Problems of Teaching -

Learning in Mathematics at

Elementary Level

Ashwani Kumar Garg Regional Institute of Education (NCERT), Bhopal

National Focus Group (2005) on ‘Teaching of

mathematics’ has laid down the following

vision statements for teaching of

mathematics-

• Children learn to enjoy mathematics.

• Children learn important mathematics.

• Children see mathematics as something to talk about, to communicate, to discuss among them-selves, to work together on.

• Children pose and solve meaningful problems.

• Children use abstractions to perceive relationships, to see structure, to reason about things, to argue about the truth or falsity of statements.

• Children understand the basic structure of mathematics.

• Teachers are expected to engage every child in class.

Issues concerning Mathematics

education

• Shifting Narrow Aims to higher Aims

• Developing the connected understanding and the reasoning power among the students.

• Recreating fun in learning mathematics and applying mathematical ability in real life situations by students.

• Develop the interest and abilities of arithmetic in school.

Issues concerning Mathematics

education

• The function of a teacher is not only to impart new knowledge to the learner but also help him in comprehending new concepts, ideas and principles.

• Makes conscious efforts to create an appropriate learning environment in the school and make the education of the concepts and theoretical content more and more interesting and effective.

Reasons behind regarding

mathematics a difficult subject

• Due to language problem students do not understand the question properly.

• During classroom teaching teachers do not use mathematics related teaching learning materials. In course of classroom observation some schools (about 25%) were found to have teaching learning materials in the classrooms but teachers do not use them during teaching.

• Many schools do not have a separate mathematics teachers in the school. One teacher teaches all subjects in a class.

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• Lack of effective and separate mathematics teachers training. During in-service teacher training some emphases to mathematics training was given, but content and process was not sufficient.

• During classroom teaching teachers do not give sufficient emphasis on each learner.

• Teachers do not give sufficient time to CCE and students practice during classroom teaching.

• Some States’ mathematics books do not have sufficient exercise.

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• Lack of teaching numbers through

concrete objects

• Lack of teaching in sequential order

• Lack of opportunities for frequent

practice

• Stress on cramming rather than on

practice

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• Teaching-mathematics without understanding the comprehension level of students

• Irregular attendance of students in the school

• Teaching Mathematics without using teaching-learning material

• Introducing a new lesson, without ascertaining the previous knowledge of children

Cont _ _ _ _ _ _ _ _

• Lack of efforts on the part of the teacher in

enhancing pedagogy level

• The uninteresting process of teaching

mathematics

• Conscious effort for ensuring the active

participation in class-room process

• Teaching mathematics without preparation

• Lack of understanding of hard spots for

students

Cont _ _ _ _ _ _ _ _

• Teaching Mathematics without linking it with the local environment

• Hurting students’ self esteem

• Lack of encouragement given by teachers to pupils

• Linking the teaching of mathematics with competency development instead of teaching it with the purpose of completing the course

• Irregular checking of written work and home work of students

• Lack of grade-wise teaching in classroom

• Lack of Mathematics Laboratory

Some Suggestive Strategies

• Teaching mathematics through games

• Developing curiosity in students and

satisfying it properly

• Art of asking questions

• Communication

• Using appropriate Methods for Teaching

Mathematics

• Linkage with the other subjects.

• Need-based mathematics.

TEST PAPER FOR KNOWING BASIC MATHEMATICS SKILLS

Max. Marks: 40 Time: 1.30 Hours

Note: Attempt all question. All Questions are equal Marks.

Questions Solved Wrong

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Mistakes

Cont..

Cont..

Cont..

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Method Selection Point

Method

Selection Point

Why to teach?

How to teach? i.e. What are the

various methods?

How can we remove those

problems?

What are the problems in

using these methods?

Whom to teach?

What to teach?

Which method is the best?

Methods

Methods of Teaching

Mathematics Teaching

Lecture-cum-

Demonstration Method

Heuristic Method

Problem-solving Method

Demonstration Method

Inductive-Deductive

Method

Laboratory method

Lecture Method

Analysis-Synthesis

Method

Project Method

Play-way Method

constructivist Following are some of the guiding principles of constructivist thinking

that teacher keep in mind during instruction.

• Learning is an active process where children construct meaning to their experiences.

• Learning is a process of changing meaning.

• In the process of learning children learn how to learn.

• Providing reflective activities as learning experiences would help in meaning making process.

• Learning and language are interdependent as learning involves language.

• Children learn in association with others as learning is a social activity.

• Learning is based on previous knowledge (what already known), experiences and beliefs and hence it is contextual.

• Learning requires time for significant learning we need to revisit ideas, ponder them, try them out, play with them and use them.

• Motivation is a key component in learning.

• Focus of learning is to understand parts in the context of whole. Hence learning process should facilitate children to understand the concepts as a whole but not in segregation.

Making Equilateral Triangles from

Knotted String

Activity: To verify that the sum of the three

angles of a triangle is two right angles.

Activity: To find the area of

Circle

So Area of circle = Area of ABC = ½ × BC × AH = ½ (2 r) r = r2

Area of the rectangle = l × b l × b = ½ × 2 r × r = r2 units.

Activity: To determine the total surface area of a given

closed right circular cylinder.

Curved surface area of cylinder = Area of rectangle

= length × breadth

= l × h = 2 r h

Both ends of cylinder are circle, each of area r square.

Total surface area of cylinder = curved surface area + 2 area of circle

= 2 rh + 2 r square

= 2 r ( h + r)

Mathematics for Entertainment

• To provide opportunity for the use of mental power;

• To emphasize the practical value of Mathematics;

• To acquaint with the application of Mathematics in learning other subjects of curriculum;

• To acquaint with the vocational value;

• To acquaint with the cultural value;

• To acquaint with the entertainment or recreational value;

• Through practical work;

• Principal of change and variety and

• Necessary facilities for learning and teaching.

Mathematics for Entertainment

• Problem 1: Place eight solders in the 8×8

square given below so that

1. Three is one and only one soldier in each row

and in each in each column,

2. No two soldiers are in any diagonal.

• Problem 2: A monkey climbs up a pole of height

12’. The monkey climbs 3 feet in one hour and

then slips back 2’. In how many hours does the

monkey reach the top?

Mathematics for Entertainment

• Problem 3: A person owns a wolf, a goat and a cabbage and he has to take these across a river in a boat which can accommodate only one more beside himself. If left alone, the wolf will eat the goat and similarly if the goat is left alone with the cabbage the goat will eat it. How should the crossing be done?

• Problem 4: A gardener want to plant 10 plants in such a way that there are 4 plants in each line and there are 5 lines in all. Can you draw the design of his plan?