AbstractThe National Policy on Education (1986) has portrayedmathematics as the vehicle to train a child to think, to reason out, to analyzeand to articulate logically. Apart from being a specific subject, it should betreated as a concomitant to other subject involving analysis and reasoning. Thecountry requires mathematics education that is affordable to every child, andat the same time enjoyable. Development of mathematical literacy inchildren is increasingly viewed as a potential source of nation’s capital andas a means to sustain healthy technological society. Programme forInternational Student Assessment (PISA) defines mathematical literacy as anindividual’s capacity to identify and understand the role played by mathematicsin the world, to make well-founded judgments and to use and engage mathematicsto meet the needs of the individual’s life as a constructive, concerned andreflective citizen. The curriculum of mathematics inindustrialized nations has been renovated to ensure that children have accessto the learning opportunities necessary to attain a high level of mathematicalliteracy (Hopkins, 2007).
The achievement of such high mathematical literacy ispossible when there is a prominent change in the teaching of mathematics. Theshift to broaden the scope of mathematics teaching is exemplified in theprinciples and standards for school mathematics proposed by the NationalCouncil of Teachers of Mathematics (2000) in the United States. Research hasshown that approximately 5 to 8 percent of school-aged children experiencedifficulty meeting the standards proposed by the NCTM. This paper tries todescribe new strategies in rendering the mathematics education to the students.
It also points out the areas requiring the changes and introduces the noveltyin the teaching of mathematics which leads for students’ smooth run with thehigher education.Keywords: Mathematics Education, Teaching of mathematics, IntroductionThe new Oxford American Dictionary 2001 describes mathematicsas the abstract science consisting of number quantity and space. It is thesystematic treatment of magnitude that gives the relationships between figuresand 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 institutesof learning. The above were the views portrayed in the words of Manjul Bhargavthe winner of the Fields Medal in the year 2014, “InIndia mathematics has been taught as a robotic subject, where we solveartificial-sounding problems via a sequence of dull memorized steps”. The OECD’s survey of adult skills shows that poormathematics skills severely limit people’s access to better-paying andrewarding jobs. People with strong skills in mathematics are also more likelyto proceed with the social and economic opportunities available to them. However,in reality math is a critically important skill for a person to feel competentand capable of interacting with and participating in society.
MathematicsEducationMathematics education, in its broad view is ascientific discipline considering how people learn and do mathematics, how thislearning and doing can be influenced by others in teaching. The foundation ofmathematics is whole number arithmetic and place value system. In every gradeof the school, the curriculum of mathematics has to be carefully revived. Thecore aim of mathematics instruction at school is to deepen the mastery over themathematical skills such as computation, problem solving, and logical reasoning.
The students should be taught the mathematics and reasoning skills to succeedin college. Students planning for a Bachelor’s degree in a quantitative discipline should take a more demanding mathematicstrack in high school which prepares them to enter college.Teaching ofMathematics in cognitive perspectivesMathematics as a school subject, represents abody of conceptual, procedural, and declarative knowledge using the language ofsymbols to solve the various problems.
Conceptual knowledge refers to themental structures that underlie children’s reasoning with mathematics. Thesemental structures have various components linked to the previously learnedconcepts that are contributing to children’s deep conceptual understanding. Carpenter and Moser (1984) suggest that themost difficult problems for children to solve are those that cannot be easilyassociated with an existing mental representation. Procedural knowledge refersto knowledge about the sequence of steps necessary to solve a mathematicalproblem. Declarative knowledge refers to mathematical ideas that areautomatically retrieved from long-term memory. There has been no importancegiven to the mathematics performance on the bases of conceptual, procedural anddeclarative knowledge.
Mathematics teaching gives stress on memorization andcomputational skills rather than in the construction of understanding of themathematical concepts through the real life situations (Montague, Warger, , 2000). The major challenge faced by the teachers is to find ways tomake the connections between the above bodies of knowledge without emphasizingon one type alone. Aim of Mathematics Education Mathematisation of the child’s thinking isthe main aim of mathematics education. According to David Wheeler (1982) it ismore useful to know how to mathematise than to know lot of mathematics.
