This presentation was prepared for orientation programme of Math teachers in Siddipet Division, Telangana, India.

1. A STUDY OF MATHEMATICS CURRICULUM
FOR
SCHOOL EDUCATION
SINCE LAST TWO DECADES
AND
ITS IMPLEMENTATION

2. WHY DO WE LEARN MATHEMATICS?
• Mathematics is the mother of all science.
• The world cannot move without Mathematics.
• Many Mathematical concepts, pattern, laws, etc. are observed in
the nature.
• Mathematics fulfils most of the human needs related to different
aspects of everyday life.
• Every person whatever he or she requires a knowledge of
Mathematics in day to day life for various purposes.

3. WHEN MATHEMATICS BEGIN?
• From early period when civilization begins man used
Mathematics for different purpose mainly for getting the answer
of ‘how many’, ‘how big’, ‘how far’, ‘how much’, etc. Counting and
symbol for number started from that period.
• Previously it was a misconception that Mathematics is required
only for being an Engineer, Mathematician or Scientist and hence
the subject was treated as a difficult subject by the society.

4. • And school student had a fear psychosis of the subject.
• But since last few decades to make the elementary education a
fundamental right for all children treatment of the subject was
made as far as possible learner friendly and relevant to child’s real
life situation.
• Accordingly all over the world Mathematics education in school
particularly at elementary stage has made a remarkable
reformation by reforming curriculum, renewing textbooks and
changing teaching-learning process.
WHEN MATHEMATICS BEGIN?

5. MATHEMATICS IN SCHOOL EDUCATION
PRE-INDEPENDENCE PERIOD
• At that period also a little amount of Arithmetic, money
transaction, a knowledge of Geometrical concepts and figures,
measurements, Zamindari accounts were there in those days of
school education.
• After coming British (in 1826) the traditional system soon made
away and British system of Schooling started in three stages-
primary, middle and high schools and took up measures for the
promotion of the indigenous system of education.

6. • At LP level: (1) Arithmetic Written and mental Arithmetic (2) Bazar
and Zamindari accounts and simple mensuration.
• At middle schools (ME/ MV) level: (1) Arithmetic (2) Theory of
Surveying (3) Bazar and Zamindari accounts (4) Handling of
money matters (5) Geometry and Mensuration.
• M.E. Madrasa and Sanskrit Middle School had a common
curriculum of study for Arithmetics/ Mathematics.
MATHEMATICS IN SCHOOL EDUCATION
PRE-INDEPENDENCE PERIOD

7. • After independence, Primary education act was passed in 1947 for
the 2nd time to introduce free, compulsory and universal primary
education in graded stage for the children up to the age 6 to 11
years.
• The Basic Education act came in 1954, the curriculum for primary
level was consists of Arithmetic, Mental Arithmetic, Accounts,
Jama Kharach (savings & expenditure), reading of clock.
MATHEMATICS IN SCHOOL EDUCATION
POST-INDEPENDENCE PERIOD

8. • The major reform in curriculum for all stages of school education
came after National Policy of School Education, 1968 as per the
report of the ‘Kothari’ commission.
• A common curriculum for class I to class X was prepared at
national level for adoption by all the states in the country with
adjustments according to local need. Then the 10+2+3 pattern
was adopted in the country.
• Mathematics and Science was made compulsory core subject at
Middle and Secondary stage.
MATHEMATICS IN SCHOOL EDUCATION
POST-INDEPENDENCE PERIOD

9. • General Mathematics was compulsory subject up to class X and at
Secondary level an advance Mathematics was there as optional
subject.
• General Mathematics comprises Arithmetic, Geometry (concept
and theory) a simple Algebra.
• Advance Mathematics mainly consists of integers, quadratic
equation, logarithm, coordinate geometry.
MATHEMATICS IN SCHOOL EDUCATION
POST-INDEPENDENCE PERIOD

10. • 1968 National Policy relates to universalization of elementary
education and eradication of adult illiteracy.
• But the system does not work much. There was huge number of
students who failed to achieve school final examination.
• Many dropped and failed in between the primary and middle
stage.
MATHEMATICS IN SCHOOL EDUCATION
POST-INDEPENDENCE PERIOD

11. NEW EDUCATION POLICY IN 1986
“Education will have to be streamlined to facilitate
modernization of production, services and infrastructure.
Besides, to enable the young people to develop
enterprisal ability, they must be exposed to challenges of
new ideas. Old concepts have to be replaced by new
ones in an effort to overcome the resource constrain and
input dynamism.”

