Chapter −I
1.1 Introduction
Mathematics is a board term in its
range. Generally, it comprises the study of number and space, logical reasoning
and many more. Besides of its scope and range, the way of discoursing it varies
according to interest, standard and so on of the individual, which is a crucial
point to conduct the general background of mathematics and the recent trends of
pre-primary and primary education. Mathematics is the central part of the
school curriculum not only in Nepal
but also in the entire world. Every society has observed mathematics as basic
needs of human civilization. Mathematics has started at the infancy level from
the beginning of human civilization to the advanced level at 21st
century. New discoveries in mathematics and mathematics education are still in
the continuation. During this period its trends and nature had been changed,
still this is changing continuously and it can be predicted that it will never
be stopped. Today, other disciplines such as science, engineering, medicine and
technology may be handicapped without mathematics and the world can not run
smoothly without it. Thus the importance of mathematics realized due to its
role for the development of science and technology in one hand and the other,
it has become a gatekeeper in the life of the students for their carrier choice
in future study.
The term “trends of Mathematics
education” refers to its nature, style, internal characteristics and overall
qualities in the case of discovering and implementing the mathematics education
from past to present in different countries including Nepal. The
trends of mathematics education also connect the historical events of
mathematics in ancient period as well as modern period that deal about the many
mathematicians and their contribution. The contributions of mathematicians show
the trend of mathematics in that period and it provides easiness to compare it
with present mathematics and its trends.
In many
countries pre-primary, primary, lower secondary and secondary school education
has become compulsory for large number of children up to the age of 6 to 15-16
years. In Nepal, grade 1-5 primary (in which grade 1-3 pre-primary), 6-8 lower
secondary and 9-10 secondary, 11-12 higher secondary and higher secondary
onwards university level. National Education System Plan 2028 had classified
for these levels as 1-3(primary), 4-7 (lower secondary), 8-10 (secondary)
secondary onwards university level.
During the last couples of years
great change have been made in the teaching of primary school mathematics.
Important new contents has been added, major change have been made in the goals
in learning and in teaching procedures. This report tries to define the major
trends in the mathematics education of children from the beginning of their school
life up to the age of 10-12 years. In many countries this age no longer
indicates the end of compulsory schooling, but it is still very often the time
when a change occurs in this pattern of education. This is the age according to
piaget, which marks the end of the stage of concrete operation. Current
development is motivated by to desire which are complementary but different in
character: (i) to enhance the content of education by promoting standardizing
and simplifying power of mathematical thoughts with the objects of improving
each individual level of understanding and grasp of environment full of
mathematics situations (ii) to improve the learning process of every child and
to introduce the study of mathematical; ideas at the most appropriate movement.
During 1960, it was essentially the
first ideas which motivated will the reform at all level of education. It was
question of bridging the gap between mathematics taught in school and the
mathematics as developed by mathematicians.
1.2 Objective of the Study
This
study intended to accomplish the following specific objectives:
a)
To
identify d historical trends in pre-primary and primary education.
b)
To
identify the recent trends on goals, method, materials, role of the teachers,
research and problem in pre-primary and primary level education.
1.3 Limitation of the Study
This
report is one of the most important part of the educational institute
especially in Master’s Degree level in education because master’s level
education helps to produce one of the qualified, trained, higher level manpower
as well as researcher of many areas of the countries. So the students of M.Ed.
should be able to guide to this level. But it is so difficult to evaluate the
recent trends in mathematics at pre-primary / primary level. In detail, but in
this report the contents are background, objectives, historical trends, recent
trends (Trends in goals, contents, method and materials, Role of teacher,
Research) at pre-primary / primary level education and we arise conclusion and
suggestions as well as references.
Chapter −II
2.1 Historical Trends in
Pre-Primary and Primary Education
The mathematics education
had very much narrower concept in ancient period. In that time; no formal
school and institutions have been opened. Babylonian and Egyptian have used
stone, sticks to court their domestic animals. For the people in those period
mathematics was limited to number and computation of numbers. In ancient time
in Nepal, mathematics was learnt in “Gurukul Shiksha”. In an ancient period children were learnt from their parents.
Especially father taught for son works related to male in the society.
