Nature of Mathematics.pptx

Nature of Mathematics

1. NATURE OF MATHEMATICS

2. MEANING Mathematics is the science of measurement , quantity and 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 be used to solve mathematical problems. It will help the students to solve difficult and novel problems quickly and correctly by following an appropriate procedure or steps required for its solution. It will also help students to draw inferences 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.