UNIT 4 METHODS OF TEACHING MATHEMATICS Methods of Teaching A method is “a scientific way of presenting the subject keeping in mind the psychological and physical requirements of children” Teacher Centred Methods In these methods the teacher‟s role is to give knowledge and have full control of the class room. Lecture Method It is the oldest teaching method. It is the most dominating method and is liked by the majority of teachers. In this method teacher presents the subject matter and the students listen. Students are not participating in this method. Merits of Lecture Method 

It is possible of handle a large number of students at a time and no laboratory, equipment, aids are required.

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Using this method the knowledge can be imparted to the students quickly and the prescribed syllabus can be covered in a short time

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Teachers feel secure and satisfied

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Lecture method trains students to listen for a long duration

Demerits of Lecture Method 

In these method students participation is negligible and students become passive recipients of information.

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We are not sure if the students are concentrating and understanding the subject matter.

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This method leads weak students develop a hatred for the subject.

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If does not cater to the individual needs and differences of the students.

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It has the lowest retention values of all teaching techniques.

Analytic Method Analysis means „breaking up‟. In this method we break up the problem in a meaningful way. Start with what is to be found out. Then think of further steps and possibilities which may connect the unknown with the known and find out the desired result. Merits of Analytic Method 

It helps in understanding the topic clearly

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It develops the power of thinking and reasoning

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It makes the students self confident and self-reliant

Demerits of Analytic Method 

It is a time consuming method

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It is difficult to acquire efficiency and speed in the method

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This method is not applicable to all topics

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This method is not useful at lower classes.

Synthetic Method Synthesis means to combine the constituent elements to produce something new. In this method we start with something already known and connect it with the unknown part of the statement. Therefore in this method one proceeds from known to unknown. This method is opposite to Analytic Method. Merits of Synthetic Method 

It is short and elegant

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Accuracy and speed are developed by this method

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This is a logical method

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Most of the topics in Mathematics are covered by this method.

Demerits of Synthetic Method 

This method is not a psychological one.

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There is no scope for discovery.

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All students cannot use this method.

Differences between Analytic and Synthetic Method S. No 1

Analytic Method

Synthetic Method

Analysis means breaking up into Synthesis means combining elements to get components.

something new

2

Leads from unknown to known

Leads from known to unknown

3

A method of discovery and thought

A method for the presentation of discovered facts

4

Lengthy

and

time

consuming Short, concise and elegant

method 5

Encourages meaningful learning

Encourages rote learning

6

It is a psychological method

It is a logical method

7

Active participation of the learner

Learner is a passive listener

Deductive and Inductive Method Deductive Method We begin with the formula or rule and it is explained to the students with the help of certain examples. This method of teaching is called Deductive Method. This method is opposite to Inductive Method. 1. General to particular case 2. Abstract to concrete 3. Rule or formula to examples Steps in Deductive Method In this method teacher announces the topic and also gives the relevant formula, which is also explained to the students with the help of few examples. Then the problems are given to the students who solve the problem following the same way as explained by the teacher, students memorize the formula for future problems. 4

Volume of the sphere V = 3 𝜋𝑟3 Solution:

4

Volume of the sphere V = 3 𝜋𝑟3 4

22

= 3 x 7 x7x7x7cm3 =

4312 3

= 1437.3 cm3

Merits of Deductive Method 

It saves time and labour for both the teacher and the students

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It enhances speed, skill and efficiency in solving problems

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It is very useful for revision and drill work

Demerits of Deductive Method 

It encourages rote memory without understanding

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It does not clarify the doubts of the student regarding the generalisation

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Once the formula or rule is forgotten, it is not possible to recover them

Inductive Method Inductive method is based on induction. Induction is the process of proving a universal truth by showing that if it is true of any particular case, it is true for the next case in the same serial order and hence true for any such cases. Concept 

Known to unknown

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Concrete to abstract

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Simple example to complex

Steps in Inductive Method 1. Preparation 2. Explaining 3. Comparison and finding common relation 4. Generalisation

5. Verification or application Merits of Inductive Method 

It helps underrating

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It encourages active participation of the students in learning

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It is a logical method and develops critical thinking

Demerits of Inductive Method 

This method cannot be used in solving all topics in Mathematics

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This method is not suitable for higher classes

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It is a lengthy, time consuming and laborious method Differences between Inductive and Deductive Method Inductive Method

Deductive Method

Based on inductive reasoning

Based on deductive reasoning

Proceeds from particular to general concrete

Proceeds from general to particular abstract

to abstract

to concrete

It is a psychological method

It is an unpsychological method

Most suitable for initial stage of learning

Most suitable for practice and revision

Lengthy, time – consuming and laborious

Short, concise and elegant

Demonstration Method Demonstration Method is a method of teaching such subjects that need live guidance on the part of the teacher. Demonstration involves showing by reason, explaining or making clear by use of examples or experiments. Advantages of Demonstration Method 

It helps in involving various senses to make learning permanent.

