MATHEMATICS
PROJECT: THE RELEVANCE OF MATHEMATICS AS A CORE SUBJECT IN SENIOR SECONDARY
SCHOOLS IN NSUKKA LOCAL GOVERNMENT AREA
CHAPTER
ONE
INTRODUCTION
Background Of The Study
The
21st century requires equipping children with basic education
in literacy and numeracy, as the more advanced completes skills needed for
living that can serve as the foundation of life, enabling the children to adapt
and change life abetting to life changing circumstances. Basic education remains
the most important factor that enables the very process in enhancing knowledge,
skills and attitudes needed for societal and national growth of any country of
the world. Learning is an activity of acquiring and applying knowledge to
facilitate meeting individual needs.
The
objectives of secondary schools as stated in the national policy on education
(NPE: 2004) are:
1. Preparation for useful living in the society
2. Preparation for higher education
The
junior secondary schools (JSS) refers to education that is prevocational and
academic designed to enable students acquire further knowledge other than
acquisition of literacy and numeracy and also develop basic life skills. This
level of education is for children of about 12-14 years and it is for three
years. The curriculum has on education are:
1. English language
2. Mathematics
3. Creative Arts
4. Basic science
5. Agriculture
6. Basic Technology
7. Business studies
8. Civic Education
9. Social studies
10. Home Economics
11. Physical and health Education
12. Christian Religious knowledge
The
knowledge acquired at this level provides the children with the ability to cope
with issues, relating to the entire spectrum of their survival, well-being
knowledge on how to deal with people and situation encountered. It also helps
them to interact with others and appreciate their own rights and respect opinions
of others. Students who have finished with this level of education and are
equipped with a little vocational knowledge for survival will go to the next
level which is the senior secondary school (SSS). This section of education is
academically and vocationally designed for those waiting to complete the six
years circle. Its core subjects in the curriculum are comprehensive and
designed to broaden students’ knowledge and outlook.
The Core Subjects Are:
1. English language
2. Mathematics
3. One Nigerian language
4. Physics or chemistry of Biology
5. Literature in English or history or Geography
6. Agricultural science
The
core subjects are basic subjects which will enable students offer and study a
particular course in higher institution of learning if need be. Mathematics is
a field of study or subject in schools.
The
origin of mathematics as a core subject in secondary school system may have
been an attempt by the policy makers to solve certain quantitative problems of
human’s daily life. Today, the importance of mathematics permeates all aspects
of human endeavour. Mathematics as the queen of sciences cannot be completely
separated from other sciences. Increasingly, applicants for the best employment
opportunities will need a good grasp of science mathematics and computer
technology. Mathematics as a core subject is one of the most important subjects
in secondary school education both in senior and junior secondary schools.
Mathematics is relevant for both those students who are likely to continue to
tertiary level of education and those who will not proceed. It equips students
with a body of knowledge to make them functional and socially relevant in the
fast changing world (Marcus 2010
Statement Of The Problem
Students
say that mathematics is a hard or difficult subject. Some agree that
mathematics is the hardest subject known to man. Some say that it ought it is
the hardest nut to crack. The rest believe that mathematics is meant for the
intelligent ones and should be studied by them alone. So many ask questions
like “why do we do mathematics?” “how and where do we apply the knowledge of
mathematics?” These questions and more other questions are being asked on daily
basis. So many have concluded that nothing on earth will make them know or
understand mathematics again. A good number of students frown fret at the mere
mention of the name “mathematics”. All these complaints and problems have not
stopped the study of mathematics in schools.
But
despite all the hatred students have on mathematics, mathematics was made and
is still one of the core subjects in both senior and junior secondary schools.
Despite the fact that many students have concluded that mathematics is hard,
“no go area”, insurmountable, difficult, it is still made compulsory for every
student even up to the tertiary level of education. Every student in the
college of education offer mathematics from the first year to the final year.
Some universities made it compulsory for every first year student.
