The document discusses the nature of mathematics and defines conceptual knowledge and procedural knowledge in mathematics. Conceptual knowledge refers to understanding mathematical concepts, while procedural knowledge involves being able to physically solve problems by applying mathematical skills and tools. The document states that conceptual understanding supports applying principles to new situations, while procedural knowledge is built upon conceptual understanding. It emphasizes that both conceptual understanding and procedural knowledge are important for students to master, as it helps them solve problems, draw inferences, and establish relationships between concepts.

2. MEANING
 Mathematics is the science of measurement , quantity
magnitude.
 It also the science of numbers, words and signs etc.
 It is the science that draws necessary conclusions.
 It deals with quantitative facts and relationships .

3. NATURE OF MATHEMATICS
• Mathematics is the science of space,
numbers , magnitude and measurement.
• Mathematics has its own language .
Language consists of mathematical terms,
mathematical concepts , formulae , theories ,
principles and signs etc.
• Mathematics is Systemised , organised and
exact branch of science.
• Mathematics involves conversion of abstract
concepts in to concrete form.
• Mathematics is the science of logical
reasoning.

4. OBJECTIVES
• Mathematics helps to develop the
habit of self confidence and self
reliance in children .
• Mathematics helps in development of
sense of appreciation among
children.
• Mathematics gives accurate and
reliable knowledge.
• Mathematics develops the ability of
induction, deduction and
generalisation.
• Mathematics drew numerical
inferences on the basis of given data
and information.

5. • Procedural knowledge in mathematics is the ability to
physically solve a problem through the manipulation of
mathematical skills , with tools used in mathematics such as
pencil, paper ,calculator and computer etc.
PROCEDURAL
KNOWLEDGE

6. CONCEPTUAL
KNOWLEDGE
• Conceptual knowledge in mathematics is the ability to
show understanding of mathematical concepts by
being able to interpret and apply them correctly to a
variety of situations .

7. H
I
S
T
O
R
Y
The general view among philosophers ,
cognitive psychologists and educators
is that humans develop concepts
through an active process of
adaptation to new and different
experiences.Therefore, according to
Bruner learning mathematics will
succeed if the learning process is
directed at understanding the concepts
and knowledge of the procedures
contained in the material being taught.

8. Many researches have shown that students have difficulty
implementing meaningful understanding of their
mathematical conceptual understanding. This is especially so
for the learning of fractions .In fraction and decimal material,
students need new understanding to understand the
relationship of each concept. But the topics of fractions and
decimals demand new and extended understanding of units
and their relationships .Learning should be able to facilitate
students in organizing understanding of concepts they have
received as provisions to receive new concept knowledge. In
fraction material, it turns out students have difficulty
organizing their knowledge. We assessed students'
knowledge on fractions using equivalent pretest, immediate
and delayed posttest versions, each of which took 30
minutes to complete . This gives an explanation that
conceptual understanding and procedural knowledge are
very needed by students in solving mathematical problems
they face.

9. RELATIONSHIP BETWEEN CONCEPTUAL
UNDERSTANDING AND PROCEDURAL
KNOWLEDGE
• Conceptual understanding supports understanding
mathematical principles that are considered as the product of
a process that connects prior knowledge with new knowledge
whereas Procedural knowledge is built on the basis of
conceptual understandings. Procedural knowledge is a series
of steps that must be followed to solve mathematical
problems. This knowledge includes knowledge of algorithm
skills ,techniques and methods.
• Procedural knowledge involves understanding rules and
routines of mathematics while conceptual understanding
involves an understanding of mathematical relationships.

10. IMPORTANCE
• It will help students to understand the
concept and skills to choose steps that will
used to solve mathematical problems.
• It will help the students to solve difficult a
novel problems quickly and correctly by
following an appropriate procedure or ste
required for its solution.
• It will also help students to draw inferenc
out of the problems.
• It will also help to establish a relationship
between mathematical concepts.
• It will also help students to represent and
communicate the idea.

11. EXAMPLES
CONCEPTUAL UNDERSTANDING
3/5=9/25
4/9=16/81
2/4=4/16
7/8=49/81
PROCEDURAL KNOWLEDGE
1/3+1/6+1/12=7/12
9/10-4/5=1/10
4/12+2/12+1/12=7/12
4/5-3/5=2/5

12. CONCLUSION
• Based on research studies, we can
conclude that conceptual
understanding and procedural
knowledge are very important to
be mastered by students.
• It will impact students as it will
help them to have mastery over
other material in mathematics.
• It will also help students to
become social as well as
intellectual citizens.