The Conceptual Approach in Teaching Mathematics

Conceptual approach

It is choosing and defining content of a certain discipline to be taught through the use of big and pervasive ideas

It is using the content as a means of leading the students to discover the laws and principles or generalizations that govern a particular subject or discipline

Fact- A simple statement of truth

Concept- Synthesis of facts

Generalization  - General statement relating two concepts

Principle - Statement of fundamental processes

Conceptual scheme- The main pervasive theme underlying a major field

A. conceptual attainment

- Is the process of defining concepts by finding those attributes that are absolutely essential to the meaning and disregarding those that are not

It also involves learning to discriminate between what is and is not an example of the concepts

It helps the learners attain the meaning of concepts through the inductive process of comparing examples and non-examples until a definition is derived

Step in the concept attainment method

1. select and define concepts..

2. select the attributes

3. develop positive and negative examples

4. introduce the process to the students

5. present the examples and list the attributes

6. develop concept definition

7. give additional example

8. discuss the process with the class

9. evaluate

B. Concept Formation

- The important principle underlying this method is that understandings are built, not acquired

It helps students think effectively, refining and extending students’ understanding to approach new information they encounter

Steps in concept formation method

1. list as many items as possible that are associated with the subject

2. Group the items because they are alike in some ways

3. label the groups by defining the reasons for grouping

4. regroup or subsume individual items or whole group under other groups

5. synthesize the information by summarizing the data and forming generalizations

6. evaluate students’ progress

C. Inductive  Method

Induction is that form of reasoning in which a general law is derived from a study of

particular objects or specific processes. Students use measurements, manipulators or constructive activities and patterns etc to discover a relationship. They later formulate a law or rule about that relationship based on their observations, experiences, inferences and conclusions.

Example 1: Ask pupils to draw a number of triangles. Ask them to measure the three

angles of each triangle and find their sum. They will find that the sum of the three

angles of all triangles is 180o.

Example 2: Ask pupils to find the sum of two odd numbers like 3+5=8, 5+7=12,

9+11=20, etc. They will find that the sum of two odd numbers is an even number.

Steps in the inductive method:

1) The first step is clear recognition of the problem. It should be clearly understood

and defined by the pupils.

2) Once the problem has been defined, the child should start searching for data from all possible sources like books, magazines, journals, making visits to certain places etc.

3) Under the guidance of the teacher, the pupils organize the data which they have collected from various sources. They select relevant data and discard irrelevant material.

4) By studying particular instances, the pupils frame possible solutions.

5) These solutions are discussed, argued and judged. Thus tentative solutions are

eliminated and only the probable solutions remain.

6) The solutions are applied to the situation and results are verified.

Merits of Inductive method

1) This method is psychological. The student feels interested in experiments,

experiences and discoveries.

2) This method fosters independence and self-confidence in the pupil which proves

very useful in later life.

3) In this method, children discover the solution themselves. Hence it develops and

encourages initiative and creative thinking.

4) All that is learnt using inductive method is remembered easily as it is self-acquired.5) In this method, the pupils observe and analyze particular objects of similar and different nature and try to arrive at general truth.

6) Inductive method takes into consideration all the maxims of good teaching. The

process of induction calls for perception, reasoning, judgment and generalization.

D. Deductive Method

Deduction is the method in which the law is accepted and then applied to a number of

specific examples. The child does not discover the law but develops skills in applying

the same, proceeds from general to particular or abstract to concrete.

Steps involved in deductive method

1) Like the inductive method, the first step is the clear understanding of the problem.

2) It may involve the study of a particular thing and phenomenon.

3) Principles and generalizations are reviewed to find the one which may be

applicable to find a solution.

3) Principles and generalizations are reviewed to find the one which may be

applicable to find a solution.

5) Verification of the inference is done by applying it to a case. If it solves the

problem then it is accepted otherwise the procedure is repeated to find the correct one.

Merits of deductive method

1) Deductive method is short and time-saving. It takes little time to solve the problem

by predetermined formulae.

2) In the deductive method, the teacher’s work is very much simplified. He/she simply gives a rule and asks the pupils to verify it by application to several concrete examples. For example, students are told that the area of rectangle = Length x Breadth. Then a few sums are solved before the students. The students apply thes eformulae to solve these problems and they memorize it for future use.

3) This method is very useful for small children because with small children we

generally use story or telling method.

4) This method glorifies memory, as the students have to memorize a considerable

number of formulae and definitions.

5) This method is adequate and advantageous during practice and revision stage.

Prepared and reported by:

Reynaldo, Alma V.

III-7 BEEd