The
researchers have therefore decided to study the relevance of mathematics that
made it to appear as one of the core or compulsory subjects despite the hatred
students have on mathematics in Nsukka Local Government of Enugu state.
Purpose Of The Study
The
purpose of this study is to investigate the relevance or importance of
mathematics to the education of the students. Our study specifically sought to:
1. Find out those factors that make mathematics
relevant to the education of the Senior Secondary School Students.
2. Find out the factors motivating the students to
learn mathematics.
3. Find out the application of mathematics in senior
secondary .
Specific Purpose:
Our study specifically sought to
1) Find out the benefits of teaching mathematics in
schools
2) Find out the ways materials would be used to
improve the performance of the students in the subject.
3) Find out the extent teachers would improve in the
subject
4) Find out the ways by which mathematics is relevant
to other subjects.
Research Questions
To
help the researchers in conducting this study, the following research questions
were posed:
1. What are the benefits of teaching mathematics in
school?
2. Are adequate instructional materials used in the
studying of the subject?
3. Are teachers encouraged to teach the subject
matter?
4. Is mathematics relevant to other subjects?
Significance Of The Study
The researchers have embarked on this
study in order to
1. Determine the benefits of teaching mathematics in
schools
2. Ascertain how the use of materials in teaching
mathematics will improve the performance of the students in the subject.
3. Determine the extent the use of necessary
incentives will improve teachers performance in teaching mathematics.
4. Determine the relevance of mathematics to other
school subjects
5. Make necessary contributions.
Scope Of The Study
The study is delimited to the relevance of mathematics as a core subject in
senior secondary schools in Nsukka Local government Area of Enugu State
Definition Of Basic Concepts
Mathematics: Mathematics is the
knowledge, learning and study of topics such as quantity (number) structure,
space and change.
School: A school is an institution
designed for the teaching of students or pupils under the direction of
teachers.
Relevance: Relevance is the concept of
one topic being connected to another topic in away that makes it useful to
consider the first topic when considering the second.
Core: Core is the central, innermost or
most essential part of anything.
Subject: A subject is a branch of
knowledge as a course of study.
CHAPTER
TWO
REVIEW
OF RELATED LITERATURE
This introduction attempts to examine the related work to this study. In this
regards, literature would be reviewed under the promoting headings.
1. The meaning of mathematics
2. The nature of mathematics
3. Meaning and relevance of mathematics Education
4. Objectives of mathematics education
5. Problems of teaching and learning Mathematics
6. Recommended solutions to the problems of teaching
and learning Mathematics
The Meaning Of Mathematics
According to Maria et al (2005), mathematics
is both the language and the tool of the sciences which enables the scientists
to carry out their work, solve their problems, interpret their findings and
inventions, investigate and predict the future and generally improve the world.
They further stated that “without mathematical methods and symbols, the
scientists would be very handicapped in their work”. Mathematics is both the
language of the scientists as well as of people in everyday life.
Galileo Galilei cited in Marcus (2010) said, “The universe cannot be read until
we have learned the language and become familiar with the characters in which
it is written It is written in mathematical language and the letters are
triangles, circles and other geometrical figures, without which means it is
humanly impossible to comprehend a single word. Without these, one is wondering
about in a dark labyrinth”. This means that mathematics is the language of the
universe.
According to Amujiri and
Eya(2013),Mathematics refers to the science of quantity and space. It is a
systematic, organized and exact branch of science. Mathematics provides an
appropriate tool of communication amongst scientists for the understanding of
theories.
According to Zieglar (2011), mathematics is the study of topics such as
quantity (number), structure, space and change. Mathematics is the abstract
science of numbers, quantity and space either as abstract concepts (pure
mathematics) or as applied to other disciplines such as physics and Engineering
(applied mathematics).
The American Heritage Dictionary defines mathematics as the study of
measurement, properties and relationships of quantities and sets using numbers
and symbols. It is an abstract representational system used in the study of
numbers, shapes, structure, change and relationship between concepts.
