EDU510 Assignment 1 solution| Spring
2023 | EDU 510 Assignment 1 solution
EDU510 Assignment 1 solution| Spring 2023
Q: Discuss
the various methods used for the teaching of Mathematics with examples? (15
Marks)
Answer:
1.
Lecture Method
It is the method
of presenting the word picture of an idea; or the method of imparting information through a speech.
Lecture is another
name for speech,
and when you are speaking
continuously to a class or an audience, you are considered to be
lecturing. It is the method of depicting everything in words.
Example:
Supposing “profit
and Loss” the topic in hand. The teacher goes
on telling and explaining „Well boys/girls, profit and loss is always to be
calculated on the cost price, because the cost price is our investment in the bargain
if you invest less and earn more you gain;
therefore, gain is to be calculated by subtracting cost price from the selling
price. When you invest more and earn less, you lose;
therefore, loss is to calculated by subtracting selling price from the cost price, so on and so forth”.
2.
Dogmatic Method
In this method of teaching
mathematics rigour is extremely emphasized. Rigour means the strict enforcement or observance of rules). The dogmatists say that the foremost educational value of mathematics
is the training in exactness which it amply provides. Mathematical knowledge observes a high standard of exactness. Any
deviation or departure from this standard of
exactness will defeat the very purpose of teaching mathematics, and will
consequently lead to inexact, aimless
and slipshod thinking. The advocates of this method ay that the inefficiency of mathematical teaching is mainly due
to lack of rigour.
Example:
Consider a math class where the
teacher uses a dogmatic teaching method. The teacher might simply provide a
list of formulas and equations for the students to memorize without delving
into the underlying concepts or their practical applications. The teacher may
not encourage questions or discussions that challenge the established
knowledge, and instead, expect the students to accept the information as
absolute truth.
3. Inductive and Deductive Methods:
It is a combination of two methods.
To be able to understand
this combination, one shall have to understand them separately.
·
Inductive method
It deals from concrete
to abstract, particular to general and from examples to general rule. It is the method of constructing a formula with
the help of a sufficient number of concrete examples. It is based on induction which means proving a universal truth
by showing that if it is true for a particular case and is further true for a reasonably adequate
number of cases, it is true for all such cases.
A formula or generalization is thus arrived at through a convincing process of
reasoning and solving of problems. After
a number of concrete cases have been understood, the student successfully attempts the generalization.
Example:
Ask students to
draw a few sets of parallel lines with two lines in each set. Let them
construct and measure the alternate
and corresponding angles
in each case.
They will find them equal
in all the cases. This conclusion in a good number of cases, will
enable them to formulate the relevant generalization.
·
Deductive Method
In this method, the learner proceeds
from general to particular, abstract to concrete
and formula to examples. A pre-constructed formula is told to the students and they are asked to solve the relevant problems
with the help of that formula. The formula is accepted by the learners
as a pre-established and well-established truth.
Example:
Find the area of a rectangle. Length =5 and Breath = 2
Formula:
Area of a rectangle = Length × Breadth
4.
Heuristic Method
The term Heuristic is derived from a Greek word which means I find. Here, the child is put in the place
of a discoverer. The method involves finding out by the student, instead of
merely telling of everything by the
teacher. It aims at removing the shortcomings attributed to lecture method. Contrary
to lecture method,
it demands complete
self-activity or self-education on the part of the learner.
It is a method by which pupils learn to reason for themselves. Professor
Armstrong was the originator of this
method. He devised it for the teaching of science. This method has been found useful in the teaching of mathematics also. It is
a sort of attempt to develop
in the learner a particular attitude, now popularly known as the scientific
and heuristic attitude.
Example:
The teacher might present a problem like investigating
the effects of different types of fertilizers on plant growth. The teacher
encourages the students to develop hypotheses, design experiments, collect
data, analyze results, and draw conclusions. The students are actively involved
in the process, asking questions, making predictions, and using their critical
thinking skills to find solutions.
5.
Analytic Method:
It proceeds
from unknown to known. Analysis means breaking up of the problems
in hand so that it ultimately gets connected with something obvious
or already known. It is the process
of unfolding of the problems
or of conducting its operation
to know its hidden aspects.
Example:
"All triangles have
three sides." This statement is analytically true because the concept of a
triangle inherently includes the idea of having three sides. By analyzing the
concept of a triangle, one can conclude that it must have three sides without
needing to consult empirical evidence or observe real-world triangles. The
truth of the statement is derived purely from the meanings of the terms
involved.
6.
Synthetic Method
It is the
opposite of the analytic method. Here, one proceeds from known to unknown. In particular, synthesis is the complement of analysis. To synthesize is to place things that are apart.
It starts with something already
known and connects
that with the known part of the statement. It starts with the data available or known and connects the same with the conclusion. It is the
process of putting together
known bits of information to reach the point where unknown information becomes
obvious and true.
Example:
"Water boils at 100 degrees
Celsius at sea level." This statement is synthetically true because it is
based on observations and empirical evidence. Through experimentation and
observation, scientists have determined that water boils at 100 degrees Celsius
under standard atmospheric conditions. The truth of the statement relies on
empirical data and cannot be deduced from the concept of water alone.
7.
Laboratory Method
Mathematics is a
subject which has to be learnt by doing rather than by reading. The doing of mathematics, gives rise to the need of a suitable method and a suitable place. Laboratory method
and the mathematical laboratories are proper answer to it. This activity
method leads the pupil to discover
mathematical facts. It is based on the principles of learning by doing,
learning by observation, and
proceeding from concrete to abstract. In one sense, it is only practical form
of the inductive method. It is more elaborated and practical form of the inductive
method. It makes the subject
interesting as it combines play and
activity.
Example:
The construction
work in geometry is on the whole a laboratory work. The drawing of a line, construction of an
angle, construction of a triangle or a quadrilateral or a parallelogram, etc.,
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