Methodology - Unit 2
Methodology - Unit 2
Subunit 1: Learning
Learning is the process of acquiring new, modifying existing, knowledge, behaviours,
or
based on meaningful
Mathematical thinking: construction of mathematical knowledge
experiences for students
mathomatics
students
Cbproxts
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College, Pathanapuram, EDU04.7: Theoretical base of
mathematics education
Subunit 1(b): Stages of learning
When I see the symbol "143' I do not
imagine one hundred and forty-three objects set out
before me. Symbols are an essential ingredient of mathematics. They condense a
concepts into 'manageable' form. You do not need to
hierarchy of
imagine one hundred and forty three
objects
in order to understand the
symbol "143", you do need to have understood our very useful
but
of notation, whereby the 4' system
represents four groups of ten and the 1 represents a hundred, which is
itself ten groups of ten. The Romans would have
symbolized the same number in another way. Such
notation enforces a complex thought
process than does our decimal notation. Symbols area very
important part of mathematics.
E-He sees, feels, tastes, holds, rolls and drops his ball. He has 'fun', and learns about many of its
properties,
L- He associates the sound of the word 'ball' with his toy. This is useful. If he says the word, he
may be given the ball to play with. He will soon associate "ball' with other objects that have the
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Mount Tabor Training College, itself. The picture
different from the ball
picture of a ball. The picture is very
with his own ball
P - H e recognizes a in common
to be called 'ball'.
'ball'. This is
that we write to represent the sound
later, he learns the symbol
S- Much
with a real ball, and it is only
properties at all in
common
has no
sophisticated. The symbol
"ball'.
sounds that utter in saying the word
artificially associated with the
we
in attaining
children need to progress through
As we proceed to analyse the stages that e
to the sequence
of abstraction,
we shall often refer
mathematical understanding and competence, only with
can be concerned
mathematics textbook for children, however carefully prepared,
1-p-s. A
children can start
the last two items pictures and symbols. No book for young
of the sequence,
where they need to start, namely with experience and spoken language.
the sequence of
Mathematics is widely regarded as an abstract subject. To help explain
Liebeck
mathematical concept, Pamela
abstraction that children need to forgo to truly understand a
area of maths that they are Both theories share similarities. Most obviously, both
learning.
their previous experiences when attempting to understand new
encourage pupils to draw upon
concepts.
Experience
As presenting children with data-orientated (abstract) worksheets would not give pupils any
connection to the 'real world', instead children should measure objects around the classroom
the
(fellow pupils, length of feet, playground area). Through this, pupils physically experience
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Mount Tabor Training College, Pathanapuram, EDU04.7: Theoreticalbase ofmathematics education
various properties of measurement through play, touch, feel and comparison in a way that related to
the real world. This is a fundamental part of Libeck's message.
A connectionist teacher will use past experiences by drawing connections to those of his
Language
Liebeck (1984) states the next
pupil has drawn upon their relevant experience,
Once a
board as it is the most effective tool when seeking to develop children's mathematical concepts.
Pictures
describe their methods, Liebeck (1984)
Once pupils have been encouraged to verbally
the
Once he calculates the number of objects in
the group he can be asked to copy exactly,
thus
of the other side of the picture. Then, he could count up both groups, and
group objects on
understand that a group of, say four, when doubled, equals eight
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mathematics education
EDU04.7: Theoretical base of
Pathanapuram,
College,
Mount Tabor Training the use of symbols
understánd a concept is
need to apply to fully form, they
The Final attribute pupils simplified
written
in a
apply their knowledge
to solve and that i n
(Liebeck, 1984). For pupils correct in stating
symbols. Liebeck (1984) is
the appropriate
need to know and recognise must have
abstract from, they
to understand
mathematical concepts in time to
order for pupils
must judge
when it is the appropriate
relative symbols. Yet teachers
understanding of the
introduce symbols to a pupil.
can be
at a very early age
to children
Research suggests that teaching conventional symbols
the conventional
ineffectual. This suggests that if children
are not yet confident in using
mathematical
their own symbols to represent
a particular
mathematical symbols, then devising
notion often gives them a greater understanding of a concept.
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Mount 1abor 1raining College, Pathanapuram, EDU04.7:
Theoretical base of mathematics education
be able to translate between
representations, within mathematics, between mathematics and other
areas as well; to communicate findings orally and in writing. Mathematics
gives people the power
and utility to express, understand and solve problems in diverse settings (NETM, 1985).
addition first and then multiplication. Otherwise, the latter will not signify much to the learner.