Carl Friedrich Gauss referred to
mathematics as “The queen of the sciences”
Benjamin (1992) called mathematics “the science that draws necessary
conclusion”.
Hilbert in Birkhauser (1992) said mathematics “we are not speaking here
of arbitrariness in any sense. Mathematics is not like a game whose tasks are
determined by arbitrary stipulated rules. Rather it is conceptual system
possessing internal necessity that can only be so and by no means otherwise”.
The Nature Of Mathematics
Albert (1923) stated that “as far as mathematics refers to reality, they are
not certain, and as far as they are certain they do not refer to reality”.
`
Mathematics relies on both logical and creativity and it is pursued both for a
variety of practical purposes and for its intrinsic interest. For some people
and not only professional mathematicians, the essence of mathematics lies in
its beauty and its intellectual challenge for others, including many scientists
and Engineers, the chief value of mathematics is how it applies to their own
work.
Mathematics is the science of patterns and relationships. As a theoretical
discipline, mathematics explores the possible relationship among abstractions
without concern for whether these abstractions have counterparts in the real
world. The abstractions can be anything from strings of numbers to geometric
figures to sets of equations. In deriving for instance, an expression for the
change in the surface area of any regular solid as its volume approaches zero,
mathematicians have no interest in any correspondence between geometric solids
and physical objects in the real world (Devlin 1996).
A central line of investigation in theoretical mathematics is identifying in
each field of study a small set of basic ideas and rules from which all other
interesting ideas and rules in that field can be logically deduced.
Mathematicians like other scientists, are particularly pleased when previously
unrelated parts of mathematics are found to be derivable from one another or
from some or more general theory. Part of the sense of beauty that many people
have perceived in mathematics lies not in finding the greatest elaborateness or
complexity but on the contrary in finding the greatest economy and simplicity
of representation and proof. As mathematics has progressed, more and more
relationships have been found between parts of it that have developed
separately-for example: between the symbolic representation of algebra and
spatial representations of geometry. These cross-connections enable insights to
be developed into the various parts; together, they strengthen belief in the
correctness and underlying unity of the whole structure.
Many mathematicians focus their attention on solving problems that originate in
the world of experience. They too search for patterns and relationships, and in
the process thy use techniques that are similar to ones used in doing
theoretical mathematics. The difference is largely one of intent. In contrast
to theoretical mathematicians, in the example given above, might study the
interval pattern of prime numbers to develop a new system for coding numerical
information, rather than as an abstract problem. Or they might take the
area/volume problem as a step in producing a model for the study of crystal
behaviour (Delvin 1996).
The
result of theoretical mathematics often influences each other. The discoveries
of theoretical decades offer to have unanticipated practical values. Studies on
the mathematical properties of random events, for example; led to knowledge
that later made it possible to improve the design of experiments in the social
and natural science. Conversely, trying to solve the problem of billing long
distance telephones users fairly, mathematicians made fundamental discoveries
about the mathematics of complex networks. Theoretical mathematics, unlike the
other sciences is not constrained by the real world, but in the ling run it
contributes to a better understanding of that world.
Mathematics Education
According to Wikipedia, mathematics education is the practice of teaching and
learning mathematics along with the associated scholarly research.
Researcher in mathematics education are primarily concerned with the tools,
methods and approaches that facilitate practice or the study of practice,
however, mathematics education research has developed into an extensive field
of study, with its own concepts, theories, methods, national and international
organizations, conferences and literature.
Relevance Of Mathematics Education
Galieo Galilei quoted in Marcus (2010) said, “The universe cannot be read until
we have learned the language and become familiar with the character in which it
is written. It is written in mathematical language and the letters are
triangles, circles, and other geometrical figures, without which means it is
humanly impossible to comprehend a single word. Without these one is wondering
about in a dark labyrinth”.
Education should be started with mathematics. For it forms the well designed
brains that are able to reason right. It is even that are able to reason right.