Thetargets of mathematics education are briefed below.Teaching the importance of mathematics: Educating the child merely on equating theformulae 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 themathematical technique helps the child to view mathematics as something to talkabout, to communicate and to discuss. Makingmathematics a part of children’s life experience is the best mathematicseducation possible.Developingthe skill of problem solving:Mathematics inculcates the skill of problem solving. The students learn thevarious ways to handle a single problem and derive at the solution throughdifferent methods. Mathematics also provides an opportunity to make upinteresting problems, and create new dialogues thereby.
Perceiving relationships through logicalthinking: Studentslearn to perceive relationships from the abstract concepts. Logicalthinking is a great gift that mathematics can offer. Inculcating such habits of thought andcommunication in childrenis a principal goal of teaching mathematics.The blemish of mathematicseducation Theanalysis of mathematics education identifies a range of issues to be changed.The area of concerns are listed belowAsense of fear and failureMathematicsis a subject that evokes the emotional comment. It has quite become a socialnorm for adults to probably declare that they could never learn mathematics. Onthe other hand, the children compelled to pass the mathematics examinationoften develop fear and anxiety. This fear is closely related with thedevelopment of failure.
With the universalisation of the Elementary Education inIndia, a serious attempt was made to examine every aspect that alienates childrenin school and contribute towards their non-participation leading to droppingout of the system. In the primary level, children become unable to cope withmathematics in grades three and four. At high school level, board exam failuresoccur mostly in mathematics. The main cause for these failures are due to the collectivenature of mathematics. If there is a struggle with decimals, then it would leadto a struggle in percentage. The other principal reason is said to be thepredominance of symbolic language.Sub-standardcurriculumThemathematics curriculum which gives importance to only procedure and knowledgeof formulas paves way to anxiety. For those children with minimal level ofachievement, the curriculum acts only as a storehouse of mathematical factsborrowed temporarily while preparing for tests.
On the other hand, for thegifted children who excel in mathematics, the curriculum is an intensedisappointment, as it fails to offer the conceptual depth of the subject.Learning becomes easy but their reasoning capacity is untouched.RudimentaryassessmentOneof the major reasons for failure in mathematics is the undeveloped assessmentand evaluation procedures. Tests are conducted to examine the students’knowledge on procedure and memorization of the formulae and facts.
Importanceis given only to the procedural knowledge than to concept learning. It isalways the application of information given to solve a specific set of problemsusing 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 studentin class VII. Such a crude assessment would never render any contribution tothe field of mathematics.Inadequateteacher preparationMathematicsis the only discipline in which the preparation of teachers plays a crucialrole in imparting education to the students.
The teachers’ understanding ofmathematics and her pedagogic technique in imparting mathematics education havea great impact on the students. Textbook centred teaching becomes verymonotonous. Due to the absence of adequate pedagogic training, the teachers atprimary level simply try to reproduce the techniques learnt in their schooldays. This ends up creating problems across time and space. On the other hand,at the secondary and the higher secondary levels, the syllabi have beencompletely changed. Due to the absence of continuing education programmes forthe teachers, their fundamentals in the concept area are not strong.
Hence,they rely on the cheap notes available in the market. The teachers fail toprovide the students the adequate knowledge on the particular concepts. The teachersfail to give link of the abstract concepts to formal mathematics and also dogive no idea of the various branches of mathematics linked with otherdisciplines.Reformative Measures in Mathematics Education leading to Higher EducationSome of the innovative measures inmathematics education have been enlistedStudent centred approachThestudent-centred approaches play an essential role in the self construction ofknowledge. This approach has its root in the constructivists theory (Roddick,2001). Over the years, a number of student-centered pedagogies such as inquirymethod, project based learning methods etc have been developed andinvestigated. Inquiry as an approach to teaching and learning mathematics has seen wide considerationinternationally (Berg, 2009). Roddick (2001), in an investigation, reported that students who followan inquiry based method of learning mathematics course tend to follow aconceptual approach in solving problems, while students who follow traditionalteaching tend to follow a procedural approach in problem solving.
It has beenfound that project based learning encourages students to search for informationstimulates thinking (Mokhtar et al., 2010). The use of student-centred methodsin mathematics instruction has been reported to increase students’ interest inthe subject (Mokhtar et al., 2010), increases students’ appreciation of therole of mathematics in life (Ward et al., 2010), and motivates to learnmathematics and realise its applicability (Mokhtar et al., 2010; Chang, 2011).Student-centred approaches in mathematics instruction give better exam scores (Roddick,2001)Teaching Mathematicsusing real-world examples Majority of students have difficulties in connectingmathematics to real world applications and this could be a reason for failurein mathematics (Chang, 2011).
