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.

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.