for B.Ed students

1. AIMS & OBJECTIVES OF
TEACHING MATHEMATICS
V. SURESH KUMAR
ASSISTANT PROFESSOR OF MATHEMATICS
RAJALAKSHMI COLLEGE OF EDUCATION
THOOTHUKUDI

2. NEED OF TEACHING MATHEMATICS
It is the only subject that encourage & develops logical
thinking.
Help the students to discriminate between essential &
non- essentials.
Knowledge of mathematics is very essential for training
rational & trustworthy.
Essential to face the challenges of the modern
technological society.
Helps to apply mathematical concepts & theorems to
new situations.

3. SIGNIFICANCE OF TEACHING
MATHEMATICS
Develops the ability to transfer the mathematical
type of thinking & reasoning to daily life situations.
Clear understanding of laws of nature.
Helps to appreciate the applications of mathematics
for the scientific & technological advancement.
Inculcates a good deal of self – reliance, self –
confidence, tolerance & open – mindedness.

4. CON/-
Essential element of communications.
Powerful tool in the hands of the learners.
Develops logical thinking & reasoning critical
mind & creative imagination.
Helps to think alternative methods of solving
problems.

5. WHAT IS AIM ?
Long term goal.
General.
Give directions for the educational
process.

6. AIM OF TEACHING MATHEMATICS
Practical aims.
Social aims.
Disciplinary aims.
Cultural aims.

7. PRACTICAL AIMS
Develop clear ideas.
Make proficient.
Make appropriate approximation.
Develop mathematical skills.
Understand the concepts.

8. SOCIAL AIMS
Develop the individual to understand & participate
in the general social & economic life.
Help the pupil acquire social & moral values.
Helps in formation of social laws & social order.
Provide knowledge for adjusting with the society.
Help the pupil interpret social & economic
phenomena.

9. DISCIPLINARY AIMS
Enable the learners to exercise & discipline mental
faculties.
Help in intelligent use of reasoning power.
Develop the character through systematic
& orderly habits.
Help the learner to be original & creative in thinking.
To help the individual to become self –reliant &
independent.

10. CULTURAL AIMS
Enable to appreciate the role played by mathematics
in cultural traditions.
Provide mathematical ideas, aesthetic, intellectual
enjoyment & satisfaction for creative expression.
Develop an aesthetic awareness of mathematical
shapes & patterns in the nature.

11. OBJECTIVES
Directed towards aims.
Short – term goals.
Attainable within the educational system.
Steps toward the realization of the aims.
Specific, precise & observable.
Vary from course to course.
Specific for each course originate from the aims.

12. Objectives
Educational objectives
Instructional Objectives

13. EDUCATIONAL OBJECTIVES
Broad & philosophical in nature.
Related to schools & educational system.
Achieved with the help of teaching (or)
instructional objectives.
A dimension of learning.
Worthwhileness of a pattern of learning for
realizing.
Level of learning to be attempted.
Serve as guide posts in learning.

14. INSTRUCTIONAL OBJECTIVE
Based on specific observable.
Behavioral in nature.
Measurable goal .
Establishes a minimal level of attainment for judgment.
Instructional objectives state both behavior is intended
to be developed (Curricular aspect) & what actual behavior
is developed & tested (Evaluation aspect).

15. BLOOM’S TAXONOMY OF EDUCATIONAL
OBJECTIVES
Dr. Benjamin S. Bloom & his associates in
the university of chicago gave the classification
of educational objectives for three domains &
classification of educational objective is known
as “ Taxonomy of Educational Objectives” or
“Bloom’s Taxonomy”

16. BENJAMIN BLOOM
Born : Benjamin Samuel Bloom
Feb /21/ 1913.
Died : Sep/13/1999. (86) Chicago.
Nationality : United state citizen.
Education : Ph.D in Education.
Alma mater : Pennsylvania state university,
university of Chicago.
Occupation : Educational Psychologist.
Employer : American Educational Research
Association.