Making mathematics relevant to the real world hasbeen stressed in a number of studies (Chang, 2011). Using real-world examplesis essential in student-centered approaches (Mokhtar et al., 2010). Real-timedata were used in a problem based learning approach to calculus (Niu &Shing, 2010). Chang (2011) utilised image processing examples from computerscience to contextualise abstract ideas from linear algebra in a mathematicscourse for mathematics specialists. Contextualising mathematics has beenreported frequently to enhance students’ experience (Chang, 2011). Bridging the gap in previous mathematical knowledge Many higher education students enter universities withgaps in necessary prerequisite knowledge of mathematical topics.
Thisultimately hinders the introduction of new mathematical ideas through novelapproaches. Turner (2009) designed a model of a program of three stages ofpredictor-corrector-refinement for supporting first year transition in acalculus 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 inlectures that encourages lecturers to stimulate discourse in the classroom viaasking thought-provoking questions.Technology as an enabler of innovative mathematicsinstruction The use of technology for mathematics teaching andlearning can be classified in two dimensions: the use of domain-specificmathematical analysis computer software packages and general use of learningtechnologies and online tools.
It is argued that technology evolution has beena driver for reform in mathematics teaching and learning (Roddick, 2001; Chang,2011). Domain-specific mathematical analysis computer software such asMathematica, together with an IBL approach, played an essential role inreforming calculus courses in the US (Roddick, 2001). Matlab has been used forin-class activities that demonstrate linear algebra concepts (Chang, 2011). Potocka(2010) implemented an online mathematics course that could be followed entirelywithout a need for an instructor. Students who followed the course haveachieved similar or better exam scores than their counterparts who attendedtraditional lectures.
Change in school mathematicsThe school mathematics should give emphasison the factual knowledge, procedural fluency and conceptual understanding. Theconceptual elements pave way for the creation of new knowledge. Proceduralfluency should be developed with the stress on conceptual understanding and theconstruction of knowledge. Creating problem solving environments would invitethe participation of the children and offer a sense of success.
High priorityshould be given for bringing changes in the mathematics curricula that pavesthe way for the transformation.Mathematics for everyoneEach child has a different mathematicaltaste. The mathematical taste of every child can be satisfied by the systematicmechanism followed in the textbooks. The textbook should provide a variety ofcontent for the children. Importance should be given in identifying andnurturing the mathematical talents of the children at the very early age.Strengthening of such talents leads the children to a higher level inmathematics. Multiple mode of assessment is required than the unique testpattern for assessing students according to their mathematical talent andskill.Adequacyof the teacherTheteacher’s perception plays a crucial role in imparting mathematics education tothe students.
Offering proper training and material to the teachers enrichestheir understanding about the subject both conceptually and historically. Thishelps them to innovate new methods of teaching such as teaching mathematicsusing technology, teaching concepts from the real world problem, askingstudents to surf through the math articles in journals, assigning them withprojects and so on. The school teachers can be helped by providing them withthe channels of communication with the teachers of the colleges anduniversities.
This linkage of the school teachers with the universitiesstrengthens their pedagogic competence. The students also can share theirthoughts about the subject with the subject experts. Educational implicationsThe mathematics education has to remove the anxietyof the students towards mathematics. The innovative methods of teachingmathematics would guide the students in finding new ways in solving theproblems. The students learn to correlate the basic mathematics with theabstract concepts in the higher education. There would be budding of newinnovations as a result of students understanding the influence of mathematicswith other subjects.
When students are nurtured according to their interest andtalents in mathematics, there would be more chances for them to pursue highereducation in their own field of interest. There would be the birth of prominent researchworks in the related areas of mathematics. Mathematics education should nurturethe ability of the student to think mathematically providing the students withrich mathematical experiences. The students should imbibe the mastery tointerpret and communicate the mathematical findings clearly and effectively andevaluate in different situations.
ConclusionThe main purpose of the current schoolmathematics has to be changed from ensuring the students entry into therenowned colleges of the society. Instead, it should take step to develop theintellectual capabilities of the student, promoting them to be the betterthinkers and effective problem solvers. Mathematics taught at school should sowthe seed for developing the research attitude in students which forms the baseof higher education.