This document discusses the principles of curriculum development in mathematics. It defines curriculum as a plan directing content and delivery of a mathematics learning program, including goals, content domains, learning philosophies, and standards. It discusses two key stages in curriculum construction: selection of content based on principles like aims of education, utility, flexibility; and organization of content through logical and topical arrangements from easy to difficult. The document emphasizes that curriculum frameworks should provide structure to content domains and cognitive processes, and establish a pedagogical approach that reflects how students learn for deep understanding.

1. Seminar I

2. 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
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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 4

5. 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. 6
Source of Goals
Society/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… 7

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.
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9. Principle of construction
Two stages are important in the
Curriculum construction
• Selection of the curriculum
• Organization of the curriculum
material
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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…10

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…
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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…
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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…
13

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…
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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…
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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
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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…
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18. • 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.
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19. 2. Organization of Curriculum
Good 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…
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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.
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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.
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22. 22
Providing Structure
Content
Domains
Cognitive
Processes

23. Content Domains
(Mathematics Strands)
• Pattern, Relationships & Functions:
• Pattern
• Variables & Change
• Geometry & Measurement:
• Shape
• Shape Relationship
• Positions
• Measurement
Cont…
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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…
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25. • Numerical, Algebraic Operations &
Analytical Thinking:
• Operations & their properties.
• Algebraic & Analytic thinking.
• Probability & Discrete Mathematics:
• Probability.
• Discrete Mathematics.
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26. 26
Interconnected Content Domains &
Cognitive Processes
Content
Domains
Concepts
Relationships
Procedure
Facts

27. 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
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