Similarly, mother taught for her daughter works related to female in the
society. After some time, education started from Gurulul system and the
children were learnt from this system.
The mathematics education has been developed through the contributions
of many mathematicians in different period of time. In Nepal, mathematics
education started after the advent of democracy in 2007 BS. In Nepal, school
levels as well as university level mathematics curriculum has been revised with
the recommendations of National Education Committee Report 2049 BS. The main
countries including Nepal have taken as an education issue for “Mathematics for
all” in order to bring drastic change in the trend of mathematics education.
2.2 Recent Trends in
Pre-Primary and Primary Education
The
recent trends on goals, method, materials, role of the teachers, research and
problem in pre-primary and primary level education is presenting as follows:
2.2.1 Trends in Goals of
mathematics Education
The
objectives of primary level in mathematics varied widely from country to
country, one consensus view has been appeared that fundamental goal of the
elementary school is no longer to help children acquire technique for solving
only. The trends rather emerge to provide them with a correct approach and a
real understanding of the mathematical concept associated with these
techniques, and a solid base for their continuing education in different manes.
i. Arithmetic Teaching
The word “Arithmetic Teaching” was
replaced by the word “Mathematics Teaching” with a view to integrate the
different domain of mathematics. The word mathematics does not use many
countries rather they wanted to use pre-mathematics or mathematical arithmetic.
Number as, quantitative literacy and mathematical literacy are the word being
used very confusingly. Quantitative literacy is widely used in North America. Although the objects of primary level in
mathematics varied widely from country to country.
ii. The Value of Attainments
In
many countries the role of selection and orientation in primary education is now
less important. There is a conflict between public’s expectation and training
provided for the teacher. The educational goal of the primary school is no
longer clearly detected by its most interest parties, parents, pupils and
teachers. The emerging trends have been shifted from arithmetical proficiency
and skills to creativity and pupil’s fresh abilities to cope with new
situation.
iii. Development
of an Exploratory Attitude
The most important trends are based
on the idea that there is no basic different between the ways in which a child
acquire knowledge and the way in which a mathematicians creates it and that as
a result the teaching of mathematics should be considered mainly as a
rediscovery.
The development of an exploratory
attitude is a goal, which has both a social and psychological basis. Socially,
the variety of questions in which mathematics occurs makes it impossible to
provide a child with sufficiently wide range of techniques to allow him to
confront all the problems he / she will meet in course of his / her life and
psychologically, the pupil does not learn mathematics by contemplating the complete
mathematical structures. But, by a reasoned dialogue, which it is a teacher’s
duty to foster. The pupil’s are presented with situations in which there are
several possible approaches to the solution, at different level of ability or
formal techniques, while care is taken not to discourage the various endeavors
or to favor one method of solution more than the other. Each pupil is capable
of doing something and can eventually move from one level of solution to
another if he is stimulated by discussion within the class.
iv. Intellectualization of Mathematics Teaching
Intellectualization means the
introduction of more precisely define mathematical concepts a more global
approach and better structural organization of knowledge. For eg. In a piece of
work on the measurement of areas there will be different type of manipulation
which will facilitate in succession compare objectives, define concepts,
construct instrument of measurement, improve instrument, produce objects,
relate different areas, develop formula for areas and volume etc. Honest
endeavor is to minimize the gaps between two societies one having a few scraps
of technical competence with little logical organization and other having a
well structured knowledge.
However, it seems that children are capable at a very
early age of creating, handling correctly and modifying according to their
needs, the simple mathematical language necessary for describing and studying well-chosen situations, while
respecting the principal criteria which constitute the efficiency of this tool
of investigation and communications; intelligibility, brevity, accuracy,
relevance, normality.
v. Mathematics as a
collective creation
Mathematics is an aspect of group
creation in which learning takes place in the form of working together
communicating with and helping each other, validating and appreciating their
results in a group. To perform above aims teacher should be also alert to play
a role of facilitator which seems to be an imaginary at present situation.
Increasing attention is being paid to
the aspect of group creation by the class at the primary level of mathematical
teaching. Mathematics is not the sole activity n which learning to work
together and to communicate with each other is an important part; but in
mathematics, especially in the early stages of learning, all the ideas and
concepts can be constructed by the children from activities devised for them.