17. TAXONOMY
Complex scheme for classification of
phenomena or idea.
Bloom’s taxonomy is an attempt to
identify , define, classify & organize a
comprehensive range of educational
objectives into a compact & measurable
structure.

18. EDUCATIONAL OBJECTIVE
Cognitive Affective Psychomotor
domain domain domain

19. COGNITIVE DOMAIN
Bloom was identify objective & specification
relating to cognitive in 1956.
Stress to acquire knowledge.
Development of intellectual abilities & skill.

20. HIERARCHY OF COGNITIVE
OBJECTIVE
Evaluation
Synthesis Higher level
Analysis
Application Middle
Comprehension level
Knowledge Lower
level

21. KNOWLEDGE:
Ability to recall or recognize already learnt information.
COMPREHENSION:
Ability to organize & arrange materials mentally.
APPLICATION:
Ability to select & apply already learnt rules.
ANALYSIS:
Ability to break up a given communication into its constituent
elements or parts.
SYNTHESIS :
Ability to produce a new communication from many sources.
JUDGEMENT :
Ability to judge values of materials & methods.

22. COGNITIVE OBJECTIVE IN BEHAVIOURAL
TERMS
Ex : Sol/- of linear equation with the help of graphical method.
S.No Objectives Expected change in behaviour
1.1. The pupil will be able to recall
1. knowledge the linear equation.
1.2. The pupil will be able to
recognize the definition of
linear equation.
2. Comprehensive 2.1. The pupil will be able to
illustrate equation.
2.2 . The pupil will be able to
explain the graphical method.
2.3. The pupil will be able to
present linear equation on graph

23. S.No Objectives Expected change in behaviour
3.1. The pupil will be able to demonstrate
3. Application linear eqn/- on graph.
3.2. The pupil will be able to solve linear
eqn/- through graphical method.
4.1. The pupil will be able to develop skills
4. Skill to solve pbm by the use of graphical
method.

24. AFFECTIVE DOMAIN
In 1964 bloom & his associates Karthwohl &
Masia explained the structure of affective
domain.
Development of attitude, values, appreciation,
adjustment etc.
Deals with emotional aspect.

25. LEVEL OF OBJECTIVE
1. Receiving.
2. Responding.
3. Valuing.
4. Organisation.
5. Characterisation.

26. PSYCHOMOTOR DOMAIN
Elizabeth Simpson & R.H.Dave have
formulated the objectives relating to
psychomotor domain in 1972.
Focus on motor skill.

27. LEVEL OF OBJECTIVES
1. Imitation.
2. Manipulation.
3. Precision.
4. Articulation.
5. Naturalisation

28. GENERAL INSTRUCTIONAL OBJECTIVES
(GIOS)
Non – behavioural objectives.
Statement contain verb like ‘knows’, ‘understand’ etc
Non – observable behaviour.

29. BEHAVIOURAL OBJECTIVE OR SPECIFIC
LEARNING OUTCOMES(SLOS)
Specific performances, which are
precise & measurable.
Observable behaviour.

30. SPECIFIC STATEMENT HAS TWO PARTS
1. The content part &
2. Behaviour modification part.
The behaviour modification is described by an
appropriate action verb.
Ex: Recalls, Explains, Compares etc

31. FIVE ELEMENTS IN WRITING SPECIFIC
BEHAVIOURAL OBJECTIVES
1. Performer (The student, trainer, the learner etc)
2. Action required
Action – verb, Ex: Identifies, compares,
classifies etc.
3. Task
Include a task to be performed.
Ex: Compares, the properties, explains the
derivation.

32. 4. Conditions
Include any condition that may be required.
Ex: Compares the properties of the given
triangles.
5. Criteria for judgement:
Any relevant criteria for clarity.
Ex: Phenomena with two examples – Computers
with speed & accuracy.