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Teacher gets cooperation of students in teaching learning process

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It develops interest in students and motivates them for their active participation.

Disadvantages 

It can be used only for skill subjects

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Students are not able to create handmade models for demonstration.

Team Teaching T

- Together

E

- Everyone

A

- Achieves

M - More Definition All arrangements that include two or more faculties in some level of collaboration in the planning and delivery of course materials to a class. Type of Team Teaching 

Interactive Team Teaching



Rotational Team Teaching



Participative Team Teaching

Learner-Centred Method In this method students gather knowledge through discussion, critical thinking, problemsolving etc., teacher‟s role is to coach and facilitate. Project Method Project is a purposeful activity related to life and it should be carried out in a natural environment in a school or outside the school. Steps in a Project Method 

Providing a situation

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Choosing a project

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Planning of the project

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Executing the project

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Evaluating the project

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Recording all activities of the project

Merits of Project Method 

It is a psychological method and learner‟s centred

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It introduces democracy in education

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It develops self confidence and self – discipline

Demerits of Project Method 

The Project Method is expensive and time consuming and it is not possible to fit into the regular timetable

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Systematic and continuous teaching is not possible

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The knowledge obtained from various activities is not continuous.

Peer Tutoring / Teaching by Students Peer tutoring is a student-led instructional strategy used to support. It improves students‟ academic achievement. Peer group members are intimate with each other and so there is no place for shyness or hesitation. Individual Activities An individual activity is primarily authored by students themselves. The individual activities help students focus on goals and develop future plans and how to use the time in high school to accomplish their personal objectives. List of Individual Activities 

Individual exercises

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Personal design

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Quiz

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Computer work

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Library work

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Interview with celebrity

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Preparing poster for a function

Experiential Learning / Experimental Learning Experimental learning is the process of learning through experience and is more specially defined as learning through “reflection on doing”. Steps of Experimental Learning 

Concrete experience



Reflective observation

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Abstract conceptualization

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Active experimentation

Teacher – Guided Learning Teacher-guided learning helps to develop concepts by themselves and the responsibility for learning rests with them. This method encourages students to build research skill that can be used throughout their education experiences. Teacher – Guided Learning Sequence 

Focus



Learning check

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Independent work

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Rework/revise

Problem Solving Method Problem Solving Method is one which involves the process of reflective thinking to solve a different problem in a purposeful manner and in arriving at satisfactory solution. The Problem Solving Method is like a research method it involves scientific thinking of a process of learning. Steps in Problem Solving Method 

Indentifying problem solving



Collecting the data

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Formulating tentative hypothesis

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Testing the hypothesis

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Verification of the result

Teacher’s Role in Problem Solving Method 

The teacher plays an important role in Problem Solving Method

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Gives an atmosphere of freedom, defining and stating the problem

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Assists the students in accepting, defining and stating the problem

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Helps the students in breaking up the problem into simple units

Merits of Problem – Solving Method 

Problem Solving provides a real life experience to the students



It develops in students good habits of planning, thinking, reasoning and independent work

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This method serves individual difference

Demerits of Problem – Solving Method 

Not all the students are problem solvers



This method does not suit the students of lower classes.

Small Group / Whole Class Interactive Learning In this method teachers and students share their ideas through interaction. Teacher and students join together in their activities. Here group learning is encouraged. Student Seminar A seminar is a form of academic instruction conducted in an educational institution. It has the function of bringing together class students for recurring meetings, focusing each time on some particular subject in which everyone present is requested to actively participate. Each seminar brings together a group of students to explore and investigate a topic through learning activities including group discussions, research papers and presentations. Students‟ leader or a student nominated by teacher will chair the seminar. Teacher will supervise the functioning of seminar.

Group Discussion Group discussion is a new trend that has come up in order to evaluate student personality. A group of participants are made to discuss on a topic or subject for a limited time and then assessed accordingly. Advantages of Group Discussion 

It helps to shed away shyness of a candidate and brings his view point amidst all.

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It stimulates to think in a different new way.

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It helps the candidate in understanding his own strengths and weakness.