Such concept of teaching also aims at giving the child opportunity to
appreciate both the futility of knowledge which is not shared, and the social
need to ascertain that one’s partner in a conversation possesses the same
models as oneself if communication with him is desirable and as a result, to
understand the benefit there is in helping him build that model.
This aim is very difficult to
achieve; it requires varied teaching methods adapted that the teacher become
much less apparent as a giver of information and much more available and alert
as an organizer and animator, this requires much greater professional ability.
Finally, the size of classes must be adapted accordingly; the optimum size is
probably somewhere between 20 and 25 pupils.
vi. Pre-primary Teaching
According
to psychologist child depends largely on the activities in which he has the
opportunity to participate. One goal of preschool teaching should therefore be
to devise activities for children which they do not necessarily find in their
family environment and construct their own pattern and structures. In most
countries no clear trends towards an intellectual approach in pre-primary
teaching can yet be importance in increasing. At this level we must concentrate
on affective problem rather than the cognitive problem.
First
of all it must be noted that the status of pre-primary education varies from
place to place. In many cases this stage of education does not even exist; if
it does exist, the attainment of skills is not an aim of prime importance.
Those who teach at this level receive a training which often differs from that
of primary school teachers, having little mathematics; they concentrate much
more on children’s affective problems rather than on the cognitive problems.
2.2.2 Trends in Contents of
Mathematics Education
The
pupil has often through that the content of primary education in mathematics
has changed completely. In actual fact, the modifications are on the whole
modest and arithmetic remains the central subject of mathematics teaching at
primary school level.
i. Operational Techniques
The implementation of the reform in
mathematics teaching at the primary level has given rise to research on the
problem linked with the attainment of operational techniques, and has afforded
an opportunity of once more laying open to doubt a large number of generally
accepted idea. The operational techniques are usually clearly separated from
the meaning of the operation that is mathematical definition, recognition of
situation where a certain operation leads to the solution of a problem.
Current research is attempting to
encourage integrated, progressive leaning, using meaning, repertoire, and
algorithms at one and the same time. The range of an operation’s meaning.
Limited at first, extends progressively by building in certain results that is
by establishing at first an algorithm using the part of the range of meaning as
a repertoire, brought about by new situations, allows an extension and
strengthening of the meaning of the operation. The development of the
repertoire is produced both of memorizing new results, judged more appropriate,
and discarding others little used; at the same time, the structuring of the
repertoire takes place in accordance with the algorithm, and in written leads
to simplification of it. At each stage a balance is established, and the
development is guided by considerations of economy. The algorithm used not
necessarily the same in a mental computation as in a written one; mental
computation plays an important role if reinforcing what has been memorize and
in simplifying algorithms.
We say that far from discarding study
of computation, primary teaching seeks to promote a better understanding of the
operation and a better control of the operational techniques by new methods
which encourage a reduction in the time devote to this study and avoid tedious
repetitions.
ii. Sets and Natural Numbers
The word “Sets” had been introduced
in a native sense to facilitate the number concept in the child with
veen-diagram creates automatic response of the children. People did think one
to one correspondence is important for the development of number.
The number concepts, taught in
primary school have been enriched, usually. Integral only, are introduced in
many countries usually beginning with temperature readings and playing games of
winning and losing points. These numbers are ordered by extending the number
line to the left. After fractions have been taught, the negative rational
numbers can be located on the number line.
iii. Computation and the
Extension of concept of Number
A trend has been seen developing in
the teaching of computation which may be termed structuralist, which emphasizes
mathematical structures with a view to changing the teaching of arithmetic with
the help of general ideas of transformations, relationships etc. Now it no
longer seems that the activities thus contrived encourage pupils to reach the
fixed goal in the expected way. This does not mean that such activities are
uninteresting on the contrary- but their interest lies in another direction.
