The document discusses different learning aids that can be used to help students understand abstract mathematical concepts. It describes how examples, illustrations, models, and hands-on objects can make abstract ideas more concrete. Specifically, it outlines graphical aids like diagrams, charts, and graphs, display boards like blackboards and bulletin boards, and three-dimensional aids like models, real objects, and mock-ups. The learning aids are meant to stimulate student participation, make teaching more engaging, and help students apply mathematics in different situations.

1. Welcome

2. Concretisation of abstract
ideas in Mathematics and
different learning aids

3. Concretisation and abstract ideas in Mathematics
 For many students, grasping concrete mathematics is the easiest part of learning
math.
 Abstract mathematics requires the student to tie previous mathematical
knowledge to bridge the gap between past and new knowledge that has not been
demonstrated to the student.
To solve these problems we use examples, illustrations and different types of
learning aids.

4. Example
Examining examples and non-examples can help students understand
definitions. For example, a square may be defined as a quadrilateral with four
equal sides and one right angle, seeing concrete examples of squares of various
sizes, as well as considering rectangular non-examples, can help children
clarify the notion of square.
Modelling examples
These are the classic ‘Worked examples’ where a process or procedure is
modelled to students so they can see it in action. For example, working through
an application of the quadratic formula, using numbers instead of a, b and c.

5. Non-examples
• These are brilliantly useful and often underused.
• Non-examples deliberately do not hold certain properties
or do not meet required definitions, so looking at non-
examples serves to clarify the boundaries of a concept or
a definition.
• Non-examples are most useful when presented alongside
specific or particular examples, because we can see the
contrast clearly.

6. Learning aids
Learning aids are the tools that teachers use them in the
classroom such as flash cards, maps, cassette and blackboard.
A learning aid is a tool used by teachers to help learners
improve reading and other skills, illustrate or reinforce a
skill, fact or idea, and relieve anxiety, fears or boredom.

7. Significance of learning aids
 They may help in clear understanding of the learning material and for
clarifying the abstract ideas by making them concrete.
 They simulate pupil participation
 They are based on ‘learning by doing’.
 Make teaching-learning process interesting.
 Help in saving time and energy.
 Help in creating a lasting impression in the mind of the learner.
 Facilitate in the application of mathematics in various situations.

8. Different types of learning aids
There are so many abstractions in mathematics, which cannot be easily
followed by the students. To make such abstract ideas rather concrete
teacher takes the help of various teaching aids. These teaching aids are
otherwise known as learning aids it can be classified into
1. Graphical aids
2. Display boards
3. Three dimensional aids

9. Graphical aids
Graphics are instructional materials that summarise significant
information and ideas through some combination of drawings, words,
symbols and pictures. Major graphic aids are graphs, diagrams and chart.
 Graphs:
A graph is a visual representation of numerical data. They are used
to consolidate data, analysis, comparison and interpretation. There are
many kinds of graphs

10. 1.Line graphs- They are used to compare the magnitude of
different measures of any given variable.
2.Bar graphs- The difference in their Heights could be
visualised and conclusions could be drawn.
3.Sector / pie graphs- They are used when a whole is divided
into parts.

11.  Diagrams (drawings):
Diagram is a condensed drawing consisting primarily of lines and
symbols designed to represent the outline, interrelationship or key
features of a process or idea.
 Charts:
A chart is combination of pictorial, graphical, numerical or normal
materials designed to present a clear visual summary of an important
process of set of relationships. For class room purpose we use two kinds
of charts.

12. 1. Outline and tabular charts
The organisation of the content into an outline of key points and sub
point, which a teacher may present systematically on the blackboard
result in useful chart form. Tabular charts present information as tables,
the points to be stressed being presented in rows and columns.

13. 2. Flow charts
Item such as tabulation and graphical representation of
data can be subject of flow charts.

14. Display boards
The stereotyped atmosphere of traditional class room, libraries and
corridors of schools is recently giving way to attractive and educational
surroundings with a variety of display materials.
 Black boards:
Black board or chalkboard still continues to be the most effective and in
dispensable visual aid for the classroom teacher. Without the use of blackboard,
the teaching of mathematics is impossible. Blackboard is the second tongue of
the mathematics teacher. The purpose of blackboard is

15. a.To write statement of problems and their solutions.
b.To write terms, symbols, formula.
c.To draw diagrams, figures.
d.To plot graphs.

16.  Roll up chalk board:
Rollup chalkboards are that which
can be conveniently rolled up. They are made up of
rexin cloth. The charts and pictures can be drawn on
it well in advance and presents as and when required.
 Bulletin board:
The bulletin board, as the name implies, is a
board for exhibiting bulletins and news items of
absorbing interest to the students.

17.  Pegboard:
Pegboards can be used for compiling flat
and even three dimensional materials, the latter
being supported by specially made hooks and
clips.
• Flannel board:
Flannel board have fibre surface to which
similar materials will adhere. This can be
prepared by stretching a suitable size of flannel
cloth on a heavy cardboard. Only flat, light
weight teaching material can be fixed on flannel
boards.

18.  Magnetic board:
A magnetic display will be useful to show the
relative movements of element of a visual. A sheet
of iron together with a piece of magnet can be used
for the magnetic board.
 Plastigraph board:
Any smooth polished surface like a glass
plate or rigid sheet may serve as a plastigraph board.
Plastic sheet may serve as a plastigraph board. Plastic
sheets of different colours cut to required shapes and
patterns may serve as display material.

19. Three dimensional aids
Models, objects, specimen, mock ups, realia, diorama and puppets are major
3-D aids used in classroom.
 Models:
Models are concrete representation of objects, their size being adjusted
to make if handy and conveniently observable. These are mostly three dimensional
or sectional and can clearly exhibit the structure of functions of the original. Most
often models prove to be more effective than the real ones.

20.  Objects:
Objects may be defined as the real things collected from their
natural setting. They are the most useful and most effective means of
providing direct experiences to the pupils. Some examples of real objects
which are generally used in mathematics teaching are beads, balls, coins,
sticks, weights, balance, measuring tapes, scale etc.
 Specimen:
A typical objects or an object, which has been remove for
convenient observation.

21.  Mock-ups:
When direct first-hand experience is either impractical or
impossible, mock-ups can be used. Mock-up is an imitation of the
real process.

22. Thankyou