1.       Course Description

Strategy or technique to teach abstract concept of mathematics falls under the area of teaching mathematics. It is possible only when new knowledge be connected to the prior knowledge/experience of child. With the aphorism of great mathematician Whitehead “Every child should experience the joy of discovery” mathematics education was initially considered as the didactics or pedagogy of mathematics. Later with the work of great psychologists Piaget, Bruner and others the discovery (research part) in teaching has been added and mathematics education deveoped into an extensive field of study like philosophies, learning theories, material construction, methods and stratgies of teaching, art of testing as well as technique of supervision in mathematics.

2. General Objectives

The general objectives of this course are as follows:

  • To enable the students differentiate between mathematics and mathematics education in terms of philosophy, nature, and structure.
  • To prepare the students to explicate learning theories and use them in designing instruction in order to teach secondary level mathematics.
  • To enable the students to classify objectives of different domains: cognitive, psychomotor, and affective.
  • To empower students to appraise critically the strong and weak aspects of curriculum, textbooks, and teacher guide (TG) of school mathematics.
  • To help the students to discover learning difficulties of learners and prepare different instructional strategies using different instructional materials to teach a particular content of secondary level mathematics.
  • To enable the students to analyze different instructional strategies supported by different school of learning theories.
  •  To enable the students to prepare different levels of instructional planning.
  • To help students to formulate questions of different domains: cognitive, affective and psychomotor.
  • To enable the students to supervise the classroom performance and suggest necessary action for the betterment of teaching performance.
Specific objectives

Unit

Contents

I

Unit 1: Philosophies of Mathematics and Mathematics Education               (14) 

1.1 Introduction of Maths and Math-education

1.2 Different philosophies of Mathematics

1.3 Different philosophies of Math-education

1.4 Nature of Maths and Math-education

1.5 Broader goal of Math-education

1.6 Principles of teaching and learning

1.7 Historical background of Maths and Math-education

II

Unit II:  Different Learning Theories      (14)

2.1 Comparison among behaviorist, cognitivist, and constuctivist learning theories

2.2 Basic principles of different learning theories

2.3 Piaget’s theory of cognitive stages of learning and its implication

2.4 Bruner’s stages of learning and its implication

2.5 Dienes’s theory of stages of learning and its implication

2.6 Gagne’s types of learning and its implication

2.7 Ausubel’s theory of learning and its implication

2.8 van Hiele’s stages of learning theory and its implication

2.9 Vygotsky’s stages of intellectual development  and its implication

2.10 Relation and differences among different learning theories

 

III

Unit III: Formulation of Instructional objectives                                (10)

3.1 Introduction objectives of mathematics of secondary level

3.2 Relation between aims, goals and objectives

3.3 Classification of objectives of different domains

 3.3.1 Bloom’s Taxonomy and application

3.3.2 Hoffer’s Taxonomy and application

3.3.3Krathwool’s Taxonomy and application

3.3.4 Interpersonal skill

3.4 Construction of different types of objectives 

IV

Unit IV: Curriculum and curricular materials                                        (10  Th+ 12 Pr)

4.1 Elements of curriculum 

4.2 Different International reform moments 

4.3 Process of curriculum development

4.4 Causes of curriculum change

4.5 Study of PSSM’s curriculum

4.6  Overview of school level curriculum of Nepal

4.7Schematic chart of school level Maths contents

4.8 Appraisal of curriculum, textbook, and TG

V

Unit V: Model of Instructional Strategies     (16)

5.1 Problem of Instruction (Understanding, Assimilation, Permanence, Transfer)

5.2    Learning disabilities in students

5.3  Individual difference caused by multiple intelligence

5.4    Classroom diversity: Gender, culture, language etc

5.5       Mathematical anxiety in students

5.6 Pedagogy and andragogy for teaching maths

5.7 Comparison among different pedagogies 

5.8 Comparison among different types of questions required in different pedagogies

VI

Unit VI: Instructional Materials     (5Th + 20 Pr)

6.1     Introduction and rationale of using instructional materials

6.2      Classification of materials (concrete, manipulative, electronic calculator, A/V  and printed materials and virtual materials

6.3       Mathematics Laboratory (on-task, off-task)

6.4       Preparation and development of materials

6.5       Use of textbook

VII

Unit VII: Instructional Planning     (8 Th + 16 Pr)

7.1 Introduction

7.2 Different planning at school

7.2.1 Annual Planning

7.2.2 Unit Planning

7.2.3 Models of Lesson Plans (Behaviorist, cognitivist, constructivist)

7.3 ) Preparation of Modules (Teaching, Learning, Training)

VIII

Unit VIII: Evaluation                     (8 Th + 12Pr)

8.1  Introduction

8.2 Measurement and Evaluation

8.2.1 Types of measurement

8.2.2 Types of Evaluation

8.2.3Difference in measurement and evaluation

8.2.4 Comparison between examination and evaluation

8.2.5Comparison among Formative/ Summative evaluation & Diagnostic test

8.3 Types of Examination in Practice

8.4 Prevention and remediation Strategies

8.5 Reliability and Validity of Test

8.6 Rehabilitation work for at-risk

IX

Unit IX: Supervision                                    (5)

9.1 Need of supervision

9.2 Techniques of supervision

9.3 Use of supervision techniques to improve classroom teaching

9.4 Rating of teacher’s teaching using different scales/Tools (ACI, FIAC, general observation form)

X

Unit 10: Teaching Contents of Secondary Level                            (30)

10.1 Components of Classroom management

10.1.1 Physical

10.1.2 Discipline

10.1.3 Administration

10.1.4 Classroom Practice

10.2  Introduction to motivational skills

10.2.1 Intrinsic and extrinsic motivation

10.2.2 Application of above motivation for the problem of instruction

10.3 Enrichment mathematics instruction: Teaching for concepts & construction, discovering relation, problem solving, theorem proving)

10.4  Teaching secondary level Maths contents

10.4.1 Compulsory mathematics IX-X (set, arithmetic, mensuration, algebra, geometry, trigonometry, statistics, probability)

10.4.2 Optional Mathematics IX-X (Algebra, matrix, co-ordinate geometry, trigonometry, vector, transformation, statistics)

10.4.3 Mathematics XI-XII (set, linear algebra, trigonometry,  co-ordinate geometry, calculus, vectors, statistics and  probability

 

Instructional Techniques

Because of the theoretical as well as practical nature of this course there is a need to inculcate the content knowledge/skill of teaching mathematics. To provide hands-on experience there is need of student-centered teaching,  like problem solving,  presentation and group discussions, project. Regular assignment will be main instructional techniques. Depending on the nature of the teaching items, the following techniques/methods will be used as general instructional techniques separately or in eclectic form.

4.1.General Instructional Techniques

·         Expository techniques followed by Problem Solving

·         Discussion, Demonstration and Inquiry

·         Presentation and group discussion

·         Eclectic techniques

4.2.  Specific Instructional Techniques

Unit

Chapter

Instructional techniques

I

Philosophies of Mathematics and Mathematics Education         

Expository, Discussion and presentation

II

Different Learning Theories   

Expository, Discussion and presentation

III

Formulation of Instructional objective

Expository, Discussion and presentation

IV

Curriculum and curriculum materials

Project work, Presentation

V

Model of Instructional Strategies

Expository, Discussion and presentation

VI

Instructional Materials                   

Project work, Home assignment

VII

Instructional Planning

Class work, project work and assignment

VIII

Evaluation                               

Project work, presentation and discussion

IX

Supervision                                 

Expository, Discussion and presentation

X

Teaching Contents of Secondary Level                

Expository, Discussion and presentation