**Teaching methods**

The process of interpreting the world of knowledge into pupil’s mind is called as the ‘method of teaching’. The world of knowledge includes the knowledge, interest, attitude, skill, etc. i.e. all the three domains- cognitive, affective and psychomotor.

They are mainly of following types:

- lecture method
- heuristic
- inductive method
- deductive method
- analytic method
- synthesis method
- laboratory method

**Lecture Method**

Lecture method is completely under the control of teacher and is information centered approach. Some of the properties of lecture method are as follows:

- This is a teacher centered method. In this method the teacher is an active participant and the child is a passive learner.
- This is not a psychological method.
- In this method the teacher speaks or delivers a lecture on a particular topic and the children listen.
- It is one way traffic because the teacher gives ideas and the children receives them.

**Merits**

- This is an easy, attractive and brief method.
- It is useful to give fact based knowledge and historical development of mathematics.
- It is beneficial for teaching higher classes.
- It is a method of presenting the word, picture of ideas and experiences.

**Demerits**

- This is a teacher controlled method. So this is against psychological principles of children centered education system.
- The learner remains passive and inactive.
- It does not provides opportunities to develop various mental abilities like reasoning, logical thinking, mathematical training etc.
- In this method, there is no provision for practical and creative work.
- It is not necessary that the children are attentive and understanding everything that the teacher is trying to explain.

**Inductive Method**

Some of the properties of inductive method are:

- Induction means proving a universal truth or theorem by showing that if it is true in any particular case, it will be true in the next case in the same serial order.
- Basically, teaching theorems, principles through examples.
- Method of teaching and learning mathematics is based on induction.
- This is a method of development in which the child is made or led to discover truth for himself.

**Merits**

- It is a scientific method because knowledge attained by this method is based on real facts.
- The knowledge gained by the use of this method is more durable because in this method child himself attains the knowledge by examples, observation and testing.
- The critical observation and logical power of children are developed by inductive method.
- In this method, children themselves attain the knowledge with the help of examples so they don’t feel bored or get fatigue. They remain active to attain new knowledge.
- This method is certainly very important and useful method of teaching mathematics.

**Demerits**

- This is a very slow process, so gaining knowledge by this method costs more time and labour.
- It needs sharp mind, proper planning and enough labour. So it is not easy to attain knowledge by this method for students of all level.
- Only an experienced and able teacher can use this method successfully.
- The ability and capacity of problem solving cannot be developed by the use of this method.

**Deductive Method**

Some of the properties of deductive method are:

- Deductive method is exactly opposite to inductive method. Deductive logic is used in this method.
- Deductive method is mainly used in algebra, geometry and trigonometry because different relations, laws and formulae are used in these sub-branches of mathematics.
- It is impossible to verify each law and formula practically.
- In this method help is taken from assumptions, postulates and axioms of mathematics. This method is used for teaching mathematics in higher classes.

**Merit**

- By using this method the speed of gaining knowledge increases because students directly use the formula for solving the problem.
- This method should be used when there is shortage of time.
- This method is used for teaching theorems and axioms of geometry, tables in arithmetic etc.
- Both the teacher and pupil do not find any difficulty in using this method.
- More knowledge can be attained in less time by the use of this method.
- This method is short as well as practical.
- Just like inductive method, deductive method is also an important method of teaching mathematics.

**Demerits**

- This method is not in accordance with psychological principles.
- In this method more emphasis is given on cramming than understanding or discovering.
- In this method there is no scope of developing powers like logical thinking and investigation.
- Children don’t get opportunities to gain new knowledge by using this method.

**Analytic Method**

Some of the properties of analytic method are:

- The original meaning of the world analysis is to unloose or to separate things that are together.
- Analysis starts with what we have to find out and traces the connection between it and the data.
- With the help of this method, the difficult parts of any problem can be analysed to find out the solution of the given problem. Thus, separation of different part of a problem is known as analysis.

**Merit**

- This method is based on psychological principles.
- The analysis is an explanatory procedure.
- It creates creativity and originality in the child and develops analytic and reasoning power.
- This develops self-confidence and logical abilities in the child.
- It is a formative method and based on inductive reasoning.

**Demerits**

- Every teacher cannot use this method successfully.
- The whole syllabus cannot be completed within the certain period.
- The use of analytical method is possible only when we have the knowledge of known facts and unknown conclusions.

**Synthesis Method**

Properties of synthesis method are:

- It is reverse of the analytical method. Synthesis means to place together things that are apart or to join separate parts.
- In this method we proceed from “known to unknown” or we start with hypothesis and end with conclusions.

**Merit**

- It is a short and quick method.
- It glorifies the memory of the child.
- It formulates records and presents concisely the discovered facts.
- If omits the trials and errors like in analysis.
- This is the method of setting out the solution in a concise form.

**Demerits**

- It creates many doubts in the mind of the child.
- There is no opportunity for developing thinking, reasoning and other mental abilities.
- The recall of each step cannot be possible for every child.

**Laboratory Method**

Some of the laboratory methods are:

- To make mathematics more interesting and meaningful, laboratory method is used in teaching of mathematics.
- In this method, students get the opportunity to acquaint themselves with the facts through direct experiences individually.
- In this method, students themselves verify the facts and laws of mathematics with the help of experiments.
- This method needs a laboratory in which equipments and other useful teaching aids related to mathematics are available.

**Merits**

- This method is based on psychological principle “learning by doing” so that students take interest in their work.
- The knowledge acquired by this method is more solid and durable.
- It helps in developing the habit of discovery and self-study.
- It develops scientific attitude in the students.
- This method helps in developing problem solving ability.
- The children get the opportunity of creative and practical work.
- The children enjoy as they remain active in the laboratory.

**Demerits**

- It is an expensive method so it is not affordable. Due to financial constraints not all schools are able to adopt this method.
- It takes more time to teach so the whole syllabus cannot be completed within the given time duration of one year.
- This method requires laboratory equipped with different apparatus.
- Individual attention cannot be paid to classes with large number of students.

**Heuristic Method**

The word heuristic is believed to be originated from Greek work “Heurisco” which means “I find out”. The profounder of this method was Professor Henry Edward Armstrong.

Properties of Heuristic method are:

- Just like other methods, heuristic method also has a special place in mathematics teaching.
- This method helps in developing scientific and mathematical attitude in students.
- Herbert Spencer has thrown light on this method and stated that- “Students should be told minimum and as much as possible they should be encouraged to discover.”

**Merits**

- This is a psychological method.
- It develops self-confidence, self-reliance and scientific attitude.
- It develops ability of observation and spirit of enquiry to solve the problems.
- Contemplation and awakening increases in the children.
- Students get the opportunity to develop the mental and thinking powers.
- This method is based on the principle of activity.
- Individual attention of the teacher is possible and the relation between the teacher and learner becomes more intimate.

**Demerits**

- It is not suitable for lower class students.
- It is a very slow method.
- There is lack of textbooks written on heuristic approach.
- This is formational method rather than informational.

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