Abstract the needs of the individual’s life as

Abstract

The National Policy on Education (1986) has portrayed
mathematics as the vehicle to train a child to think, to reason out, to analyze
and to articulate logically. Apart from being a specific subject, it should be
treated as a concomitant to other subject involving analysis and reasoning. The
country requires mathematics education that is affordable to every child, and
at the same time enjoyable. Development of mathematical literacy in
children is increasingly viewed as a potential source of nation’s capital and
as a means to sustain healthy technological society. Programme for
International Student Assessment (PISA) defines mathematical literacy as an
individual’s capacity to identify and understand the role played by mathematics
in the world, to make well-founded judgments and to use and engage mathematics
to meet the needs of the individual’s life as a constructive, concerned and
reflective citizen. The curriculum of mathematics in
industrialized nations has been renovated to ensure that children have access
to the learning opportunities necessary to attain a high level of mathematical
literacy (Hopkins, 2007). The achievement of such high mathematical literacy is
possible when there is a prominent change in the teaching of mathematics. The
shift to broaden the scope of mathematics teaching is exemplified in the
principles and standards for school mathematics proposed by the National
Council of Teachers of Mathematics (2000) in the United States. Research has
shown that approximately 5 to 8 percent of school-aged children experience
difficulty meeting the standards proposed by the NCTM. This paper tries to
describe new strategies in rendering the mathematics education to the students.
It also points out the areas requiring the changes and introduces the novelty
in the teaching of mathematics which leads for students’ smooth run with the
higher education.

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Keywords: Mathematics Education, Teaching of mathematics,

 

 

 

 

 

 

 

 

Introduction

The new Oxford American Dictionary 2001 describes mathematics
as the abstract science consisting of number quantity and space. It is the
systematic treatment of magnitude that gives the relationships between figures
and forms and also relations between quantities that are expressed symbolically
(The Random House College Dictionary, 1984). The focus is on getting good grades to get into revered institutes
of learning. The above were the views portrayed in the words of Manjul Bhargav
the winner of the Fields Medal in the year 2014, “In
India mathematics has been taught as a robotic subject, where we solve
artificial-sounding problems via a sequence of dull memorized steps”. The OECD’s survey of adult skills shows that poor
mathematics skills severely limit people’s access to better-paying and
rewarding jobs. People with strong skills in mathematics are also more likely
to proceed with the social and economic opportunities available to them. However,
in reality math is a critically important skill for a person to feel competent
and capable of interacting with and participating in society.

Mathematics
Education

Mathematics education, in its broad view is a
scientific discipline considering how people learn and do mathematics, how this
learning and doing can be influenced by others in teaching. The foundation of
mathematics is whole number arithmetic and place value system. In every grade
of the school, the curriculum of mathematics has to be carefully revived. The
core aim of mathematics instruction at school is to deepen the mastery over the
mathematical skills such as computation, problem solving, and logical reasoning.
The students should be taught the mathematics and reasoning skills to succeed
in college. Students planning for a Bachelor’s degree in a quantitative discipline should take a more demanding mathematics
track in high school which prepares them to enter college.

Teaching of
Mathematics in cognitive perspectives

Mathematics as a school subject, represents a
body of conceptual, procedural, and declarative knowledge using the language of
symbols to solve the various problems. Conceptual knowledge refers to the
mental structures that underlie children’s reasoning with mathematics. These
mental structures have various components linked to the previously learned
concepts that are contributing to children’s deep conceptual understanding.  Carpenter and Moser (1984) suggest that the
most difficult problems for children to solve are those that cannot be easily
associated with an existing mental representation. Procedural knowledge refers
to knowledge about the sequence of steps necessary to solve a mathematical
problem. Declarative knowledge refers to mathematical ideas that are
automatically retrieved from long-term memory. There has been no importance
given to the mathematics performance on the bases of conceptual, procedural and
declarative knowledge. Mathematics teaching gives stress on memorization and
computational skills rather than in the construction of understanding of the
mathematical concepts through the real life situations (Montague, Warger, &
Morgan, 2000). The major challenge faced by the teachers is to find ways to
make the connections between the above bodies of knowledge without emphasizing
on one type alone.

Aim of Mathematics Education

Mathematisation of the child’s thinking is
the main aim of mathematics education. According to David Wheeler (1982) it is
more useful to know how to mathematise than to know lot of mathematics. The
targets of mathematics education are briefed below.