For example, hoping to help in the
construction of (Z, +), the study of several finite groups is introduced in
which the elements are one –one mappings of a set onto itself, and where the
law of combination of mappings. The dynamic character of the mapping is brought
out by arrow diagrams or with the ideas of “function machine”. Combinatorics
was taught to allow the teacher to present open situations for investigation,
to organize their works, to discover through systematic exploration some
interesting properties of numbers and in many cases to actual demonstrations.
iv. Geometry
Great changes have come about in the
teaching of geometry. Some years ago this teaching was usually normative and
formal. A new kind of teaching is taking shape at present, incorporating the
skills of the former. Two trends stand out.
One is a structural trend in which a
simplified model of plane affine geometry is studied, starting with notions of
parallel lines and using parallel linkages and squared paper. The relationships
of incidence of parallel lines are studied as well as certain simple
transformations. The labeling of points by pairs of numbers them helps to
enrich this model by developing analytic geometry on D2 with an
approach to R2. A distance is introduced which is sometimes called
“taxi distance” which helps to set problems of type: find the shortest distance
between one point and a set of points; find the median point, etc. The solution
of these problems requires numerical investigation. Many other activities are
possible along the same lines.
The second is an exploratory trend
based on active participation. Children are given objects or plane figures to
calssify and the study of classification criteria helps to define certain
concepts such as polyhedrons, polygons, convexity, etc. Problem of reproducing
the object introduce some properties of symmetry, of the incidence of parallel
lines, and of some plane transformations, which also come into constructions of
tiling of the plane, and regular polygons or polyhedrons. The use of squared
paper helps to simplify certain constructions, facilitates these solutions by
introduction of numbers, and stimulates arithmetical research. The use of
assemblies of cubes affords an opportunity of setting and solving problems from
the point of view of shadow cast and representation with the help of
projections, etc. Many others activities may be introduced stimulated by the environment.
v. Probability and
Statistics
One of the most important of the new
subject stands firm after the penetration in elementary teaching is
probabilities and statistics. The various goals are as follows which
corresponds to four different levels of abstraction:
·
To
provide children with the experience of chance.
·
To
introduce a useful and precise vocabulary.
·
To
construct models of probability.
·
To
start a more systematic study.
Two principle trends can be discerned
in the teaching of probability. A first trend is restricted to the teaching of
statistics to meet the first two goals. A second trend deals more or less with
all four goals. There is a risk of stressing the third goal too soon and of
reducing the teaching of probability to a use of arithmetic and combinatory
techniques, and of making the simulations without the pupils having actually
constructed the models which justify it.
vi. Influence of Computer
Science
Three trends can discerned which shows
the effect of computer science in pre-primary teaching. A first trends is the
use of arrows, boxes etc, which encourages the understanding for the dynamic
aspect of mathematical thought much more easily then a classical arithmetic
written sequence.
A second trend is the use of diagrams
of the above type to solve and present the solutions of problems, and then to
generalize from one category of problems in which the terms are similar in
nature but different in value. Flow diagrams with or without loops are used
with the same end in view and also to describe algorithms etc.
A third
trend consists of using imaginary machines even if access to a computer is not practicable;
children are ready to write a program for n imaginary machine which as a rule can
only do elementary computation and which must be given precise orders to be
able to function. This program completes the children to be very strict in the
writing of instructions, and to clarify the properties they use in their
elementary instructions.
vii. Language and Logic
Reforms have often blamed in a sad
way which changing and increasing use of vocabulary in elementary grades. This
is a very popular trend that school vocabulary has always been found to contain
more means of indicating the pictorial representation that the signified
concepts. Many concepts can not be treated in class discussion by the teacher
or pupils other than through the intermediary of a pictorial presentation of a
concrete situation, which like any presentation, is accompanied by many other
things besides the concept itself.
No
country has probably been able to escape totally this language perversion,
which in other respect is probably no worse than that which has always existed.
One of the goals of reforms was and still is the disappearance of this
prevention. It is still out of reach and prolonged efforts are still required,
as this problem is for many people a question of teacher training and of
mathematical and didactic ability on the part of textbook authors.
Some
practices have been observed while using language phrases “The set of girls
wearing non-dresses”. Such non-mathematical and unnatural language made
mathematicians aware of pseudo-math-jargon. The current trend is to try and
avoid the trap of this artificial language which transforms what is easily
understood.