33. EXAMPLE FOR SLO (OR) SBO
1. The pupil recall the formula for the area of
P A.V Task C
equilateral triangle.
J
2. The pupil selects an appropriate
P A.V
method/formula to solve the given problem.
Task C J

34. Some time SLO’s have any three factors –
performance, Action, Tasks.
3. The pupil list the properties of an equilateral triangle.
P A.V T C
4. The pupil state Pythagoras theorem.
P A.V T

35. EXAMPLE FOR GIO
The pupil acquires knowledge of polynomial
multipulations.
The pupil understands the meaning of the
term “Probability”
The pupil applies the formula to find the area
of a given quadrilateral.

36. REVISED BLOOM’S TAXONOMY
Taxonomy of cognitive objectives.
1950s – developed by Benjamin bloom.
Means of expressing qualitatively different kinds of
thinking
Been adapted for classroom use as a planning tool.
Continues to be one of the most universally applied
models.
Continues to be one of the most universally applied
models.

37. CON/-
Provides a way to organize thinking skills into six
levels, from the most basic to the more complex levels
of thinking.
1990 – Lorin Anderson (former students of
Bloom) revised the taxonomy.
As a result, a number of changes were made.

38. CHANGES IN TERMS
Six categories changed from noun to verb forms.
Taxonomy reflects different forms of thinking & thinking is
an active process verbs were used rather than nouns.
Some sub – categories are re – organised.
Knowledge is an product of thinking, the word knowledge
was inappropriate to describe a category of thinking & was
replaced with the word “ remembering” instead.
Comprehension & synthesis are retitled to understanding &
creating respectively, in order to better reflect the nature of the
thinking defined in each category.

39. REPRESENTED IN DIAGRAM

40. REMEMBER
Retrieve relevant knowledge from long – term memory.
Understand:
Construct meaning from instructional messages.
Include oral, written & graphic communication.
Apply:
Carryout (or) use a procedure in a given situation.
Analyze:
Break material into consistent parts.
Determine how parts relate to one another.

41. EVALUATE
Make judgements based on criteria & standards.
Create:
Put elements together to form a coherent or functional
whole.
Re – organize elements into a new pattern or structure.

42. WEAKNESS OF TAXONOMY
Weakness noted by bloom himself.
Fundamental difference between his “knowledge”
category & the other five level of his model.
Intellectual abilities & skills in relation to
interactions with types of knowledge.
Bloom aware that there was an acute difference
between knowledge & mental & intelligence
operation.

43. TYPES OF KNOWLEDGE
Bloom identified specific types of knowledge as
1. Terminology.
2. Specific facts.
3. Convention.
4. Trends & Sequences.
5. Classifications & Categories.
6. Criteria.
7. Methodology.
8. Principles & Generalizations.
9. Theories & Structures.

44. LEVEL OF KNOWLEDGE
1. Factual learning. Identified in the
2. Conceptual knowledge. original
3. Procedural knowledge. work
added in the
4. Meta cognitive knowledge. revised version

45. FACTUAL KNOWLEDGE
Basic to specific disciplines.
Essential facts, terminology, details or
elements, students must know or be familiar with
in order to understand a discipline or solve a problem
in it.

46. CONCEPTUAL KNOWLEDGE
Knowledge of classifications, principles,
generalizations, theories, models or structures
pertinent to a particular disciplinary area.

47. PROCEDURAL KNOWLEDGE
Knowledge that helps students to do something
specific to a discipline, subject or area of study.
Methods of inquiry, very specific or finite
skills, algorithms, techniques & particular
methodologies.

48. META COGNITIVE KNOWLEDGE
Awareness of one’s own cognition &
particular cognitive processes.
Reflective knowledge about how to go
about solving problems, cognitive tasks.
Include contextual & conditional knowledge
& knowledge of self.

49. Theknowledgedimension
Cognitive
De
Re
Procedural
Recall
Clarity
Carry
Out
Integrate
Judge
Design
Conceptual
Recognize
Classify
Provide
Differentiate
Determine
Assemble
Factual
List
Summarize
RespondTo
Select
CheckOut
Generate
ber
and
y
ze
te
e