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Answer the following questions

i) Explain the nature of Mathematics.(250 words)

Solution:

Mathematics reveals hidden patterns that help us understand the world around us.

Now much more than arithmetic and geometry, mathematics today is a diverse

discipline that deals with data, measurements, and observations from science; with

inference, deduction, and proof; and with mathematical models of natural phenomena,

of human behavior, and of social systems.

As a practical matter, mathematics is a science of pattern and order. Its domain is not

molecules or cells, but numbers, chance, form, algorithms, and change. As a science

of abstract objects, mathematics relies on logic rather than on observation as its

standard of truth, yet employs observation, simulation, and even experimentation as

means of discovering truth.

The special role of mathematics in education is a consequence of its universal

applicability. The results of mathematics--theorems and theories--are both significant

and useful; the best results are also elegant and deep. Through its theorems,

mathematics offers science both a foundation of truth and a standard of certainty.

In addition to theorems and theories, mathematics offers distinctive modes of thought

which are both versatile and powerful, including modeling, abstraction, optimization,

logical analysis, inference from data, and use of symbols. Experience with

mathematical modes of thought builds mathematical power--a capacity of mind of

increasing value in this technological age that enables one to read critically, to identify

fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics

empowers us to understand better the information-laden world in which we live.

ii) Discuss the importance, use and limitation of ‘Drill and Practice’

or play way method of teaching of mathematics with suitable

examples.(250 words)

Solution:

It refers to small tasks such as the memorization of spelling or vocabulary words,

or the practicing of arithmetic facts and may also be found in more supplicated

learning tasks or physical education games and sports. Drill-and-practice, like

memorization, involves repetition of specific skills, such as addition and subtraction,

or spelling. To be meaningful to learners, the skills built through drill-and-practice

should become the building blocks for more meaningful learning.

Importance:

Drill & Practice can provide an important "practice phase" to instruction and can be

useful for learning information that requires fluency such as math skills, vocabulary,

spelling and foreign languages.

Uses:

Drill and practice software is one of the earliest types of educational software. Many

educators have criticized the use of drill and practice software claiming they are boring

and do not utilize the full capabilities of the computer for higher level learning objectives.

However, drill and practice does have its place in the overall learning environment.

Drill and practice software is not intended to teach new concepts, but instead reinforce

concepts already taught through review and practice. It provides immediate, relevant

feedback and prevents students from learning something incorrectly. Drill and practice

allows students to work at their own pace while focusing on skills they need to work on

rather than forcing them to work on concepts they already know. Drill and practice can

also help identify mastery of a skill for both the student and the teachers.

Limitations:

Many are poorly designed

Usually lack high tech graphics and sound effects

Limited uses

Can lead to boredom through repetition

Does not promote higher level thinking

iii) You as a mathematics teacher must have felt the importance of

a good “Mathematics Laboratory”. Explain the essential aspects

with examples which you will consider for establishing good

Mathematics Laboratory for quality teaching of mathematics at

secondary level ( 1000 words)

Solution:

Mathematics, according to National Education Policy 1986, should be visualized as

the vehicle to train a child to think, reason, analyze and articulate logically. Apart from

being a specific subject, it should be treated as a concomitant to any subject involving

analysis and reasoning.

With the introduction of computers in schools, educational computing and emergence of learning

through understanding of cause-effect relationships and the interplay of variables, the teaching of

Mathematics will be suitably redesigned to bring it in line with modern technological devices so that

learning takes place effectively.

Learning often takes place best when students have opportunities to express ideas and get feedback

from their peers. But for feedback to be most helpful to learners, it must consist of more than the

provision of correct answers. Feedback ought to be analytical, to be suggestive, and to come at a time

when students are interested in it. And then there must be time for students to reflect on the feedback

they receive, to make adjustments and to try again- a requirement of mathematics education that was

neglected, due to rigorous practice of traditional methods of teaching.

