist views in research of mathematics education with suitable examples.

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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 "A"10 X 1 marks =10

1. Which of the followings was not an issue for second wave reform in Mathematics Education?
   1. Abstract verses concrete
   2. Gifted verses slow learners
   3. Global verses local
   4. Tradition verses modernity
2. Which of the following course managed at higher level of mathematics education?
   1. General course
   2. Technical course
   3. Skill course
   4. All of the Above
3. The developmental trends of Algebra does not consist of
   1. Rhetorical algebra
   2. Syncopated algebra
   3. Symbolic algebra
   4. Linear algebra
4. Euclidean theorems’ proof became easier by the development of ......
   1. Projective Geometry
   2. Transformation Geometry
   3. Euclidean Geometry
   4. Elliptic Geometry
5. “Students learn through mistakes” is a philosophy of ......
   1. Pure mathematics
   2. Applied mathematics
   3. Abstract mathematics
   4. Simple mathematics
6. Which is the correct order of organization of last three international conferences of ICME in different countries?
   1. Germany, Mexico, South Korea
   2. Germany, South Korea, Mexico
   3. Mexico, Germany, South Korea
   4. Mexico, South Korea, Germany
7. "Mathematics for All" is a slogan which was set in ......
   1. ICME VI (1988)
   2. ICME VII (1992)
   3. ICME VIII (1996)
   4. ICME IX (2000)
8. Which of the following is study about structure?
   1. Algebra
   2. Number theory
   3. Solid geometry
   4. Graph theory
9. Which of the following is not the cause of individual difference in learning?
   1. Learning habits
   2. Family environment
   3. Cultural background
   4. Educational achievements
10. Which one of the following is not an aim of applied research?
    1. Advocacy of knowledge
    2. Adaptation of knowledge
    3. Evaluation of knowledge
    4. Extension of new knowledge

Group "B"6 X 5 marks =30
Short answer questions

1. Discuss the problems and challenges of Adult and Continuous Education System.
2. Describe the major reforms in the instruction of school geometry with respect to its teaching methods and materials.
3. Justify the rationale to teach application of mathematics.
4. State the relationship between ICMI and ICME. Write down the objectives and activities of IMU?
5. Write down your views on popularization of mathematics education. Illustrate its major issues in the context of Nepal.
   
   OR
   
   Explain the issues and problems in regard to teachers’ judgment in students’ mathematical works.
6. Compare Empiricist’s and Constructivist’s views with reference to researches in mathematics education.
   
   OR
   
   How is the importance of Action Research in classroom teaching/learning practices? Illustrate its different stages.

Group "C"2 X 10 marks = 20
Long answer questions

7. What are the issues and problems in use of technology in teaching/learning mathematics in Nepalese schools? Describe them with your own observation.
   
   OR
   
   Identify the issues and problems in teaching/learning Algebra in schools for 21st Century.
8. How is the trend that you have found in goals and content of mathematics education at pre-primary and primary levels?
   
   Explain this trend with the suitable examples from your own experience.

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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 "A"10 X 1 marks =10

1. Whose statement is this "Every child should experience the joy of discovery"?
   1. Piaget
   2. Vygotsky
   3. Whitehead
   4. Bruner
2. Which of the following was not an issue for second wave reform in Mathematics Education?
   1. Abstract verses concrete
   2. Tradition verses modernity
   3. Global verses local
   4. Gifted verses slow learners
3. Which one of the following was established first?
   1. IMU
   2. ICMI
   3. IMO
   4. ICME
4. Which Mathematics belongs to the philosophy of "Students learn through mistakes"?
   1. Pure mathematics
   2. Applied mathematics
   3. Abstract mathematics
   4. Simple mathematics
5. Which is not an issue for popularization of mathematics?
   1. Gifted child
   2. Exceptional child
   3. Gender differences
   4. Language
6. In which country the 13th ICME was organized?
   1. Mexico
   2. South Korea
   3. Germany
   4. China
7. Which of the following is not included in IMO competition?
   1. Algebra
   2. Solid geometry
   3. Number theory
   4. Graph theory
8. Which of the following statement is true?
   1. Geometry as a way of thinking
   2. Geometry is a visual representation
   3. Geometry as a meeting point of theory and practice
   4. All of above
9. Which geometry development made easy to prove Euclidean theories?
   1. Elliptical Geometry
   2. Hyperbolic Geometry
   3. Transformation Geometry
   4. Projective Geometry
10. Which of the following is not an aim of applied research?
    1. Extension of new knowledge
    2. Adaptation of knowledge
    3. Evaluation of knowledge
    4. Advocacy of knowledge