Teaching the importance of mathematics: Educating the child merely on equating the
formulae and mechanical procedures does not develop the child’s knowledge on mathematics.
Instead, providing the child with the understanding of when and how to use the
mathematical technique helps the child to view mathematics as something to talk
about, to communicate and to discuss. Making
mathematics a part of children’s life experience is the best mathematics
education possible.

Developing
the skill of problem solving:
Mathematics inculcates the skill of problem solving. The students learn the
various ways to handle a single problem and derive at the solution through
different methods. Mathematics also provides an opportunity to make up
interesting problems, and create new dialogues thereby.

Perceiving relationships through logical
thinking: Students
learn to perceive relationships from the abstract concepts. Logical
thinking is a great gift that mathematics can offer.  Inculcating such habits of thought and
communication in children
is a principal goal of teaching mathematics.

The blemish of mathematics
education

The
analysis of mathematics education identifies a range of issues to be changed.
The area of concerns are listed below

A
sense of fear and failure

Mathematics
is a subject that evokes the emotional comment. It has quite become a social
norm for adults to probably declare that they could never learn mathematics. On
the other hand, the children compelled to pass the mathematics examination
often develop fear and anxiety. This fear is closely related with the
development of failure. With the universalisation of the Elementary Education in
India, a serious attempt was made to examine every aspect that alienates children
in school and contribute towards their non-participation leading to dropping
out of the system. In the primary level, children become unable to cope with
mathematics in grades three and four. At high school level, board exam failures
occur mostly in mathematics. The main cause for these failures are due to the collective
nature of mathematics. If there is a struggle with decimals, then it would lead
to a struggle in percentage. The other principal reason is said to be the
predominance of symbolic language.

Sub-standard
curriculum

The
mathematics curriculum which gives importance to only procedure and knowledge
of formulas paves way to anxiety. For those children with minimal level of
achievement, the curriculum acts only as a storehouse of mathematical facts
borrowed temporarily while preparing for tests. On the other hand, for the
gifted children who excel in mathematics, the curriculum is an intense
disappointment, as it fails to offer the conceptual depth of the subject.
Learning becomes easy but their reasoning capacity is untouched.

Rudimentary
assessment

One
of the major reasons for failure in mathematics is the undeveloped assessment
and evaluation procedures. Tests are conducted to examine the students’
knowledge on procedure and memorization of the formulae and facts. Importance
is given only to the procedural knowledge than to concept learning. It is
always the application of information given to solve a specific set of problems
using the formulae. Moreover, the question pattern is the same for all standards.
The student of class X gets the same pattern of questions just as the student
in class VII. Such a crude assessment would never render any contribution to
the field of mathematics.

Inadequate
teacher preparation

Mathematics
is the only discipline in which the preparation of teachers plays a crucial
role in imparting education to the students. The teachers’ understanding of
mathematics and her pedagogic technique in imparting mathematics education have
a great impact on the students. Textbook centred teaching becomes very
monotonous. Due to the absence of adequate pedagogic training, the teachers at
primary level simply try to reproduce the techniques learnt in their school
days. This ends up creating problems across time and space. On the other hand,
at the secondary and the higher secondary levels, the syllabi have been
completely changed. Due to the absence of continuing education programmes for
the teachers, their fundamentals in the concept area are not strong. Hence,
they rely on the cheap notes available in the market. The teachers fail to
provide the students the adequate knowledge on the particular concepts. The teachers
fail to give link of the abstract concepts to formal mathematics and also do
give no idea of the various branches of mathematics linked with other
disciplines.

Reformative Measures in Mathematics Education leading to Higher Education

Some of the innovative measures in
mathematics education have been enlisted

Student centred approach

The
student-centred approaches play an essential role in the self construction of
knowledge. This approach has its root in the constructivists theory (Roddick,
2001). Over the years, a number of student-centered pedagogies such as inquiry
method, project based learning methods etc have been developed and
investigated. Inquiry as an approach to teaching and

learning mathematics has seen wide consideration
internationally (Berg, 2009). Roddick (2001), in an  investigation, reported that students who follow
an inquiry based method of learning mathematics course tend to follow a
conceptual approach in solving problems, while students who follow traditional
teaching tend to follow a procedural approach in problem solving. It has been
found that project based learning encourages students to search for information
stimulates thinking (Mokhtar et al., 2010). The use of student-centred methods
in mathematics instruction has been reported to increase students’ interest in
the subject (Mokhtar et al., 2010), increases students’ appreciation of the
role of mathematics in life (Ward et al., 2010), and motivates to learn
mathematics and realise its applicability (Mokhtar et al., 2010; Chang, 2011).
Student-centred approaches in mathematics instruction give better exam scores (Roddick,
2001)

Teaching  Mathematics
using real-world examples

Majority of students have difficulties in connecting
mathematics to real world applications and this could be a reason for failure
in mathematics (Chang, 2011). Making mathematics relevant to the real world has
been stressed in a number of studies (Chang, 2011). Using real-world examples
is essential in student-centered approaches (Mokhtar et al., 2010). Real-time
data were used in a problem based learning approach to calculus (Niu &
Shing, 2010). Chang (2011) utilised image processing examples from computer
science to contextualise abstract ideas from linear algebra in a mathematics
course for mathematics specialists. Contextualising mathematics has been
reported frequently to enhance students’ experience (Chang, 2011).