Mental maths is the process of doing mathematical calculations in your head, without the use of
a calculator, abacus or even pen and paper. This is used in many walks of life outside of the
Working out the cost of sale goods when shopping. For example, if there's a 20% off sale,
you'll know exactly how much you expect to pay.
Calculating a tip. If you dine out and receive a good service, chances are you'll leave a tip.
Metric conversions. You don't have to travel far to see measurement units change
Working out exchange rate. Ifyou enjoy a summer holiday abroad, you'll no doubt need to
there.
exchange currency to spend while you're
There are many other places mental maths is used, probably without even thinking about it, in
Many will argue that we now all have a calculator to hand in every life situation, thanks to
from good mental
ever-evolving smart phones. There are plenty of benefits for children, stemming
skills are
maths skills development. At a basic level, things like concentration levels and listening
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mathematics education
EDU04.7: Theoretical base of
Pathanapuram,
Training College,
Mount Tabor mental
arithmetic problem
as a result of practicing
is also improved efficient with use.
improved, and
self-confidence
stronger
and more
Subunit 2: Teacher
works in a classroom.
A teacher is a person who helps people to learn. A teacher often
There are many different kinds of teachers. Some teachers teach
Others teach older children in middle, junior
young children in kindergarten or primary schools.
colleges
high and schools. Some teachers teach adults in more advanced schools (for example,
high
and universities). Some are called professors
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Mount Tabor Training College,
Pathanapuram, EDU04.7: Theoretical base of mathematics
education
Definition
A teacher is one that
teaches; especially: one whose occupation is to instruct. A
thing that teaches something; that is a person or
person whose job is to teach students about certain subjects
There are different ways of teaching. Most teachers use a
variety of methods to teach.
Teachers often explain new knowledge, write on a blackboard or whiteboard, sit behind
their desks on chaira, help students with their work, or mark students' work. They may use
a computer to write tests, assignments or report cards for the class. A teacher in a sentence can be
The role of a teacher is to help students apply concepts, such as math, English, and science
through classroom instruction and presentations. Their role is also to prepare lessons, grade papers,
manage the classroom, meet with parents, and work closely with school staff.
The role of a teacher changes depending upon the grade in which they teach. Elementary
school teachers play an important role in the development of students. Aside from the primary role
of lesson planning and classroom instruction, teachers are taking on other roles in education. They
are:
Knowledge manager
Facilitator
Mentor
Social engineer
Teacher as knowledge manager
Teaching becomes a profession of knowledge management. Teachers use technology to
design projects and communicate with students on site or off site. They create knowledge systems
of projects. They use the knowledge systems for collaboration with students and with other
teachers.
Knowledge managers are whose main capital is knowledge. Working with the knowledge
means providing; updating and making children understand all the relevant information and
knowledge. For a child to survivein this competitive world he should possess knowledge on
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base of mathematics edn
Tabar Training College,
be high level ir
teachers must
So
various aspects. that of their profession.
as well a s
knowledge
own
professional
>Teacher as facilitator
Parents are the first mentors for any child and then are teachers. A teacher has a great power
fact that children are like
to influence all development of a child. Teachers need to realize the
over
hones his skills and prepares him for his challenging tomorrow
information
offer counsel and provide
Subunit 3: Teaching
function is to impart
Its special
the process of education.
Teaching is an important part of associated with 3
R's i.e.
skill. Teaching is usually three focal
develops understanding and among
knowledge, which is established
relationship
Arithmetic. Teaching is a is a tripolar
Reading, Writing and matter. Thus teaching
the subject
education- the teacher,
the student and
points in
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Mount Tabor
Training College, Pathanapuram, EDU04.7:
Theoretical base of mathematics education
process. Teaching is a process of interaction.between teacher and student.
The teacher and the
taught are active, the former in teaching and the latter in
learning.
Aspects of teaching:
1. Who is to teach?
A teacher is to teach.
2. Whom to'teach?
A child is to be taught.
3. Why to teach?
Teaching is not for storing information but to enabling the child to deveop his
various faculties.
,
4. What to teach?
Those experiences and activities are to be provided which enable the learner acquire
desirable knowledge, skills and attitudes.
5. How to teach?
This implies that the teacher must be well versed in methodology of teaching as well
as technology.