Group "B"6 X 5 marks =30
Short answer questions

1. Discuss the different types of mathematics courses provided at University level.
2. Describe the major reforms in the instruction of School Geometry with reference to its teaching/learning methods and materials.
3. Assess the problems of teaching Applied Mathematics in our context.
4. Introduce IMU and write down its major objectives and activities.
5. Explain the issues and problems in regard to Teachers’ Judgment in students’ mathematical tasks.
   
   OR
   
   State the major problems appeared in Popularization of Mathematics Education in the context of Nepal.
6. Why do academic experts prefer Action Research to improve classroom teaching/learning situation? Illustrate its different stages.
   
   OR
   
   State Intuitionist’s view in the research. Compare the Empiricist’s and Constructivist’s views in the researches of Mathematics Education.

Group "C"2 X 10 marks = 20
Long answer questions

7. State the importance of "Adult and Continuous Education System".
   Discuss its problems and challenges in Nepalese context.
   
   OR
   How are the trends of teaching methods and materials of mathematics at primary levels? Evaluate with own experiences.
8. Describe the trends of issues and problems appeared in teaching/learning Algebra at school level for the 21st Century.

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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 "A"10 X 1 marks =10

1. Which theory of learning believes ‘Learning is a product of self-organization’?
   1. Constructivism
   2. Behaviorism
   3. Connectivism
   4. Cognitivism
2. Who solved Cubic and Quadratic equations?
   1. Galois
   2. Descartes
   3. Cardano
   4. Viete
3. Which property will be lost while transforming “Shearing”?
   1. Parallelism
   2. Angle measure
   3. Distance measure
   4. Straightness
4. Which one from the following is included in IMO curriculum?
   1. Geometry
   2. Calculus
   3. Algebra
   4. Number theory
5. Which one from the following is not the importance of applied mathematics?
   1. To serve as a service subject
   2. To motivate learners towards mathematics
   3. To develop mathematical model
   4. To develop abstraction in mathematics
6. What is the assessment pattern (formative and summative) according to school curriculum at basic level?
   1. 30% formative - 70% summative
   2. 25% formative - 75% summative
   3. 50% formative - 50% summative
   4. 40% formative - 60% summative
7. Which one from the following is the main objective of IMU?
   1. Developing network of mathematician in international level
   2. To conduct research for the promotion of the mathematics education
   3. Journal publication
   4. To monitor and help study group prepared for ICME
8. When did ICMI established for the first time?
   1. 1908
   2. 1914
   3. 1920
   4. 1951
9. What is the source of knowledge construction in empiricist view?
   1. Through social interaction
   2. Through mental schema
   3. Through sense organ
   4. Through networking
10. What is the ontology in Qualitative research?
    1. Reality is single and objective
    2. Reality is undefine
    3. Reality is multiple and subjective
    4. None of the above

Group "B"6 X 5 marks =30
Short answer questions

1. How do we trace the philosophical changes in mathematics education? Explain in brief.
2. Explain the development of arithmetic with reference to national curriculum of mathematics at school level.
3. Establish the relationship logically between applied mathematics and mathematical modeling with example.
4. Argue for the 'issues on assessment system' at school level mathematics with example.
5. 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.
6. 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

7. Sketch the trends of basic level of mathematics education with respect to content, method and assessment system with example according to nation level curriculum.
   
8. 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.