It is even admitted that those who have studied mathematics during their
childhood should be trusted, for they have acquired solid bases for arguing
which becomes to them a sort of second nature.
Mathematics is around us. It is present in different forms whenever we pick up
the phone, manage the money, travel to place, play soccer, meet new friends;
unintentionally in all these things mathematics is involved. For examples, in
cooking, we apply percentage, in Bank. We apply saving and credit (Arithmetic),
medicine/pharmacy. We apply percentage. We apply probability in the chance to
win lottery. We apply geometry in clothing, house decoration, art,
architecture.
Carl Friedrich Gauss referred to mathematics as “the queen of sciences”. This
implies that mathematics is the sense behind all the sciences.
Maria
et al (2005) deduced that “without mathematical methods and symbols, the
scientists would be very handicapped in their work”. Mathematics is both the
language of the scientists as well as of people in everyday life.
Most
of the school subjects cannot be harnessed without the application of
mathematics for example, Algebra is applied in computer sciences, cryptology,
networking, studying of symmetry in chemistry and physics, Calculus
(differential equations) is applied in chemistry, physics, engineering, the
motion of water, rocket sciences, molecular structure, option price modeling in
business and Economics model etc.
None
of the social and natural sciences can be fully discussed without the
application of mathematics.
Students are encouraged to give serious attention to their future. The career
world is competitive. Most of the university degrees require mathematics. Students
who choose not to take mathematics seriously or to ignore it in high school
forfeit many future career opportunities that they could have. They essentially
turn their backs on more than half the hob market. The importance of
mathematics for potential careers cannot be over emphasized. It is almost
impossible to get through a day without using mathematics in some way, because
our world is full of numbers to handle and problems to solve. Studying
mathematics provides you with the tools to make sense of it all, making life
that little bit easier.
So we can conclude that mathematics
play an important role in our daily life.
Objectives Of Mathematics Education
According to Maria et al (2005), at
different times and different cultures and countries, mathematics education has
attempted to achieve a variety of different objectives. These objectives have
included:
1. The teaching and learning of basic numeracy skills
to all students.
2. The teaching of practical mathematics (arithmetic,
elementary algebra, trigonometry) to most students to equipping them to follow
a trade or craft.
3. The teaching of abstract mathematical concepts
(such as set and function) at an early age.
4. The teaching of abstract mathematical concepts
(such as set and function) as an example of the intellectual achievement
of the modern world.
5. The teaching of selected areas of mathematics (such
as Euclidean geometry) as an example of axiomatic system and a model of
educative reasoning.
6. The teaching of advanced mathematics to those
students who wish to follow a career in science, technology, Engineering and
mathematics fields.
7. The teaching of heuristics and other problem
solving strategies to solve non-routine problems.
Problems Of Teaching And Learning Of
Mathematics
According to Woodward and Montague
(2002), the problems in teaching and learning of mathematics include the
following:
1. Fear and failure: If any subject area of
study evokes wide emotional comment, it is mathematics. While no one educated
person would profess (or at the least; not without a sense of shame) ignorance.
It is quite the social norm for anyone to proudly declare that he/she never
could learn mathematics. While these may be adult attitudes, among children,
there is often fear and anxiety. Mathematics anxiety and ‘math phobia’ are
terms that are used in popular literature.
Such fear is closely linked to a sense
of failure, by SS I, many students start seeing themselves as unable to cope
with the demands made by mathematics. In senior secondary schools, among
students who fail only in one or two subjects in year-end examination and hence
are detained, the maximum numbers fail in mathematics. The largest numbers of
Board Exam failures also happen in mathematics.
1. Inadequate teacher preparation. More so than any
other content discipline, mathematics education relies very heavily on the
preparation that the teacher has, in his own understanding of mathematics, of
the nature of mathematics and in his boy of pedagogic techniques. Textbook
centered pedagogy dulls the teacher’s own mathematics activity. At two ends of
the spectrum, mathematics teaching poses special problems. At the primary
level, most teachers assume that they know all the mathematics needed, and in
the absence of any specific pedagogic training, simply try and uncritically
reproduce the techniques they experienced in their school days. Often this ends
up perpetuating problems across time and space.
