R. Raj Kumar,Master of Education,

Department of Education,Periyar University,

Salem – 11,2013-14

Pedagogy of Mathematics

Seminar I

Mathematics Curriculum

Characteristics - Principles - Framing of curriculum in

mathematics

3

Curriculum• Not just a syllabus or textbook• Includes

• Aims• Content• Methods• Assessment procedures

• Depends on one’s position• Plan• Experience

• A linear path through a multi-dimensional domain

4

What is a curriculum?• A plan of action directing the content and

delivery of a program of mathematics learning for a specified group of students

• This plan consists of an articulated set of statements that provide:• general goals for the plan• a structure of content domains and cognitive

processes to be developed• a philosophy concerning the general conditions of

learning expected• a listing of general standards and specific outcomes of

learning related to levels of schooling germane to the population for which the curriculum is intended

5

Curriculum Definition and Instruction

• "Curriculum is 'a system of planned actions for instruction' and instruction is the 'system for putting the plans into action.” (MacDonald, 1965)

• "Basically the curriculum is what happens to children in school as a result of what teachers do." (Kansas, 1958)

• "By 'curriculum' we mean the planned experiences offered to the learner under the guidance of the school.” (Wheeler, 1967)

6

Source of GoalsSociety/Workforce

Discipline

Psychology

Mathematics Education

Assessments

7

Characteristics• It should faster the growth of development of

attitude & skills required for maintaining a planned social order of democratic type.

• It should not be conceived but dynamic and forward looking, sample adequately both the scientific content and the abilities of the pupils to the developed. Should cater to the right use of leisure later on and should be related to the environment in which the children live.

Cont…

8

• It is tested & improved through research.• Mathematics helps to convey & clarify meaning. Its

language provides a powerful & concise means by which information may be organised, manipulated & communicated.

• Indeed the application of increasingly sophisticated mathematics in a growing range of economic, technical, scientific, social & other contexts has had a profound influence on the development of contemporary society.

9

Principle of construction

Two stages are important in the

Curriculum construction

• Selection of the curriculum

• Organization of the curriculum

material

10

1. Selection of the Curriculum

Curriculum has to be properly planned & to be

based on certain principles.

• Aims of Education & Objectivity:

• Life is complex. A curriculum should reflect the

complexible of life. In other words, informing the

curriculum one should take into consideration the

aims & objectives of Education.

Cont…

11

• Principles of utility:• It should be useful in everyday life.• It should be useful in the study of other subject.• It should have some vocational utility.• It should enable students to understands.

• Principles of Child Centeredness:• The curriculum should be framed according to

the actual needs, interests & capacities of the child. That means a curriculum must be child-centric as modern education is child-centered.

Cont…

12

• Principle of Disciplinary Values:• Teaching of maths disciplines the mind. The students

used to study certain puzzles & riddles which had no practical utility.

• In the words of Thorndike, “Teach nothing merely because of its disciplinary value but teach everything so as to get, what disciplinary value it does have”.

• Principles of civic & social needs:• The child develops in the Society. Modern Education

aims at both developments of the individuality of the child as well as the development of the society.

Cont…

13

• Principles of Culture Value:• Schools & Colleges are homes of Culture. So the

curriculum should be useful to understanding and

the develop & production the culture.

• Principle of Creativeness:• Education not only conserves that past experiences of

humanity but also helps in individual to develop his

innate potentialities.

Cont…

14

• Principles of community:• The social needs & the local needs of the learner

should be taken in to account while we construct the curriculum.

• It should be reflect the values of democracy, ethos and main concern of the country.

• Principle of flexibility/Elasticity:• Flexibility is an important parting curriculum

development.• It should given enough time & sufficient chance to

the students, to search their own examples & experiences from the surroundings.

Cont…

15

• Principle of Time:• Relative significance & importance of each

subject in the curriculum has to be judged and determined in the light of the time available in the timetable, which is regarded as the mirror of the school programme.

• Principle for utilization of leisure:• Principle of individual difference:• Principle of learning ability:• Principle of integration and correlation:

Cont…

16

• Principle of Need • Principle of sequencing• Principle of Continuity • Principle of Accuracy • Principle of Adequacy • Principle of Interest • Principle of Readiness • Principle of Meaningfulness• Principle of Continuous Evaluation

17

J.W.A, Young, guided following principles

• To exhibit most clearly & to the best advantages the mathematical type of thought.

• To bring out early the mathematical relationships that exist in the social organism & in the activities of modern life, & to exhibit how maths helps in solving their problems.

Cont…

• To help to a better understanding of the laws of nature.

• To give self skill in the actual perform of mathematical process so as to meet the future needs of the students.

• To allow the organization of the material into a homogenous whole, meeting the demands of the pedagogy.

18

19

2. Organization of CurriculumGood arrangement requires that,o Every topic should be divided into parts.o These parts should be graded according to

difficulty.o Each part should be introduced at a proper

stage.1. Psychological & logical arrangement.2. Topical & spiral arrangement.3. From easy to difficult.

Cont…

20

4. Principle of activity.

5. Principle of correlation.

6. Scope of Individual Teaching.

7. Voice of the teacher.

8. Child centered syllabus.

9. From imperial to rational.

10.From concrete to abstract.

21

Mathematics Curriculum Frame Work

What does the Frame work mean to me?• It is not only just the teacher learning what

the word mean, but the teacher being able to translate it into class room practices.

- Kathy Grzesiak• Frame work establishes some big ideas, it

talks about what we value in the community of mathematics.

- Elizabeth Jones.

22

Providing Structure

Content DomainsCognitiv

eProcesses

23

Content Domains (Mathematics Strands)

• Pattern, Relationships & Functions:• Pattern• Variables & Change

• Geometry & Measurement:• Shape • Shape Relationship• Positions• Measurement

Cont…

24

• Number sense & Numeration:• Concepts & properties of numbers.

• Representation & use of numbers.

• Number Relationships.

• Data Analysis & Statistics:• Collection, Organization & Presentation of Date.

• Description and Interpretation.

• Inference & Prediction.

Cont…

25

• Numerical, Algebraic Operations &

Analytical Thinking:• Operations & their properties.

• Algebraic & Analytic thinking.

• Probability & Discrete Mathematics:• Probability.

• Discrete Mathematics.

26

Interconnected Content Domains & Cognitive Processes

ContentDomains

Concepts

Relationships

Procedure

Facts

27

Pedagogical Framework• While the instructional implementation is a

partially separate matter, a broad statement of the boundaries and shape of the program should be included.

• “What you learn reflects how you learned it.”• Such a framework also reflects the

approaches and conditions for achieving “depth of understanding.”

28

Thank you