Now
learning the written language is often a slower process. The methods of
classification, organizing information, and substitution, developed in
mathematics, simplifying the learning of the written language in spelling as
well as in syntax. Therefore a reserve trend in the relationship between
mathematics and the written language. There is a trend to minimize the handicap
of an inadequate grasp of language which burdens children of a deprived
socio-cultural background.
2.2.3 Trend in Teaching
Methods and Materials
At
present pupils is the center of teaching process. Much thinking, many resources
have been done the empower students on their own to visualize the situation
where problem might be originated and solve on their own way.
i. Choice of Situation and Materials
The variety of situations presented
to pupils within the framework of mathematics, allows them to be shown
different aspects of mathematical activity. On one hand can see and emphasize
the application aspect of mathematics more. On the other hand, one may value
and emphasize the nature of mathematics i.e. discovery / rediscovery aspect of
mathematics more important. Of course, many situations combine these two
aspects. A balance is on the way to being established at present, but has not
been immediately discovered. At the outset of the reform, much more attention
was paid to the pure aspect of mathematics, in accordance with the principle
concern of time, which was to introduce the fundamental mathematical concepts
into teaching.
At the
other end of the scale one finds mathematical game or structured materials,
they encourage the certain of artificial situations which often depend on a
certain number of parameters on which the teacher can play in order to adapt
the activity to the children’s reactions.
One of
the aims of some current research is to characterize situations which may be
described precisely in terms of the teacher’s strategy corresponding to the
development of the pupil’s strategy of research. The universal trend of
providing more variety in the materials for presentation, by the use of square
paper, abaci, sketches etc, with the aim either of communicating or of
promoting the production of conjectures and investigations.
ii. Technological Recourses
Over recent years, certain technological resources for
written or pictorial communication have come into general use in the elementary
school. They make team preparation work of visual documents much easier and
provide the whole class with a good quality pictures. Some of these materials
are related to abaci and some are investigatory instruments. Some of them are
very expensive but essential to the new style of teaching. Some of them are of
low / less sophisticated would probably be better suited in many cases.
Some
countries also use the media to introduce activities to children, or even
something to relieve the lack of qualified teachers, but these facilities are
used more generally in teacher training. Pocket calculators continue to increase
in number; they can no longer be ignored by elementary education; they will
have to be combined with other the learning of operational techniques and
problem solving; they will provide an opportunity to explore more widely
certain areas where overlong numerical computations restrict possibilities at
present but research has still to be done in this field where there can no
question of leaving it to machine manufacturers.
iii. Books and School
Publications
Traditionally, a school textbook has
two distinct purposes. On one hand, the textbook suggests outline of lessons to
teachers, who use them adding examples, exercise and motivations, anecdotes,
etc. On the other hand, the textbook is a collection of exercise on
applications of taught materials.
A general
claim a textbook authors put that his book appeals more directly the pupils,
present more attractively, contains varied examples, supply open situations,
covering all kinds of areas, stores photographs, drawings, sketches, graphs
etc. A pupil can organize his work better than before by following his book.
Some authors go further in the direction of individualization and suggest,
instead of textbooks, collections of word-cards, forming a sort of programmed
teaching.
iv. Change of Methods as
Regards Pupils
The
child is no longer regarded as a receptacle for knowledge; he is urged to use
his intelligence much more. He finds more sources of motivation during his
activities. Mathematics may be considered according to various kinds of
diversity:
·
Diversity
of situations which allow the child to exercise his intelligence and skills in
the areas he finds interesting.
·
Diversity
of work methods which allows him successively to carry out his work at his own place, to take part in a group
within which the activities are shared out and where the findings are
discussed, to present his group in a collective discussion where he must
justify the results not only to the teacher but especially to his companies.