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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 "A"10 X 1 marks =10

1. The recent trends in role of primary level mathematics teachers belongs to:
   1. Freedom of teachers in teaching
   2. Polyvalence of teachers
   3. Teachers’ teaching situation
   4. All of the above
2. Which was not an issue for Second wave reform in Mathematics Education?
   1. Inductive or deductive
   2. Enrichment or acceleration
   3. Theory or practice
   4. Intuition or formalization
3. The developmental trends of Algebra doesn’t consist of:
   1. Rhetorical algebra
   2. Abstract algebra
   3. Syncopated algebra
   4. Symbolic algebra
4. The statement “Students learn through mistakes” belongs to:
   1. Applied mathematics
   2. Abstract mathematics
   3. Theoretical mathematics
   4. Analytical mathematics
5. Which is not an issue for popularization of mathematics?
   1. Teaching/learning strategy
   2. Science and technology
   3. Genius learner
   4. War
6. Which one of the followings is not in Study group of ICMI?
   1. International Mathematical Union
   2. World Federation of National Maths Competition
   3. Psychology of Maths Education
   4. History of Pedagogy of Maths
7. Which of the following is not included in IMO competition?
   1. Graph theory
   2. Solid geometry
   3. Number theory
   4. Algebra
8. The individual difference in learning is not caused by
   1. Learning habits
   2. Family environment
   3. Cultural background
   4. Learning achievements
9. Which of the following is not an aim of Applied research?
   1. Extension of new knowledge
   2. Adaptation of knowledge
   3. Evaluation of knowledge
   4. Advocacy of knowledge
10. Which is not a research component of Mathematics Education?
    1. Enquiry
    2. Evidence
    3. Theory
    4. Practice

Group "B"6 X 5 marks =30
Short answer questions

1. Discuss on trends of using different teaching methods while teaching Mathematics at primary level.
2. How is the developmental trends of Algebra? Describe its different developmental phases.
3. Assess the problems of teaching/learning Applied Mathematics in Nepalese context.
4. State the relationship between ICMI and ICME. Write down the major activities of ICMI.
5. What do you understand by ‘Individual difference in learning Mathematics’? Write down its causes.
   
   OR
   
   Why ‘social context’ is considered as an issue in Mathematics Education? Discuss on it with examples.
6. Compare Empiricist’s and Constructivist’s views with reference to researches in Mathematics Education.
   
   OR
   
   State the importance of Action Research in classroom teaching/learning practices. Illustrate its different stages.

Group "C"2 X 10 marks = 20
Long answer questions

7. State two perspectives of using methods and media in teaching/learning (T/L) mathematics. Trace the trends of T/L mathematics by using different methods and media.
8. Critically examine the issues and problems of teaching and assessment in mathematics in the context of Nepal.
   
   OR
   
   Describe the trends of issues and problems appeared in teaching/learning school level Geometry for 21st Century.

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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 "A"10 X 1 marks =10

1. Which one philosophy doesn't belong to "Three school-of-thoughts"?
   1. Behaviorist
   2. Curricularist
   3. Constructivist
   4. Cognitivist
2. The statement “Students learn through mistakes” belongs to:
   1. Analytical mathematics
   2. Abstract mathematics
   3. Applied mathematics
   4. Theoretical mathematics
3. Why is teaching of Applied Mathematics necessary for?
   1. cultural reason
   2. motivation
   3. as a service subject
   4. Above all
4. Which of the following is not included in IMO competition?
   1. Graph Theory and Combination
   2. Number theory
   3. Solid Geometry
   4. Algebra
5. Which one of the following is not a Study group of ICMI?
   1. Psychology of Maths Education
   2. International Mathematical Union
   3. History of Pedagogy of Maths
   4. World Federation of National Maths Competition
6. Which is not an issue for popularization of mathematics?
   1. Genius learner
   2. Science and technology
   3. Teaching/learning strategy
   4. War
7. Which of the followings is a component of Ethno-mathematics?
   1. Institutional Mathematics
   2. Mathematical modeling
   3. Cultural anthropology
   4. Above all
8. The individual difference in learning is not caused by
   1. Learning habits
   2. Family environment
   3. Learning achievements
   4. Cultural background
9. Which is not a research component of Mathematics Education?
   1. Enquiry
   2. Evidence
   3. Theory
   4. Practice
10. Which of the following is the most recent approach of researches in Mathematics Education?
    1. Social and Cultural
    2. Cognitive
    3. Socio-psychological
    4. Empirical