12. • As per 1986 policy – up to a given level, all students irrespective of
caste, creed, location or sex have access to education of
comparable quality.
• Quality in education through quality learning was more
emphasized.
• The policy recommended identification of Minimum Level of
Learning (MLL) for all subjects at primary level.
NEW EDUCATION POLICY IN 1986

13. • 1992 MLL was identified at National level for all subjects including
Mathematics at primary stages.
• Child-centric approach was suggested and reformation starts in
curriculum and textbooks.
• The Mathematics curriculum for that time was –
• At L.P. level:
Arithmetic consists of number, four operations,
simplification, money, metric system, reading clock, basic
Geometrical concept.
NEW EDUCATION POLICY IN 1986

14. • At U.P. level (V to VII):
‐ Number
‐ Fractions, decimal fraction
‐ Money, measurement
‐ Idea of simple Geometric term/concept/properties
‐ Unitary method, simple interest ‐ Ratio proportion
NEW EDUCATION POLICY IN 1986

15. • At Secondary level (VIII to X):
‐ Number system
‐ Sets
‐ Irrational number, complex number ‐ Indices and logarithm
‐ Algebra- expression, equations, factors ‐ Quadratic equation ‐ Inequality and
inequations
‐ Geometry - theorem, properties, proofs and application –Mensuration.
‐ Discount ‐ Shares ‐ Graphs ‐ Compound interest ‐ Banking
‐ Introduction to Trigonometry
‐ Statistics
NEW EDUCATION POLICY IN 1986

16. • After NPE 1986 and POA 1992 major reformation in school
education was attempted in respect to Science and Mathematics.
• Science and Mathematics kits were supplied to schools under OBB
scheme to learn the subject by doing.
• Free textbooks were started distributed to the children.
• To handle the subject separate Science Graduate teachers were
appointed at the middle and secondary stage.
NEW EDUCATION POLICY IN 1986

17. 1993 YASHPAL COMMITTEE REPORT
‐ The curriculum was over loaded.
‐ Content was not related to children’s life and were not
integrated to social and cultural life.
‐ The approach in the textbook was extremely mechanical.
‐ Problem in the textbook are usually unfamiliar and
uninteresting and not relevant.
‐ Teacher teaches the subject in a very mechanical manner
without using any concrete object or TLM.
‐ Traditional Mathematics teaching is not related to real life.
‐ Rote memorization was more stressed than understanding.

18. • In the year 1998 in our state with the outcomes of DPEP new
curriculum was developed at primary level for the first time where
the following were given much importance.
‐ Competency based approach.
‐ Child centric approach.
‐ Joyful approach.
‐ Activity based approach.
1993 YASHPAL COMMITTEE REPORT

19. • The primary curriculum developed in the year 1998 consisted of
following:
‐ Pre number concept
‐ Number concept
‐ Four operation (in spiralling order in accordance with the
competency of number)
‐ Measurement
‐ Fraction ‐ Time ‐ Shape (Geometry)
‐ Puzzle, riddle, rhythm, etc.
1993 YASHPAL COMMITTEE REPORT

20. DEVELOPMENT OF MATHEMATICS CURRICULUM
AS PER NCF 2005 AND RTE ACT 2009
Guiding principles of NCF‐2005
• Connecting knowledge to life outside the school.
•Ensuring that learning is shifted away from the rote methods.•Enric
hing the curriculum to provide for overall development
of children rather than remain textbook centric.
•Making examination more flexible and integrated into
classroom life.

21. MATHEMATICS CURRICULUM AS PER NCF 2005
‐ Children learn to enjoy Mathematics rather than fear it.
‐ Children learn important Mathematics: Mathematics is more
than formulas and mechanical procedures.
‐ Children see Mathematics as something to talk about, to
communicate through, to discuss among them, to work
together on.
‐ Children pose and solve meaningful problems.

22. • Children use abstractions to perceive relation-ships, to see
structures, to reason out things, to argue the truth or falsity of
statements.
• Children understand the basic structure of Mathematics:
Arithmetic, Algebra, Geometry and Trigonometry, the basic
content areas of school Mathematics, all offer a methodology for
abstraction, structuration and generalization.
• Teachers engage every child in class with the conviction that
everyone can learn Mathematics.
MATHEMATICS CURRICULUM AS PER NCF
2005

23. NCERT NEW CURRICULUM AS PER NCF-2005
(a) For class I to V:
‐ Geometry (shapes and spatial understanding)
‐ Number and operation
‐ Mental Arithmetic
‐ Money
‐ Measurement
‐ Data Handling
‐ Pattern

24. NCERT NEW CURRICULUM AS PER NCF-2005
(b) For class VI to VIII:
‐ Number system and playing with numbers
‐ Algebra (introduction and expression)
‐ Ratio and proportions
‐ Geometry (basic ideas 2D and 3D) • Understanding
shapes • Symmetry • Construction
‐ Mensuration
‐ Data handling ‐ Introduction to graphs

25. NCERT NEW CURRICULUM AS PER NCF-2005
(c) At class IX and X:
‐ Number system
‐ Algebra
‐ Co-ordinate Geometry
‐ Geometry
‐ Mensuration
‐ Statistics & Probability
‐ Trigonometry

26. • Problem Solving 40%
• Reasoning Proof 20%
• Communication 10% 100%
• Connections 15%
• Visualization & Representation 15%
ACADEMY STANDARDS

27. PROBLEM SOLVING
• Identify what is given?
• Identify what is to be found?
• Understanding what concepts are involved.
• Visualizing whole the above items.
• Get ideas about procedures, formulas for the solution.
• Selection of the best procedure or formula.
• Substitution.
• Manipulation / calculation.