·
Diversity
of activities linked with mathematics. Unfortunately too many classes still
exist in which the pupil’s life is not organized in this way, but the work does
not allow the pupil to take any initiative. In extreme cases, content change
without method change leads to a lower standard of teaching. In fact the repeated
chanting of multiplication tables was an ineffective memorizing process, it was
aimed however at acquiring a useful skill; and accepted as such by the children
while chanting pupil even do not know what is expected of them.
v. Change of Methods as Regards Teachers
Teaching based on the idea that
mathematics is a creation by the class rather than passive recipients of
knowledge given by, becomes the most influential methods that before. The
teacher’s role is especially delicate. On the end he is called dogmatic and on
the other end he may be called as laissez-faire. He must remain neutral and
lead the discussion without showing his feelings or his ideas. These methods
are much more fatiguing for the teacher and also for the pupils because they
must bear periods of frustrations and lack of confidence when their early ideas
fail. This is the point where the teacher must judge whether he may help and
how he may do so. These methods demand special abilities on the part of
teacher. In the eyes of many people they seem costly both in time and energy.
These methods can only be effective if they are constantly used.
vi. Assessment
The attitude towards the assessment
of pupil’s work is considered as most difficult issues to reform. Previously
teacher had to evaluate a limited number of taught concepts and skills. The
current situation reveals that a certain perplexity is felt by all when faced
with the problem of assessment. One trend, can be discerned which consists in
arranging exercises during each activity which provide the teacher with an
opportunity of assessing the efficiency of his teaching, so that he may adapt
the sequel according to the difficulties he has noticed.
vii. Slow and
Handicapped Children
Slow children have always been the
despair of their teachers, who did not succeed in the helping them maintain the
same level as the others. It seems that the new methods of learning the wider
variety of activities and the more suitably adapted pace of the learning
children to overcome emotional blockages to their progress.
Much progress remains to be made in
this field where emotional questions play an important role. But the result
obtained leads us to think in favor of inclusive education (IE). The results of
such a separation are generally catastrophic on the psychological plane and
moreover unfavorable to collective creation. Physical or mentally handicapped
children are generally taken into specialist institutions, where the educators
have very little training in mathematics. Some of the experiments carried out
in an attempt to adapt the new approach to arithmetic in this field are very
promising. E. g. Diagrams with arrows, mini-computers available to defective
children and manipulative / visual representation to deaf and dumb children.
2.2.4 Trends in the Role of
Teachers
In
elementary teaching much more than at other levels of teaching, the role of the
teachers is fundamental. A reform, whatever it may be, can only succeed if the
teachers understand its aims are masters of the new content, and are capable of
modifying their teaching methods as a result. Naturally, they can not be
expected to modify their behavior in the desired way from one day to the next.
i. Freedom of Teachers in
their Teaching
It
must be remembered that the administrative and pedagogic organization of
elementary education varies widely from country to country, ranging from a very
centralized organizations, where the teachers receive strict directives, to a
decentralized organization, where the teacher accept a local education curriculum
which they themselves have often helped to define. The reform in teaching
generally is visualized by increasing the freedom of the teachers. Freedom of
the teachers has several aspects require the teachers to develop a strategy to
cope the prepared teachers an opportunity to teach as they wish according to
multiplicity of viewpoints concerning content, methods and goals. For the least
prepared teachers this state is uncertain and confusing. They do not accept
this idea rather they show their refusal.
ii. Teachers in the Teaching
Situation
Teachers
talk about the change in their way of teaching but resist about the change.
Some teachers adopt one method of teaching which produce what we call
caricature of the method chosen. Experience shows that a teacher only change
his teaching if he has opportunity to experiment with new patterns of behavior
and to note the reactions of the pupils to this change.
A
teacher is afraid of not being able to pick out the productive ideas in the
pupils suggestions. Many teachers are afraid of not having the necessary
capabilities, which places them in a very uneasy moral position for not
updating himself.
iii. Polyvalence of the
Teachers
Primary
level teachers are not the specialist. They must know many subjects. In many
countries the reform in mathematics teaching has been accompanied by teaching
reforms in other subjects. All subjects of elementary education have a common
aim. So, placing equal importance to other subjects should not be considered as
slow down in mathematics.
iv. Teacher Training
Most
teachers receive on initial training in which the levels of mathematics are not
high. In many cases not only the teachers but also their trainers have had to
redevelop their idea towards the new content. This at first led to an emphasis
on content much more than on methods.
The
current trend is to bring theoretical training in content and practical
preparation for the profession closer together, linking them by an
epistemological and didactical analysis. This development is only taking place
slowly, as the training institutions are often very lethargic, and their
burdens have increased with the in-service teacher training but without any
increased in their resources. As a result the trainers have therefore no chance
to think sufficiently about their work.