It was also observed that students who frequently try to solve exercises related to new mathematics

topics by finding the inter-connections and who discuss practical problems related to everyday life

tend to score good in mathematics examinations. Teachers, who use of active learning strategies

like students working on mathematics projects, connecting mathematical knowledge to everyday life

when solving mathematics problems and actively participating in peer-group interaction have always

significantly contributed to good performance in mathematics.

So, a strategy for teaching mathematics in a different but suitable atmosphere that would transform

the position of the teacher to facilitator of learning from an authoritarian and active speaker’s role was

the need of the hour. Hence this experimental study was taken up.

Objectives:

1. To find out various methods being used in teaching Mathematics in regular classes

2. To find out teachers views about Mathematics Laboratory

3. To develop a strategy to be used in a Mathematics Laboratory setup

4. To test the effectiveness of the strategy developed for teaching in Mathematics Laboratory setup

5. To suggest recommendations for the development of Mathematics Laboratory and training of Mathematics teachers Variables of the Study of the Use of Mathematics Laboratory

Independent Variable:

Use of Strategy evolved to teach mathematics in a Mathematics Laboratory

Dependent Variable:

Performance of students and improvement in their result

Strategy Evolved for Teaching Mathematics in a Mathematics Laboratory

A strategy consisting of three different methods namely; Expository method, Co-operative Learning

Method and Problem Solving method coupled with Modeling should be evolved. These three methods

are administered as one unit but in three stages while teaching mathematics in a Mathematics

Laboratory. Each stage is defined with specific input and anticipated output. The role of teacher here is

Active during first stage as teacher teaches mathematics using Expository method and

Where Cooperative Learning at 2nd stage and

Problem solving coupled with modeling at 3rd stage the role of teacher is a facilitator of

learning. At 3rd stage teacher’s role is not only a facilitator of learning but also ensures a

learning outcome viz., social relevance of knowledge being assimilated by students.

Recommendations

•

The teachers of mathematics shall the newly developed methods or strategies to teach

mathematics instead of following age-old methods of teaching.

The teachers shall use the strategy evolved for teaching mathematics in mathematics

laboratory to enrich their teaching experiences.

Mathematics laboratory should be made an integral part of curriculum of mathematics

Mathematics Teaching could be carried out in a Mathematics Laboratory by integrating

mathematics laboratory into regular curriculum.

A specific curriculum in the form of credits shall be prescribed as regular syllabi for

Mathematics Laboratory and could be made it mandatory to students to complete.

Process of Evaluation and Assessment shall be based on minimum number of credits

completion. Completion of this minimum number of mandatory credits by each student at each

class could be made mandatory. Promotion to next class could be linked with this mandatory

completion.

Process of Evaluation and Assessment techniques shall be changed to a different format

such as making rubrics for positive interdependence, group investigation skills etc., so

that; academic performance of students could be improved along with social skills and peer

interaction.

Teaching through computers shall be introduced in the Basic teaching degree pursuit. All

the pre-service teachers shall get ample exposure in using embedded atmosphere to teach

mathematics.

All In-service teachers shall be given training in Information & Communication Technologies,

so that; the teaching experiences could be enriched. Pre-service teacher-students be given an

exposure to Mathematics Laboratory and its usage in teaching mathematics. Techniques or

strategies to integrate it ICT shall be taught during their teacher education programme.

Addition human resources with mathematics background could be given for mathematics

laboratory so as to enable the students to use the laboratory not only during their allotted

periods, but also during leisure periods

In every school Mathematics Laboratory shall be established and teaching of mathematics

shall be carried out through mathematics laboratory.

Conclusion

The study established that; traditional methods of teaching do not facilitate learning by understanding

nor providing opportunities to students to relate their knowledge with real life, besides making low

performers in the subject of mathematics. It was further established that, use of strategy evolved

integrating three different methods for teaching mathematics in a Lab atmosphere yielded improved

performance of students.

So, the study found a positive and significant correlation between the academic achievement of

secondary school students and the use of different methods of teaching in a Laboratory atmosphere.

Hence, teachers teaching mathematics shall use Mathematics Laboratory as a platform and by using

the strategy or any method other than didactic methods to make a significant impact in the knowledge

construction so as to improve the performance of secondary school students.