Bridging the gap in previous mathematical knowledge

Many higher education students enter universities with
gaps in necessary prerequisite knowledge of mathematical topics. This
ultimately hinders the introduction of new mathematical ideas through novel
approaches. Turner (2009) designed a model of a program of three stages of
predictor-corrector-refinement for supporting first year transition in a
calculus course. However, it was not fully successful due to gaps in students’
knowledge. Passive lectures are criticised for many factors; for instance,
Chang (2011) proposed a framework of mathematics teaching and learning in
lectures that encourages lecturers to stimulate discourse in the classroom via
asking thought-provoking questions.

Technology as an enabler of innovative mathematics
instruction

The use of technology for mathematics teaching and
learning can be classified in two dimensions: the use of domain-specific
mathematical analysis computer software packages and general use of learning
technologies and online tools. It is argued that technology evolution has been
a driver for reform in mathematics teaching and learning (Roddick, 2001; Chang,
2011). Domain-specific mathematical analysis computer software such as
Mathematica, together with an IBL approach, played an essential role in
reforming calculus courses in the US (Roddick, 2001). Matlab has been used for
in-class activities that demonstrate linear algebra concepts (Chang, 2011). Potocka
(2010) implemented an online mathematics course that could be followed entirely
without a need for an instructor. Students who followed the course have
achieved similar or better exam scores than their counterparts who attended
traditional lectures.

Change in school mathematics

The school mathematics should give emphasis
on the factual knowledge, procedural fluency and conceptual understanding. The
conceptual elements pave way for the creation of new knowledge. Procedural
fluency should be developed with the stress on conceptual understanding and the
construction of knowledge. Creating problem solving environments would invite
the participation of the children and offer a sense of success. High priority
should be given for bringing changes in the mathematics curricula that paves
the way for the transformation.

Mathematics for everyone

Each child has a different mathematical
taste. The mathematical taste of every child can be satisfied by the systematic
mechanism followed in the textbooks. The textbook should provide a variety of
content for the children. Importance should be given in identifying and
nurturing the mathematical talents of the children at the very early age.
Strengthening of such talents leads the children to a higher level in
mathematics. Multiple mode of assessment is required than the unique test
pattern for assessing students according to their mathematical talent and
skill.

Adequacy
of the teacher

The
teacher’s perception plays a crucial role in imparting mathematics education to
the students. Offering proper training and material to the teachers enriches
their understanding about the subject both conceptually and historically. This
helps them to innovate new methods of teaching such as teaching mathematics
using technology, teaching concepts from the real world problem, asking
students to surf through the math articles in journals, assigning them with
projects and so on. The school teachers can be helped by providing them with
the channels of communication with the teachers of the colleges and
universities. This linkage of the school teachers with the universities
strengthens their pedagogic competence. The students also can share their
thoughts about the subject with the subject experts.

 

Educational implications

The mathematics education has to remove the anxiety
of the students towards mathematics. The innovative methods of teaching
mathematics would guide the students in finding new ways in solving the
problems. The students learn to correlate the basic mathematics with the
abstract concepts in the higher education. There would be budding of new
innovations as a result of students understanding the influence of mathematics
with other subjects. When students are nurtured according to their interest and
talents in mathematics, there would be more chances for them to pursue higher
education in their own field of interest.  There would be the birth of prominent research
works in the related areas of mathematics. Mathematics education should nurture
the ability of the student to think mathematically providing the students with
rich mathematical experiences. The students should imbibe the mastery to
interpret and communicate the mathematical findings clearly and effectively and
evaluate in different situations.

Conclusion

The main purpose of the current school
mathematics has to be changed from ensuring the students entry into the
renowned colleges of the society. Instead, it should take step to develop the
intellectual capabilities of the student, promoting them to be the better
thinkers and effective problem solvers. Mathematics taught at school should sow
the seed for developing the research attitude in students which forms the base
of higher education.

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