Mixed Ability Grouping Title clearly indicates “mixed ability grouping” refers to grouping together students of different abilities. Usually this kind grouping occurs in our class room. Group consist of students with different ages with one or two years span. In mixed ability group, there are some students that are more mature and experienced than other students and thus they have more advanced ability to acquire knowledge. Recent Trends in Teaching In these methods students get knowledge through experience or with the help of audio-visual aids and e-learning. Constructivist Learning Constructivism is a learning theory found in psychology which explains how people might acquire knowledge and learn. It therefore has direct application to education. The theory suggests that humans construct knowledge and meaning from their experiences. Characteristics of Constructivist Teaching 

The learners are actively involved

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The environment is democratic

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The activities are interactive and student-centred

Classroom Activities of Constructivist Learning 

Experimentation

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Research projects

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Field trips

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Films

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Class discussions

Benefits of Constructivist Learning 

Students learn more, enjoyable and are more likely to retain learning



Students learn how to think and understand.

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It is a transferable skill to other settings

Problem – Based Learning Problem – based learning (PBL) is a student-centred pedagogy in which students learn about a subject through the experience of solving an open-ended problem. Students learn both thing strategies and domain knowledge. Advantages of Problem-Based Learning 

It focuses on student-centred learning

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Collaborative research work takes place instead of Lecture Method

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It fosters in-depth learning

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It helps in self learning

Brain-Based Learning Brain based learning theory is based on the structure and function of the brain. As long as the brain is not prohibited from fulfilling its normal, processes learning will occur. BrainBased Education is best understood in three words: engagement, strategies and principles. You must engage your learners and do it with strategies that are based on real science. Principle of Brain Based Learning 

Brain can perform several activities simultaneously like tasting and smelling

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Learning engages whole physiology

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The search of meaning is innate

Collaborative Learning Collaborative learning is based on the view that knowledge is a social construct. Collaborative activities are most often based on four principles. 

The learner or student is the primary focus of instruction.

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Interaction and “doing” are of primary importance

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Working in groups is an important mode of learning.

Flipped Learning Flipped learning is an approach that allows teachers to implement a methodology or various methodologies in their classrooms. It means “School work at home and home work at school”. Flipped classroom inverts traditional teaching methods, delivering instruction online outside of class and moving “homework” into the classroom. Definition The flipped learning is a pedagogical approach in which typical lecture and home work element of a course are reversed. Short video lectures of instructional content are viewed by students at home before the class session, while in the class time is developed to solve problems exercise, projects or discussions with the guidance of the teacher. Four Pillars of Flipped Learning F - Flexible Environment L - Learning Culture I - Intentional Content P - Professional Educators Flipped Classroom The flipped classroom describes a reversal of the traditional teaching where students gained first exposure to new material outside of class, usually via reading or lecture, videos and then class time is used to do the harder work of assimilating that knowledge through certain strategies such as 1. Problem-solving

2. Discussion and 3. Debates Advantages 

Students take control of their learning



Student can develop foundation of factual knowledge

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Students can understand facts and ideas in the context of a conceptual framework.

Blended Learning Blended learning is about effectively integrating ICTs into course design to enhance the teaching and learning experiences for student and teachers by enabling them to engage in ways that would not normally be available in their usual environment, whether it is primarily face-to-face. Blended learning technologies are as follows. 

Broaden the space and opportunities available for learning



Support course management activities

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Support the provision of information and resource to students

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Engage and motivate students through interactivity and collaboration.

Definition 

The thoughtful integration of classroom face-to-face learning experiences with online learning experiences.



Mixed mode or hybrid-learning is the integration of face-to-face (F2F) learning with online learning activities.

e-Learning Trends E-Learning can involve a greater variety of equipment than online training or education, for as the name implies, “online” involves using the internet or an intranet. CD-ROM and DVD can be used to provide learning materials. Advantages of e-Learning 

Class work can be scheduled around personal and professional work, resulting in flexible learning



Reduces travel cost and time to and from school.

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Learners can study wherever they have access to a computer and internet.

Disadvantages of e-Learning 

Unmotivated learners or those with poor study habits may fall behind



Lack of familiar structure and routine may take time getting used to it.

Video Conferencing Meaning A video-conferencing is a set of interactive telecommunication technology which allows two or more locations to interact via two-way video and audio transmissions of groupware. This service is especially cost-effective and allows students and teachers from various parts of the world to see, speak, hear each other at the same time. Benefits of Video Conferencing 1. Expands learning opportunities 2. Adds excitement to traditional methods 3. Teaches planning and organizational skills 4. Teaches public speaking skills 5. Improves students‟ memory retention 6. Enhances students‟ understanding 7. Minimal investment 8. Time saving