Group "B"6 X 5 marks =30
Short answer questions

1. Describe the trends in four areas of courses of Mathematics Education provided at College level.
2. State the trends of major reforms observed in teaching/learning 'School Algebra' with reference to its 'Evaluation system'.
3. How is the recent trends of 'Applied Mathematics'? Compare pure and Applied Mathematics with suitable examples.
4. Name the different Nepalese Mathematical Organizations and write down each one's mathematical activities.
5. 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.
6. 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

7. 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.
8. 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.

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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 "A"10 X 1 marks =10

1. Which one of the following does not belong to organization of the content of Secondary level Mathematics?
   1. Internal integration
   2. External integration
   3. Horizontal integration
   4. Vertical integration
2. What are different types of courses provisioned at College level?
   1. General courses
   2. Skill courses
   3. Technical courses
   4. All of above
3. The developmental trends of Algebra does not consist of:
   1. Linear algebra
   2. Symbolic algebra
   3. Syncopated algebra
   4. Rhetorical algebra
4. Which Geometry had made easier the proofs of Euclidean theorems?
   1. Projective Geometry
   2. Transformation Geometry
   3. Euclidean Geometry
   4. Elliptic Geometry
5. Why is teaching Applied Mathematics necessary for?
   1. Motivation
   2. Cultural reason
   3. Service subject
   4. All of above
6. Which is the correct order of organization of last three international conferences of ICME in different countries?
   1. Germany, China, South Korea
   2. South Korea, Germany, China
   3. China, Germany, South Korea
   4. China, South Korea, Germany
7. Which of the following is not included in IMO competition?
   1. Algebra
   2. Number theory
   3. Solid geometry
   4. Graph theory
8. The individual difference in learning is not caused by
   1. Educational achievements
   2. Family environment
   3. Cultural background
   4. Learning habits
9. Which of the following is a component of Ethno-mathematics?
   1. Cultural anthropology
   2. Mathematical modeling
   3. Institutional mathematics
   4. All of the above
10. Which of the following is the most recent approach of carrying out researches in mathematics education?
    1. Cognitive approach
    2. Empirical approach
    3. Social and cultural approach
    4. Psychological approach

Group "B"6 X 5 marks =30
Short answer questions

1. What trends do you sketch in use of different materials for teaching Mathematics at secondary level? Describe briefly.
2. Explain shortly the issues and problems in regard to content and teaching/learning system of Algebra for 21st century.
3. Justify the rationale to teach Application of Mathematics.
4. State the relationship between ICMI and ICME. Write down the major activities of ICMI.
5. State the contribution of International Mathematical Olympiad (IMO) in order to popularize the Mathematics. Write down few points about the importance of IMO.
   
   OR
   
   Give critical appraisals to address the issues of ethno-mathematics in the context of Nepal.
6. Describe the three components of research in Mathematics Education with suitable examples.
   
   OR
   
   What are the major areas of research in mathematics education? Describe them briefly.

Group "C"2 X 10 marks = 20
Long answer questions

7. How are the trends of setting goals and contents of Mathematics Education at primary level? Explain the trends with suitable examples.
   
   OR
   
   Assess the recent trends of use of different methods while teaching Mathematics at University level. Also link it with our real classroom scenario.
8. What are the issues and problems of using technology in teaching/learning Mathematics especially in Nepalese schools? Describe them with your observation.