2.2.5 Effects of
Sociological Components on Math Education
When
reforms in mathematics teaching at school level became a matter of discussion
nearly everywhere in the world, during the sixties, the public and elementary
school teachers did not feel concerned. Elementary schools formed a closed
world in which the responsible persons were mainly guided by the social
sciences, especially the educational sciences. The educational sciences are
little concerned with the teaching of arithmetic. The progress observed into
the innovations was totally misunderstood.
i. Projects
The first innovations were the
introduction of professional mathematics and mathematical specialists into the
domain of elementary teaching in the form of commissions and projects. The
following trends can be discerned: (a) a structural tendency which emphasizes
the structures treating traditional subjects in a new way. (b) the language of
sets making much more autonomous unit of skill than a tool used in the quantitative
study of the environment (c) an empirical tendency which is done through varied
activities (measurement, geometry, function etc.) concerning on the didactic
approach rather than on a vertical logically arranged organization.
ii. Transformations
Change in current produced a shock
for the mathematics educators. It should be focused on method. Different view
points were observed. One of them was an article “Teaching of new mathematics”.
It should be concentrated rather on “New teaching of mathematics”. Change in
methods requires that teachers should have both a long psychological and
technological preparation. But to carry out this preparation certain resources
are necessary which have long demand in vain. The authorities understood the
need to provide teachers with training in content than training in methods when
innovations are preset in subject matter.
Teaching of real contents had to be
set at the same time in many countries. The role of publications became
therefore fairly important. It is through the intermediary of textbooks for the
pupils and accompanies handbooks for the teachers. The majority of teachers
came in contact with the innovations which it is their duty to teach. The early
textbooks, often hurriedly produced and relying only incidentally on the
author’s actual experience, helped to emphasize the gap between the initial
efforts and their implementation.
iii.
Difficulties
A gap is to be seen the
pedagogic wishes of the teachers. They are to pass on knowledge, to correct
through their teaching socio-cultural disparities and to encourage maturity in
the children. The teacher’s everyday practices are concentrating their efforts
on technical skills which reduce the cultural role of mathematics. These
cultural roles of mathematics do not convinced the parents who generally prefer
basic techniques in mathematics. The antagonism between two roles (cultural and
technical) expressed by many people as an erroneous idea. Many experiments show
that by incorporating cultural part will produce convince in delivering the
skill part of mathematics. Attitude towards mathematics plays a vital role in
this direction. Teacher should have opportunity during training, of practicing
mathematics themselves in a constructive way, and to look over mathematics as a
fine building for the children to climb one at a time.
2.2.6
Trends in Research and Problems
The most widely spread idea on elementary teaching of
mathematics are based on learning by conditioning. However, the reforms have
been introduced precisely to fight against this method of learning, which
seemed to have a special link with the learning of arithmetic.
When psychologist’s information on the child’s operational
stages coincided with t he endeavor to recognize mathematics into large
structures, it seemed an opportune moment for the creation of a new didactics
of arithmetic at the elementary level, based on the learning structures and
integrated with the wave of unification in scientific thought.
i. Current Research
Investigations designed
on the experimental base should be treated with caution. Numerous studies
designed to help teachers adopting short teaching session emphasizes learning
by conditioning. Researches that are based on the idea that all knowledge can
be reorganized in the framework of large structures, only interesting if it
encompasses enough things carried out at a sufficiently high level.
ii. Some problems
Recent years have seen
the appearance and formulation of many problems. Among the most important and
whispered tropics opened are:
a) What are the choices open to the children and
the choices open to the teacher? Can criteria of choices be
established so that the teacher may construct his strategies ?
b) Research on the operating conditions to prevent
knowledge becoming a theory detached from the problem at the classroom level as
well as at teacher training level.
c) Is
analogy a method of discovery structures?
d) Study of the importance of a child’s personal discovery as he
acquires knowledge and its effects on teaching methods.
e) Research into the
difficulties of slow learning or handicapped children. How can a diagnosis be
made, and what treatment can be provided which is not pedagogical but medical ?
f) Elaboration of didactical
theories taking the topological aspect of contents into account.