At the secondary and higher secondary level, some teachers face “different
situation. The syllable have considerably changed continuing education
programme for teachers, their fundamentals in many concept areas are not
strong. This encourages reliance on notes” available in the market, offering
little or depth for the studies.
2. Curricular Acceleration: A generation ago, calculus
was first encountered by a student in college another generation earlier;
analytical geometry was considered college mathematics. But these are all part
of secondary school curriculum now. Such acceleration has naturally meant
pruning of some topics; there is far less solid geometry or spherical geometry
now. One reason for the narrowing is that calculus and differential equations
are critically important in undergraduate sciences, technology and engineering,
and hence it is felt that early introduction of these topics helps students
proceeding further on these lines. Whatever the logic, the shape of mathematics
education has become father and more spindly, rather than broad and rounded.
3. Disappointing curriculum: Any mathematics
curriculum that emphasizes procedure and knowledge of formulas over
understanding is bound to enhance anxiety. The prevalent practice of school
mathematics goes further: a silent majority give up early on, remaining content
to fail in mathematics, or at best, to see it through, maintaining a minimal
level of achievement. For these children, what the curriculum offers is a store
of mathematical facts, borrowed temporarily while preparing for test.
On the other hand, it is widely acknowledged that more than in any other
content disciplines mathematics is the subject that also sees great motivation
and talent ever at early age in a small number of children (Krutetki, 2006).
These are children who take to quantization and algebra easily and carry on
with great facility.
What the curriculum offers for such children is also intense disappointment. By
not offering the conceptual depth, by not challenging them, the curriculum
settles for minimal use of their motivation. Learning procedures may be for
them, but their understanding and capacity for reasoning remain under
exercised.
4. Crude Assessment:
We talked of fear and failure while what happened in class may alienate, it
never evokes panic as does the examination. Most of the problems cited above
relate to the tyranny of procedure and memorization of formulas in school
mathematics, and the central reason for the ascendancy of procedure is the
nature of assessment and evaluation. Tests are designed (only) for assessing a
student’s knowledge of procedure and memory of formulas and facts and given the
criticality of examination performance in school life, concept learning is
replaced by procedural memory. Those children, who cannot do such replacement
successfully experience panic and suffer failure.
While
mathematics is the major ground for formal problem solving in school, it is
also the only arena where children see little room for play in answering
questions. Every question in mathematics is seen to have on unique answer, and
either you know it or you don’t. in language or in sciences, you may try and
demonstrate partial knowledge, but (as the students see it), there is no
scope for doing so in mathematics. Obviously, such a perception is easily
coupled to anxiety.
Amazingly, while there has been a great deal of research in mathematics
education and some of it has led to changes in pedagogy and curriculum, the
area that has seen little change in our schools over hundred years or
more is evaluation procedures in mathematics.
Recommended Solutions To The Above
Problems
According to wheeler (2012) while the litany of problems and challenges
magnifies the distance we need to travel to arrive at the goals of mathematics
education, it also offers hope by way of pointing us where we need to go and
steps we may/must take.
We
summarize what we believe to be the central direction for actions towards the
goals of mathematics education. We group them into four central themes.
I. . Shifting the focus of mathematics education from
achieving “narrow” goals to “higher” goals.
II. Engaging every student with a sense of success,
while at eh same time offering conceptual challenges to the emerging
mathematician.
III. Changing mode of assessment to examine students’
mathematisation abilities rather than procedural knowledge.
IV. Enriching teachers with a variety of mathematical
resources.
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PROJECT: THE RELEVANCE OF MATHEMATICS
AS A CORE SUBJECT IN SENIOR SECONDARY SCHOOLS IN NSUKKA LOCAL GOVERNMENT AREA