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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 "A"10 X 1 marks =10

1. Who is the proponent of “Advance Organizer”?
   1. Ausubel
   2. Dienes
   3. Gagne
   4. Skimp
2. The theme “Adult and Continuing Education in Mathematics Education” was emerged for the first time at
   1. Lyon Congress
   2. Adelaide Congress
   3. Seoul Congress
   4. Karlsruhe Congress
3. Which organization gives the two awards: Hans Freudenthal and Felix Klein in mathematics education?
   1. ICM
   2. ICME
   3. ICMI
   4. IMO
4. Who coined the word “Ethno-mathematics” at first?
   1. Orey
   2. Ernest
   3. Cobb
   4. Ambrosio
5. The IQ level of mentally defective child is
   1. Below 70
   2. Below 80
   3. Below 60
   4. Above 140
6. The research idea of concentrating in the experience of “Gifted practitioners” is connected to:
   1. Empiricist’s view
   2. Teacher’s view
   3. Intuitionist’s view
   4. All of above
7. The first IMO was held in ......
   1. England, 1950
   2. Romania, 1959
   3. Romania, 1960
   4. Chiba, 1980
8. Which one of following is a study Group of ICMI?
   1. IMU
   2. ICSU
   3. PME
   4. EC
9. Which of the following view favors the experimental studies?
   1. Intuitionist’s view
   2. Empiricist’s view
   3. Teacher’s view
   4. None of the above
10. In an intervention based action research process, which of following is usually recommended sequence?
    1. Plan, Act, Observe and Reflect
    2. Observe, Plan, Act, and Reflect
    3. Reflect, Plan, Act, and Observe
    4. Observe, Act, Reflect and Plan

Group "B"6 X 5 marks =30
Short answer questions

1. 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.
2. Discuss briefly the reforms in school algebra.
3. What is applied mathematics? Analyze the trends in teaching of applied mathematics in secondary level.
4. Describe the aims and activities of ICMI.
   OR
   State the aims and objectives of IMU.
5. Give critical appraisal on the issue "Popularization of mathematics education"
6. 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

7. 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.
8. 1. What are the issues and problems in teaching geometry for 21st century?
   2. Why is Ethno-mathematics an issue in mathematics education?

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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 "A"10 X 1 marks =10

1. Who is the founder of connectivism?
   1. Ausubel
   2. Gardner
   3. Vygotsky
   4. Georgs Siemens
2. Which of the followings is not the family of higher algebra?
   1. Linear Algebra
   2. Boolean Algebra
   3. Rhetoric Algebra
   4. Vector Algebra
3. Who believes that “Learning is the product of self-organization”?
   1. Constructivist
   2. Behaviourist
   3. Cognitivist
   4. Socialist
4. When the term popularization of mathematics was used for the first time?
   1. 1983 AD
   2. 1989 AD
   3. 1986 AD
   4. 1990 AD
5. Which one of the following is not a type of qualitative research?
   1. Ethnography
   2. Case study
   3. Survey
   4. Narrative inquiry
6. Areas of research in mathematics education is taken as:
   1. Research on curricula, methods and materials
   2. Research on learning and the learner
   3. Research on teaching and the teacher
   4. All of the above
7. What are the major ways of integrating mathematics curriculum?
   1. Internal
   2. External
   3. Vertical
   4. Axial
8. “Students learn through mistakes” is a philosophy of...
   1. Applied mathematics
   2. Pure mathematics
   3. Abstract mathematics
   4. All of the above
9. Which one of the following stands in the highest position?
   1. ICM
   2. IMU
   3. ICME
   4. IMO
10. Which one of the following is not the purpose of modeling?
    1. To explain
    2. To explore
    3. To generalize
    4. To predict

Group "B"6 X 5 marks =30
Short answer questions

1. Sketch the Trends in contents of mathematics education at secondary and higher secondary level.
2. Write the major reform in teaching school algebra with reference to its teaching methods and materials.
3. Describe briefly the major reforms in the instruction of school Geometry.
   
   OR
   
   State and compare ethno-mathematics with global mathematics.
4. List out the aims and objectives of ICMI.
   
   OR
   
   Sketch the relationship between ICMI and ICME. Also write the importance of ICME in the development of mathematics.
5. Why do the social context being an issue in mathematics education? Discuss with example.
6. Explain the recent trends in research of mathematics education.

Group "C"2 X 10 marks = 20
Long answer questions

7. Discuss about the three traditions of research in mathematics education with suitable examples.
8. Discuss the recent trends of qualitative and quantitative research in mathematics education with their major types.
   
   OR
   
   How are the trends of teaching methods and materials of mathematics at primary level? Explain them with own experience and examples.