The study of these problems raises many political and
institutional issues which are not peculiar to research on mathematics
teaching. It makes difficult to study in a total and controlled manner the
whole of the innovation process, ranging from experiments with pupil’s to the
training of teachers and application in the classroom.
Chapter −III
3.1
Conclusions and Suggestions
Even if the new trend,
new technology, new method and new assessment systems are introduced in
mathematics education, it will not worth if implementation is not effective.
The developed countries have changed the school level mathematics curriculum on
the demand of 21st century. They have also implemented properly. But
many developing countries including Nepal is still waiting to do so
effectively. So for the improvement of mathematics education from pre-primary
school to university levels, some conclusions and suggestions are given in
following sections.
3.1.1 Conclusions
The mathematics education had very much narrower concept in
ancient period. In that time; no formal school and institutions have been
opened. Babylonian and Egyptian have used stone, sticks to court their domestic
animals. For the people in those period mathematics was limited to number and computation
of numbers. In ancient time in Nepal, mathematics was learnt in “Gurukul
Shiksha”. The mathematics education has been developed through the
contributions of many mathematicians in different period of time. In Nepal,
mathematics education started after the advent of democracy in 2007 BS. In
Nepal, school levels as well as university level mathematics curriculum has
been revised with the recommendations of National Education Committee Report
2049 BS. The main countries including Nepal have taken as an education issue
for “Mathematics for all” in order to bring drastic change in the trend of
mathematics education.
Most of the developed countries have computerized the
teaching of mathematics and use computer, internet in mathematics. The problem
of mathematics can be done by these means very accurately and immediately. But,
the Nepal is still waiting to introduce the computer in mathematics education.
At present, the structure and content of mathematics has changed drastically
and attempt carried out to make it relevancy and secondary level mathematics
seems to be overcome the domestic problems of people. In most of the
educational institutions of Nepal, the tendency of evaluating student is only
through paper pencil test detained twice or thrice a year. Most of the teachers
and institutions holds in mathematics written test by informing to the students
through examination schedule. Nepal has introduced the continuous assessment
system in school level but not implementing successfully. Some alternatives
assessment techniques such as class work, homework, participation and
regularity are used in Nepal but not sufficient and not applying in
mathematics.
The failure rate in mathematics is high in many developing
countries including Nepal. So, “mathematics for fail” is the main trend of
mathematics in Nepal. The trend of mathematics be made globalization in terms
of its new technology, new innovation and in order to provide basis
mathematical concept and skills at the lower secondary and secondary level. The
concept of computer and internet are related with mathematics from the
beginning of post-elementary level.
3.3.2
Suggestions
1) Mathematics curriculum
should be relevance to the life of learner, content should be included from
vocational mathematics and should help to provide mathematical power for the
student after completed the study.
2) School mathematics
education must be able to produce a mathematically oriented man who can observe
work, intensively, explore, widely, feel deeply, think seriously, describe quantitatively,
represent vividly argue logically, communicate correctly, solve problems
satisfactorily and make connection within and outside of mathematics.
3) For the improvement of
mathematics, we should reform appropriately in school structure, goal and objectives,
evaluation procedure, contents and its organizations, teacher training, effects
of computer and its use, applied and vocational mathematics, research in
mathematics education, government’s role and responsibility etc.
4) A sound national’s goals
and objectives should be formulated according to national’s need, socitey’
expectation, learner level, community and international trends in mathematics
education. Curriculum should be formulated accordingly.
5) The concept of
integration versus diversified mathematics curriculum should be emphasized.
Local level mathematics curriculum developments process and appropriateness of
mathematics for the twenty first century are highly increased.
References
Howard
Eves. An Introduction to the History of mathematics
Htt/www.google.com
Izaak Wirszup and Robort Streit (Editors). Development
in School Mathematics Teaching. Volume III, Proceeding of the ICME, NCTM.
Pandit, R.P.(2007). Recent trends in Mathematics
Education. Shantinager: Kathmandu.
Upadhyaya, H.P. (2010). Recent Trends in Mathematics
Education, Vidharthi Prakashan. Kathmandu.