6. When to teach?
Teaching situations should be such as they develop motivation in the students to
learn.
7. Where to teach?
Classrooms, library, laboratory, workshops, playgrounds etc. are the various places
to carry on teaching.
Subunit 3(a): Phases of teaching
Teaching is to be considered in terms of various steps and the different steps constituting
the process are called the phases of teaching. The teaching can be divided into three phases:
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Mount Tabor Training College,
nstruction
Ev tlon eum
Eeorton S t a feedbmc
e t r e t l v e Phese o t - A e t i v es t m g )
Phases o f teaching
provided to students through suitable modes. It is the stage for actual teaching. All those activities
which are performed by a teacher after entering a class are combined together under interactive
phase of teaching. The teacher provides pupil verbal stimulation of various kinds, makes
explanations, ask questions, listen to the student's response and provide guidance. The major
Diagnosis
to their abilities,
A teacher tries to access the achievement level of his students with regrds
Reaction Process
The student
Here teacher observes the response of
the students to the teacher's questions.
various stimuli and teaching
has to lean the proper way of reacting and responding to the
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techniques presented to it. The teachers performs the following activities in order to analyze the
nature of verbal and non-verbal inter-action of teaching activities
The word maxim means a statement giving general truth or rule of conduct. A maxim is a
instruction. The
statement, which acts as a guiding principle to the teacher in the task of imparting
the active involvement and participation of the
maxims of teaching are very helpful in obtaining
of the learners and motivate
learners in the teaching learning process. They quicken the interest
them to learn. Some of them are as follows:
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Mount Tabor Training College, Pathanapuram, EDU04.7: Theoretical base of mathematics education
his means that what issimple and easy must precede the difficult and complex. That is,
the
subject matter should be divided into different
aspects and all these aspects should be arrange
according to the difficulty value of
the content.
3. From actual to
representative
when actual
objects are shown to children, they learn
Tor a
long time. easily and retain them in their minds
Representative objects in the form of pictures, models etc. should be used tor tne
grownups.
4. From
particular to general
This maxim is based
upon the effectiveness of the
inductive approach in drawing
generalizations. As per this maxim a number of
pupils should be enabled to arrive at particular examples should be given first and then
some
cases. generalizations by closely observing these particular
5. From
empirical to rational
A child's imagination is greatly aided by a concrete material. Things first and words after
is the common saying. Children in the beginning cannot think in abstractions.
In the teaching process, the teacher should move from definite to indefinite because we have
basis of
the knowledge of definite things and the known facts are more reliable. For example, on the
tables, we teach mathematics. With the help of tables we can teach how to solve the sums of
1aeas or children in theinitial stages are indefinite, incoherent and very vague. 1nese a are
to be made
definite, clear, precise and syvstematic, Effective teaching necessitates tnat
and
cv
idea presented should
stand out clearly in the child's mind as a picture.
to particular examples. Both inductive and deductive approaches have their own importance.
According to the famous philosopher Rousseau, we should follow nature. That is, the
teaching work should be done in a natural way. In this method, education should be
according
the physical and mental level of the
pupils. The application of this maxim of teaching proves
appropriate for teaching all types of subject matters and for all age groups.
Benefits of the maxims of teaching
Learns by doing
Subunit 5: Classroom
A classroom is a learning space, a room in which both children and adults learn about
things. Classrooms are found in educational institutions of all kinds, from preschools to universities,
and may also be found in other places where education or training is provided, such as corporations
classroom to provide a space where
and religious and humanitarian organizations. The attempts
outside distractions.
learning can take place uninterrupted by
Types of classrooms
hundreds of
of five or six to big classrooms with
Classrooms can range from small groups
lecture hall. A few examples of classrooms
students. A large class room is also called a and
used for IT lessons in schools, gymnasiums for sports,
are computer labs which are
warm, safe, and caring environment allows students to influence the nature of the activities they
undertake, engage seriously in their study, regulate their behaviour, and know of the explicit criteria
and high expeotations of what they are to achieve. Everything from the colour of the walls to the
arrangement of the desks sends impressions to students and can affect the way a student learns. The
main factors of classroom environment are
Emotional environment
Physical environment
Classroom climate
Psychological environment
Creating a positive learning environment is essential for success inthe classroom. Teachers
should create a welcoming atmosphere where student feel safe and willing to share. Classrooms
should represent the students equally and everyone should know each other's name. Teachers who
use humor in the classroom also create more positive environments.