28. • Arriving solution.
• Verification.
• Conclusion.
• Generalisation.
• Trying out other strategies, formulas, procedure for the solution.
• Finding shortcut.
• Explaining procedures and reasoning.
• Creating similar problems in various situation and with various
types of numbers.
PROBLEM SOLVING

29. The complexity of the problems depends upon the following things.
 Making connections as defined in connections section.
 Number of steps.
 Number of operations.
 Context unravelling.
 Nature of procedures.
PROBLEM SOLVING

30. REASONING – PROOF
• Understanding and making mathematical generalizations,
intuitions and conjectures.
• Understanding and justifies procedures.
• Examining logical arguments.
• Uses inductive and deductive logic.

31. COMMUNICATION
• Writing and reading mathematical expressions.
• Creating mathematical expressions.
• Explaining mathematical ideas in her own words.
• Explaining mathematical procedures.
• Explaining mathematical logic.

32. CONNECTIONS
• Connecting concepts within a mathematical domain fore relating
adding to multiplication, parts of a whole to a ratio, to division.
Patterns and symmetry, measurements and space.
• Making connections with daily life.
• Connecting mathematics to different subjects.
• Connecting concepts of different mathematical domains like
data – handling and arithmetic or arithmetic and space.
• Connecting concepts to multiple procedures.

33. VISUALIZATION & REPRESENTATION
• Interprets and reads data in a table, number line, pictograph, bar
graph, linear graphing, quadratic graphing, 2-D figures, 3-D
figures, pictures etc.
• Making tables, representing number line, pictures etc.

34. EXPECTATIONS OF A CLASSROOM BY TEACHER
• Regularity
• Proficiency
• Familiarity
• Computational Ability Learning Readiness
• Conceptual Understanding
• Active Participation
• Skills of Application

35. REGULARITY
• Regular to school
• Regular to class
• Regular to
assignments
• Regular to works
• Regular to activities
related to co-
curricular areas
• Irregular to school
• Irregular to class
• Irregular to
assignments
• Irregular to works
• Irregular to activities
related to co-
curricular areas
Vs

36. WHAT TO DO?
• Make friendly atmosphere and timings which give scope to be
regular.
• Before giving assignments take the opinion from students.
• Approach simple to complex.
• Provide work assignments according to students environment.
• Encourage them to participate with their will and wish.

37. PROFICIENCY
• Can define terms,
formats, structures,
formulae, relations
etc.,
• Can write well with
interest.
• Can express/speak
about his ideas.
• Can’t define terms,
formats, structures,
formulae, relations
etc.,
• Can’t write well with
interest.
• Can’t express/speak
about his ideas.
Vs

38. WHAT TO DO?
• Language proficiency of children is influenced by number of
factors
• Parents, neighbourhood, rearing practices etc.,
• Some children may have inhibitions, shyness, fear etc.,
• Some children may be suffering from marginal learning problems
like dyslexia, dysgraphia & dyscalculia.
• Some children may not have expression.

39. • Special attention and care need to be provided.
• Continuous encouragement should have been given to children
with special needs.
• Special programmes need to be developed to participate them
into various school activities, so that they gradually improve
themselves.
• Teachers should take some initiative to identify each ones innate
abilities of children, so that they can design activities accordingly.
WHAT TO DO?

40. FAMILIARITY
• Can identify terms,
structures, formulae.
• Can able relate
unknown with known
• Can able to choose
proper examples
• Can’t identify terms,
structures, formulae.
• Can’t able relate
unknown with known
• Can’t able to choose
proper examples
Vs

41. WHAT TO DO?
• The school and classroom should have been decorated in such a
way that it should create congenial & learning atmosphere in the
minds of child.
• For this the teachers have to maintain wall papers, posters,
students achievements, and their work.
• Before beginning of any topic an introduction and need of the
topic should be provided to students.
• A topic should have been introduced to the students only by
providing suitable examples from their surroundings.

42. COMPUTATIONAL ABILITY
• Can use operators
• Can deal with
fractions
• Can deal with decimal
numbers
• Can deal with
irrational forms, and
other structures.
• Can’t use operators
• Can’t deal with
fractions
• Can’t deal with
decimal numbers
• Can’t deal with
irrational forms, and
other structures.
Vs

43. WHAT TO DO?
• Students should have been thoroughly exposed to those exercises
in which they can learn pre-require skills before attempting a
topic.
• For example “Order of operations” improves computational skills
among the children.
• Simple linear equations with single variable and various verbal
problems can improve operations involved in solving various
algebraic equations.
• Puzzles, pictorial diagrams improve children graphical plane
knowledge.

44. LEARNING READINESS
• Conceptual Understanding
• Active Participation
• Skills of Application

45. THANK YOU
FOR LISTENING